diff --git a/BlankProjectTemplate/Doc/TestPlan/TestPlan.pdf b/BlankProjectTemplate/Doc/TestPlan/TestPlan.pdf
index a10c6ab2c73656fa8e05cbd36d04595c504755fa..94eea354e1a5259890002025c721fdb7eee33319 100644
Binary files a/BlankProjectTemplate/Doc/TestPlan/TestPlan.pdf and b/BlankProjectTemplate/Doc/TestPlan/TestPlan.pdf differ
diff --git a/BlankProjectTemplate/Doc/TestPlan/TestPlan.tex b/BlankProjectTemplate/Doc/TestPlan/TestPlan.tex
index 82c7a96a60a179f5f9066c09f9b09bb750d8a713..7e50964d118f937070684e3257072c514906a662 100644
--- a/BlankProjectTemplate/Doc/TestPlan/TestPlan.tex
+++ b/BlankProjectTemplate/Doc/TestPlan/TestPlan.tex
@@ -12,29 +12,20 @@
}
\usepackage[round]{natbib}
-\title{SE 3XA3: Test Plan\\Title of Project}
-
-\author{Team \#, Team Name
- \\ Student 1 name and macid
- \\ Student 2 name and macid
- \\ Student 3 name and macid
-}
-
-\date{\today}
-
\input{../Comments}
\begin{document}
+\title{Project Title}
+\author{Author Name}
+\date{\today}
+
\maketitle
\pagenumbering{roman}
-\tableofcontents
-\listoftables
-\listoffigures
-\begin{table}[bp]
-\caption{\bf Revision History}
+\section{Revision History}
+
\begin{tabularx}{\textwidth}{p{3cm}p{2cm}X}
\toprule {\bf Date} & {\bf Version} & {\bf Notes}\\
\midrule
@@ -42,49 +33,41 @@ Date 1 & 1.0 & Notes\\
Date 2 & 1.1 & Notes\\
\bottomrule
\end{tabularx}
-\end{table}
-\newpage
+~\newpage
-\pagenumbering{arabic}
+\section{Symbols, Abbreviations and Acronyms}
-This document ...
+\renewcommand{\arraystretch}{1.2}
+\begin{tabular}{l l}
+ \toprule
+ \textbf{symbol} & \textbf{description}\\
+ \midrule
+ T & Test\\
+ \bottomrule
+\end{tabular}\\
-\section{General Information}
+\wss{symbols, abbreviations or acronyms -- you can reference the SRS tables if needed}
-\subsection{Purpose}
+\newpage
-\subsection{Scope}
+\tableofcontents
-\subsection{Acronyms, Abbreviations, and Symbols}
-
-\begin{table}[hbp]
-\caption{\textbf{Table of Abbreviations}} \label{Table}
+\listoftables
-\begin{tabularx}{\textwidth}{p{3cm}X}
-\toprule
-\textbf{Abbreviation} & \textbf{Definition} \\
-\midrule
-Abbreviation1 & Definition1\\
-Abbreviation2 & Definition2\\
-\bottomrule
-\end{tabularx}
+\listoffigures
-\end{table}
+\newpage
-\begin{table}[!htbp]
-\caption{\textbf{Table of Definitions}} \label{Table}
+\pagenumbering{arabic}
-\begin{tabularx}{\textwidth}{p{3cm}X}
-\toprule
-\textbf{Term} & \textbf{Definition}\\
-\midrule
-Term1 & Definition1\\
-Term2 & Definition2\\
-\bottomrule
-\end{tabularx}
+This document ...
+
+\section{General Information}
+
+\subsection{Purpose}
-\end{table}
+\subsection{Scope}
\subsection{Overview of Document}
@@ -94,13 +77,24 @@ Term2 & Definition2\\
\subsection{Test Team}
+\wss{Probably just you. :-)}
+
\subsection{Automated Testing Approach}
-\subsection{Testing Tools}
+\subsection{Verification Tools}
+
+\wss{Thoughts on what tools to use, such as the following: unit testing
+ framework, valgrind, static analyzer, make, continuous integration, test
+ coverage tool, etc.}
-\subsection{Testing Schedule}
+% \subsection{Testing Schedule}
-See Gantt Chart at the following url ...
+% See Gantt Chart at the following url ...
+
+\subsection{Non-Testing Based Verification}
+
+\wss{List any approaches like code inspection, code walkthrough, symbolic
+ execution etc. Enter not applicable if that is the case.}
\section{System Test Description}
@@ -182,52 +176,48 @@ How test will be performed:
\subsection{Traceability Between Test Cases and Requirements}
-\section{Tests for Proof of Concept}
+% \section{Tests for Proof of Concept}
-\subsection{Area of Testing1}
+% \subsection{Area of Testing1}
-\paragraph{Title for Test}
+% \paragraph{Title for Test}
-\begin{enumerate}
+% \begin{enumerate}
-\item{test-id1\\}
+% \item{test-id1\\}
-Type: Functional, Dynamic, Manual, Static etc.
+% Type: Functional, Dynamic, Manual, Static etc.
-Initial State:
+% Initial State:
-Input:
+% Input:
-Output:
+% Output:
-How test will be performed:
+% How test will be performed:
-\item{test-id2\\}
+% \item{test-id2\\}
-Type: Functional, Dynamic, Manual, Static etc.
+% Type: Functional, Dynamic, Manual, Static etc.
-Initial State:
+% Initial State:
-Input:
+% Input:
-Output:
+% Output:
-How test will be performed:
+% How test will be performed:
-\end{enumerate}
+% \end{enumerate}
-\subsection{Area of Testing2}
+% \subsection{Area of Testing2}
-...
-
-
-\section{Comparison to Existing Implementation}
+% ...
\section{Unit Testing Plan}
-\subsection{Unit testing of internal functions}
-
-\subsection{Unit testing of output files}
+\wss{Unit testing plans for internal functions and, if appropriate, output
+ files}
\bibliographystyle{plainnat}
diff --git a/Examples/MeshGenToolbox/ReadMe.txt b/Examples/MeshGenToolbox/ReadMe.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6919c5146a25f7ae6bd3705d4a8b60cea777edff
--- /dev/null
+++ b/Examples/MeshGenToolbox/ReadMe.txt
@@ -0,0 +1,11 @@
+This is the serial version of PMGT, also known as MGT
+
+September, 2008
+
+The directories and their contents are as follows:
+
+/doc The documentation for the serial version of PMGT, or MGT
+/mgt The source files for the mesh generation toolbox
+/testdriver An example test driver that uses mgt to refine a mesh
+
+Readme.txt This file
\ No newline at end of file
diff --git a/Examples/MeshGenToolbox/doc/Preamble.tex b/Examples/MeshGenToolbox/doc/Preamble.tex
new file mode 100644
index 0000000000000000000000000000000000000000..421b41415bc64f50d1edbc759dbd79632d9b6d1e
--- /dev/null
+++ b/Examples/MeshGenToolbox/doc/Preamble.tex
@@ -0,0 +1,83 @@
+\usepackage[top=1.75in,left=1.5in,right=1.5in,bottom=1.25in,verbose]{geometry}%footskip=.25in,
+\usepackage{graphicx}
+\usepackage{rotating}
+\usepackage{amssymb,amsmath}\allowdisplaybreaks[4]
+\usepackage{multirow}
+\usepackage{fancyhdr}
+\usepackage{overpic}
+\usepackage{epsfig}
+\usepackage{setspace}
+\usepackage{makeidx}
+\usepackage{epsfig}
+\usepackage{paralist}
+\usepackage{appendix}
+\usepackage{changebar}
+\usepackage[round]{natbib}
+
+\newcounter{funnum}
+\newcommand{\fthefunnum}{F\thefunnum}
+\newcommand{\fref}[1]{F\ref{#1}}
+
+\newcounter{nfnum}
+\newcommand{\nthenfnum}{N\thenfnum}
+\newcommand{\nref}[1]{N\ref{#1}}
+
+\newcounter{goalnum}
+\newcommand{\gthegoalnum}{G\thegoalnum}
+\newcommand{\gref}[1]{G\ref{#1}}
+
+\newcounter{assnum}
+\newcommand{\atheassnum}{A\theassnum}
+\newcommand{\aref}[1]{A\ref{#1}}
+
+\newcounter{tmnum}
+\newcommand{\tmthetmnum}{TM\thetmnum}
+\newcommand{\tmref}[1]{TM\ref{#1}}
+
+\newcounter{ddnum}
+\newcommand{\dtheddnum}{D\theddnum}
+\newcommand{\dref}[1]{D\ref{#1}}
+
+\newcounter{acnum}
+\newcommand{\actheacnum}{AC\theacnum}
+\newcommand{\acref}[1]{AC\ref{#1}}
+
+\newcounter{ucnum}
+\newcommand{\uctheucnum}{UC\theucnum}
+\newcommand{\uref}[1]{UC\ref{#1}}
+
+\newcounter{mnum}
+\newcommand{\mthemnum}{M\themnum}
+\newcommand{\mref}[1]{M\ref{#1}}
+
+\newcounter{qfnum}
+\newcommand{\qftheqfnum}{QF\theqfnum}
+\newcommand{\qfref}[1]{QF\ref{#1}}
+
+\newcounter{casenum}
+\newcommand{\cthecasenum}{TC\thecasenum}
+\newcommand{\cref}[1]{TC\ref{#1}}
+
+\newcommand{\mi}[1]{#1\index{#1}}
+%\makeindex
+
+\addtocounter{secnumdepth}{3}
+
+\newcommand{\colAwidth}{0.36\textwidth}
+\newcommand{\colBwidth}{0.45\textwidth}
+\newcommand{\firstCol}{0.17\textwidth}
+\newcommand{\secondCol}{0.7\textwidth}
+\newcommand{\colOne}{0.1\textwidth}
+\newcommand{\colTwo}{0.15\textwidth}
+
+\DeclareGraphicsRule{.jpg}{eps}{}{}
+
+\pagestyle{fancy}
+\renewcommand{\headrulewidth}{0pt}
+\renewcommand{\footrulewidth}{0pt}
+\fancyhf{} \fancyfoot[C]{\thepage} \fancyhead[C]{\itshape Wen Yu -- McMaster University -- Computing and Software}
+
+\setlength{\parindent}{0.5in}
+
+\newcommand{\HRule}{\rule{\linewidth}{0.5mm}}
+%\doublespacing
\ No newline at end of file
diff --git a/Examples/MeshGenToolbox/doc/WenRef.bib b/Examples/MeshGenToolbox/doc/WenRef.bib
new file mode 100644
index 0000000000000000000000000000000000000000..f65f68cdbe598b390537f8cf644346932f26fdec
--- /dev/null
+++ b/Examples/MeshGenToolbox/doc/WenRef.bib
@@ -0,0 +1,589 @@
+@TECHREPORT{Bauer1995,
+ AUTHOR ="Brian Bauer",
+ TITLE ="Documenting Complicated Programs",
+ YEAR ="1995",
+ NUMBER ="CRL Report 316",
+ INSTITUTION ="Department of Computing and Software, McMaster University"
+}
+
+@inproceedings{Beohm1988,
+ author = {Barry W. Beohm},
+ title = {A Spiral Model for Software Development and Enhancement},
+ booktitle = {Computer},
+ year = {1988},
+ volume = {vol. 21, no. 5},
+ pages = {pp.61 - 72},
+ month = {May},
+ }
+
+
+@inproceedings{Bern1993,
+ author = {Marshall W. Bern and David Eppstein and Shang-Hua Teng},
+ title = {Parallel Construction of Quadtrees and Quality Triangulations},
+ booktitle = {WADS '93: Proceedings of the Third Workshop on Algorithms and Data Structures},
+ year = {1993},
+ isbn = {3-540-57155-8},
+ pages = {188--199},
+ publisher = {Springer-Verlag},
+ address = {London, UK},
+ }
+
+@InProceedings {Berti2000,
+ AUTHOR = "Guntram Berti",
+ TITLE = "Generic Components for Grid Data Structures and
+ Algorithms with {C++}",
+ BOOKTITLE = "First Workshop on {C++} Template Programming,
+ Erfurt, Germany",
+ MONTH = "October 10",
+ YEAR = "2000",
+
+}
+
+@mastersthesis{Cao2006,
+AUTHOR = {Fang Cao},
+TITLE={A Program Family Approach to Developing Mesh Generators},
+SCHOOL={McMaster University},
+MONTH={April},
+YEAR=2006,
+ANNOTE={NUMBER OF PAGES: vii, 211},
+}
+
+@mastersthesis{Chen2003,
+AUTHOR = {Chien-Hsien Chen},
+TITLE={A Software Engineering Approach to Developing Mesh Generators},
+SCHOOL={McMaster University},
+MONTH={Novermber},
+YEAR=2003,
+ANNOTE={NUMBER OF PAGES: vii, 247},
+}
+
+@MISC(Cirincione1992,
+ AUTHOR = "Joseph Cirincione",
+ TITLE = "The Performance of the Patriot Missile in the Gulf War",
+ NOTES = "An Edited Draft of a Report prepared for the Government Operations Committee, U.S. House of Representatives",
+ YEAR = "1992",
+ MONTH = "October",
+ )
+
+@BOOK(CSTE2006,
+ AUTHOR = {CSTE},
+ TITLE = "2006 Guide to the CSTE COMMON BODY OF KNOWLEDGE",
+ PUBLISHER = "Quality Assurance Institute",
+ YEAR = 2006)
+
+@BOOK(Davis1990,
+ AUTHOR = {Alan M. Davis},
+ TITLE = "Software Refquirements: Analysis and Specification",
+ PUBLISHER = "Prentice Hall Inc.",
+ YEAR = 1990)
+
+@BOOK(Dijkstra1972,
+ AUTHOR = {Dijkstra, E. W.},
+ TITLE = "Structured Programming, Chapter Notes on Structured Programming",
+ PUBLISHER = "Academic Press, London",
+ YEAR = 1972)
+
+ @article{Duff1989,
+ author = {I. S. Duff and Roger G. Grimes and John G. Lewis},
+ title = {Sparse matrix test problems},
+ journal = {ACM Trans. Math. Softw.},
+ volume = {15},
+ number = {1},
+ year = {1989},
+ issn = {0098-3500},
+ pages = {1--14},
+
+ publisher = {ACM Press},
+ address = {New York, NY, USA},
+ }
+
+@Article{ElSheikh2003,
+ author = "A. H. ElSheikh",
+ title = "A review of GRUMMP mesh generation code",
+ year = "2003",
+ month = "August",
+}
+
+@article{ElSheikh2004,
+ author = {A. H. ElSheikh and S. Smith and S. E. Chidiac},
+ title = {Semi-formal design of reliable mesh generation systems},
+ journal = {Adv. Eng. Softw.},
+ volume = {35},
+ number = {12},
+ year = {2004},
+ issn = {0965-9978},
+ pages = {827--841},
+
+ publisher = {Elsevier Science Ltd.},
+ address = {Oxford, UK, UK},
+ }
+
+@article{Floyd1979,
+ author = {Robert W. Floyd},
+ title = {The paradigms of programming},
+ journal = {Commun. ACM},
+ volume = {22},
+ number = {8},
+ year = {1979},
+ issn = {0001-0782},
+ pages = {455--460},
+
+ publisher = {ACM Press},
+ address = {New York, NY, USA},
+ }
+
+
+@BOOK(FreyAndGeorge2000,
+ AUTHOR = {Pascal Jean Frey and Paul-Louis George},
+ TITLE = "Mesh generation Application to Finite Elements",
+ PUBLISHER = "Hermes Science Europe ltd.",
+ YEAR = 2000)
+
+@BOOK(Ghezzi2003,
+ AUTHOR = {Carlo Ghezzi and Mehdi Jazayeri and Dino Mandrioli},
+ TITLE = "Funcamentals of software Engineering",
+ PUBLISHER = "Pearson Education, Inc.",
+ Address = "Upper Saddle River, New Jersey 07458",
+ YEAR = 2003)
+
+@InProceedings{Grabmueller2003,
+ author = {Martin Grabm{\"u}ller and Petra Hofstedt},
+ title = {{Turtle: A Constraint Imperative Programming Language}},
+ editor = {Frans Coenen and Alun Preece and Ann Macintosh},
+ booktitle = {Twenty-third SGAI International Conference on Innovative
+ Techniques and Applications of Artificial Intelligence},
+ year = {2003},
+ number = {XX},
+ series = {Research and Development in Intelligent Systems},
+ address = {Cambridge, UK},
+ month = {December},
+ organization = {British Computer Society},
+ publisher = {Springer-Verlag},
+ isbn = {1-85233-780-X},
+}
+
+@BOOK(Gries1993,
+ AUTHOR = {David Gries and Fred B. Schneider},
+ TITLE = "A Logical Approach to Discrete Math",
+ PUBLISHER = "Springer-Verlag New Yourk, Inc.",
+ YEAR = 1993)
+
+@inproceedings{Gueziec1995,
+ author = {Andre Gueziec},
+ title = {Surface simplification with variable tolerance},
+ booktitle = {Second Annual Intl. Symp. on Medical Robotics and Computer Assisted Surgery (MRCAS '95)},
+ year = {1995},
+ month = {November},
+ pages = {132-139},
+ }
+
+@misc{Guillard1993,
+ author = "H. Guillard",
+ title = "Node-nested multi-grid with Delaunay coarsening",
+ text = "Herve Guillard. Node-nested multi-grid with Delaunay coarsening. Technical
+ Report 1898, Institute National de Recherche en Informatique et en Automatique,
+ 1993.",
+ year = "1993" }
+
+@BOOK(Hoffman1999,
+ AUTHOR = {Daniel Hoffman and Paul Strooper},
+ TITLE = "Software Design, Automated Testing and Maintenance",
+ PUBLISHER = "International Thomson Computer Press",
+ YEAR = 1999)
+
+@BOOK(IEEE1990,
+ AUTHOR = {IEEE},
+ TITLE = "IEEE Standard Glossary of Software Engineering Terminology ",
+ PUBLISHER = "IEEE Computer Society, Washington, DC, USA",
+ YEAR = 1990)
+
+@BOOK(IEEE2000,
+ AUTHOR = {IEEE},
+ TITLE = "IEEE Recommended Practice for Software Requirements Specifications",
+ PUBLISHER = "IEEE Computer Society, Washington, DC, USA, 2nd edition",
+ YEAR = 2000)
+
+@BOOK(IEEE1998,
+ AUTHOR = {IEEE},
+ TITLE = "IEEE Guide for Developing System Requirements Specifications",
+ PUBLISHER = "IEEE Computer Society, Washington, DC, USA",
+ YEAR = 1998)
+
+@MISC(Khedri2001,
+ AUTHOR = "R. Dhedri",
+ TITLE = "Software Requirements Activeties",
+ NOTES = "Lecture Notes",
+ SCHOOL = "Department of Computing and Software, McMaster University",
+ YEAR = 2001
+ )
+
+@MASTERSTHESIS{Koenig2003,
+ TITLE = "An Efficient Implementation of {C}harm++ on {V}irtual
+ {M}achine {I}nterface",
+ AUTHOR = "Gregory Allen Koenig",
+ SCHOOL = "University of Illinois at Urbana-Champaign",
+ YEAR = "2003"
+}
+
+@MASTERSTHESIS{Lai2004,
+AUTHOR = {Lei~Lai},
+TITLE={Requirements Documentation for Engineering Mechanics Software: Guidelines,
+Template and a Case Study},
+SCHOOL={McMaster University},
+MONTH={Sept.},
+YEAR=2004,
+ANNOTE={NUMBER OF PAGES: xx, 256},
+}
+
+@inproceedings{Lamsweerde2001,
+ author = {Axel van Lamsweerde},
+ title = {Goal-Oriented Requirements Engineering: A Guided Tour},
+ booktitle = {Proceedings of the fifth IEEE International Symposium on Requirements Engineering},
+ year = {2001},
+ pages = {249--263},
+ location = {IEEE},
+ publisher = {IEEE Computer Society, Washington, DC, USA},
+ }
+
+ @BOOK(Lee2003,
+ AUTHOR = {Copeland, Lee},
+ TITLE = "A Practioner's Guide to Software Test Design.",
+ PUBLISHER = "Artech House Publisher",
+ YEAR = 2003)
+
+ @BOOK(Lewis2004,
+ AUTHOR = {William E Lewis and Cunasakaran Veerapollai},
+ TITLE = "Software testing and continuous quality improvement 2nd ed.",
+ PUBLISHER = "CRC Press LLC",
+ YEAR = 2004)
+
+@book{McCall1977,
+ author = {J. McCall and P. Richards and G. Walters},
+ title = {Factors in Software Quality},
+ publisher = {NTIS AD-A049-014, 015, 055},
+ year = {1997},
+ month = {Novermber},
+ }
+
+@inproceedings{Miller1997,
+ author = "Miller and Talmor and Teng",
+ title = "Optimal Good-Aspect-Ratio Coarsening for Unstructured Meshes",
+ booktitle = "{SODA}: {ACM}-{SIAM} Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms)",
+ year = "1997",
+ }
+
+@inproceedings{Mitchell2000,
+ author = {Scott A. Mitchell and Stephen A. Vavasis},
+ title = {Quality Mesh Generation in Higher Dimensions},
+ booktitle = {SIAM Journal on Computing},
+ year = {2000},
+ isbn = {1095-7111},
+ volume = {29},
+ pages = {1334--1370},
+
+ publisher = {Society for Industrial and Applied Mathematics},
+ address = {3600 University City Science Center, Philadelphia, PA 19104 USA},
+ }
+
+@article{Ollivier2003,
+ author = {Carl F. Ollivier-Gooch},
+ title = {Coarsening unstructured mesh by edge constraction},
+ journal = {International Journal for Numerical Methods in Edgineering},
+ volume = {57},
+ number = {3},
+ year = {2003},
+ month = {May},
+ pages = {391-414},
+ }
+
+@inproceedings{Owen1998,
+ author = {Owen, Steven J.},
+ title = {A Survey of Unstructured Mesh Generation Technology},
+ booktitle = {Proceedings 7th International Meshing Roundtable},
+ year = {1998},
+ month = {October},
+ doi = {www.andrew.cmu.edu/user/sowen/survey},
+ address = {Dearborn, MI},
+ }
+
+@article{Parnas1972,
+ author = {David L. Parnas},
+ title = {On the Criteria to be Used in Decomposing System into Modules},
+ journal = {Communications of th ACM},
+ year = {1972},
+ volume = {vol. 15, No. 12},
+ pages = {pp.1053 - 1058},
+ month = {December},
+ }
+
+
+@article{Parnas1976,
+ author = {David L. Parnas},
+ title = {On the Design and Development of Program Families},
+ journal = {IEEE Transactions on Software Engineering},
+ year = {1976},
+
+ }
+
+@inproceedings{Parnas1978,
+ author = {David L. Parnas},
+ title = {Designing Software for Ease of Extension and Contraction},
+ booktitle = {ICSE '78: Proceedings of the 3rd international conference on Software engineering},
+ year = {1978},
+ isbn = {none},
+ pages = {264--277},
+ location = {Atlanta, Georgia, United States},
+ publisher = {IEEE Press},
+ address = {Piscataway, NJ, USA},
+ }
+
+@inproceedings{Parnas1984,
+ author = {D. L. Parnas and P. C. Clements and D. M. Weiss},
+ title = {The Modular Structure of Complex Systems},
+ booktitle = {ICSE '84: Proceedings of the 7th international conference on Software engineering},
+ year = {1984},
+ isbn = {0-8186-0528-6},
+ pages = {408--417},
+ location = {Orlando, Florida, United States},
+ publisher = {IEEE Press},
+ address = {Piscataway, NJ, USA},
+ }
+
+@book{Pressman1999,
+ author = {Roger S. Pressman},
+ title = {Software Engineering, A Practitioner's Approach, fourth Edition},
+ publisher = {McGraw-Hill},
+ year = {1999},
+ }
+
+
+ @MISC(Qao727Notes,
+ AUTHOR = "Sanzheng Qiao",
+ TITLE = "Lecture Notes of CAS727: Design of Numerical Software",
+ NOTES = "Lecture Notes",
+ SCHOOL = "Department of Computing and Software, McMaster University",
+ doi = {http://www.cas.mcmaster.ca/~qiao/courses/cas727/index.html},
+ YEAR = 2004
+ )
+
+
+ @inproceedings{Raccoon1995,
+ author = {Raccoon, L.B.S.},
+ title = {The Chaos Model and the Chaos Life Cycle},
+ booktitle = {ACM Software Engineering Notes},
+ year = {1995},
+ volume = {vol. 20, no. 1},
+ pages = {pp.55 - 66},
+ month = {January},
+ }
+
+ @misc{ rivara1995,
+ author = "M. Rivara and P. Inostroza",
+ title = "A discussion on mixed (longest side midpoint insertion) delaunay techniques
+ for the triangulation refinement problem",
+ text = "M. C. Rivara and P. Inostroza, A discussion on mixed (longest side midpoint
+ insertion) delaunay techniques for the triangulation refinement problem,
+ Proceedings 4th International Meshing Roundtable. Albuquerque, pp. 335--346,
+ 1995.",
+ year = "1995",
+ }
+
+
+ @article{Rivara1997,
+ author = {Rivara, Maria-Celilia},
+ title = {New Longest-Edge Algorithms for the Refinement and/or Improvement of Unstructured Triangulation.},
+ journal = {International Journal for Numerical Methods in Engineering},
+ volume = {40},
+ year = {1997},
+ pages = {3313--3324},
+ publisher = {Wiley},
+ }
+
+ @inproceedings{Royce1970,
+ author = {Royce, W.W.},
+ title = {Managing the Development of Large Software System: Concepts and Techniques},
+ booktitle = {Proc. ICSE},
+ year = {1970},
+ month = {August},
+ publisher = {Computer Society Press},
+ }
+
+@inproceedings{Ruppert1993,
+ author = {Jim Ruppert},
+ title = {A new and simple algorithm for quality 2-dimensional mesh generation},
+ booktitle = {SODA '93: Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms},
+ year = {1993},
+ isbn = {0-89871-313-7},
+ pages = {83--92},
+ location = {Austin, Texas, United States},
+ publisher = {Society for Industrial and Applied Mathematics},
+ address = {Philadelphia, PA, USA},
+ }
+
+@incollection{Shaw95,
+ author = "Mary Shaw and David Garlan",
+ title = "Formulations and Formalisms in Software Architecture",
+ booktitle = "Computer Science Today: Recent Trends and Developments",
+ pages = "307-323",
+ year = "1995",
+ publisher="Springer-Verlag",
+ series="Lecture Notes in Computer Science",
+ editor = "Jan van Leeuwen",
+ volume = "1000",
+ }
+
+
+@TECHREPORT{Smith2004,
+ KEY ="S.~Smith and C.~H.~Chen",
+ AUTHOR ="S. Smith and C. H. Chen",
+ TITLE ="Commonality Analysis for Mesh Generation System",
+ YEAR ="2004",
+ NUMBER ="CAS-04-10-ss",
+ INSTITUTION ="Department of Computing and Software, McMaster University"
+}
+
+@MISC{Smith2006,
+ author = {Spencer Smith},
+ title = {Systematic Development of Requirements Documentation for General Purpose Scientific Computing Software},
+ year = {2006},
+ }
+@article{Smith2007,
+Author = {W. Spencer Smith and Lei Lai and Ridha Khedri},
+Journal = {Reliable Computing, Special Issue on Reliable Engineering Computation},
+Pages = {83--107},
+Title = {Requirements Analysis for Engineering Computation: A Systematic Approach for Improving Software Reliability},
+Year = {2007},
+Volume = {13}
+}
+
+@inproceedings{Smith2005,
+Address = {Paris, France},
+Author = {W. Spencer Smith and Lei Lai},
+Booktitle = {Proceedings of the First International Workshop on Situational Requirements Engineering Processes -- Methods, Techniques and Tools to Support Situation-Specific Requirements Engineering Processes, SREP'05},
+Editor = {J. Ralyt\'{e} and P. \.{A}gerfalk and N. Kraiem},
+
+Organization = {In conjunction with 13th IEEE International Requirements Engineering Conference},
+Pages = {107--121},
+Title = {A New Requirements Template for Scientific Computing},
+Year = {2005}}
+
+
+@BOOK(Sommerville1997,
+ AUTHOR = {Ian Sommerville and Pete Sawyer},
+ TITLE = "Requirements Engineering A Good Practice Guide",
+ PUBLISHER = "John Wiley and Sons",
+ YEAR = 1997)
+
+@BOOK(Sommerville1992,
+ AUTHOR = {Ian Sommerville},
+ TITLE = "Software Engineering",
+ PUBLISHER = "Addison-Wesley Publishing Company",
+ YEAR = 1992)
+
+
+@article{Tomayko1995,
+author = {James Tomayko},
+title = {Anecdotes},
+journal = {IEEE Annals of the History of Computing},
+volume = {17},
+number = {2},
+year = {1995},
+issn = {1058-6180},
+pages = {62-63},
+
+publisher = {IEEE Computer Society},
+address = {Los Alamitos, CA, USA},
+}
+
+@MISC{Volere2001,
+ author = {James Robertson and Suzanne Robertson},
+ title = {Volere Requirements Specification Template},
+ year = {2001},
+ doi = {www.systemsguild.com},
+ publisher = {The Atlantic Systems Guild Inc.},
+ }
+
+ @article{Wilson2006,
+ author = {Gregory V. Wilson},
+ title = {Where's the Real Bottleneck in Scientific Computing: Scientists would do well to pick up some tools widely used in the software industry},
+ journal = {American Scientist},
+ volume = {94},
+ number = {1},
+ page = {5},
+ year = {2006},
+ month = {January -- Febrary},
+
+ }
+
+
+@book{Zienkiewicz2005,
+Author = {O. C. Zienkiewicz and R. L Taylor and J. Z. Zhu},
+Edition = {6th},
+Publisher = {Elsevier Butterworth-Heinemann},
+Title = {The Finite Element Method Its Basis and Fundamentals},
+Year = {2005}}
+
+ @MISC{AOMD2006,
+ AUTHOR = {SCOREC},
+ TITLE = {Algorithm Oriented Mesh Database},
+
+ URL = {http://www.scorec.rpi.edu/AOMD/},
+ YEAR = {Last Access: January, 2006},
+ }
+@MISC{Blackpawn,
+ AUTHOR = {Blackpawn},
+ TITLE = {Point in Triangle Test},
+
+ URL = {http://www.blackpawn.com/texts/pointinpoly/default.html},
+ YEAR = {Last Access: January, 2006},
+ }
+
+@MISC{OwenWeb2006,
+ AUTHOR = {Owen, Steven J.},
+ TITLE = {Meshing Research Corner},
+ URL = {http://www.andrew.cmu.edu/user/sowen/mesh.html},
+ YEAR = {Last Access: January, 2006},
+ }
+
+@MISC{sharcnet2006,
+ AUTHOR = "SHARCNET",
+ TITLE = "Shared Hierarchical Academic Research Computing Network",
+
+ URL = {www.sharcnet.ca},
+ YEAR = {Last Access: January, 2006},
+ }
+@MISC{Triangle2006,
+ AUTHOR = "Jonathan Shewchuk",
+ TITLE = "Triangle, A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator",
+
+ URL = {http://www.cs.cmu.edu/\~ quake/triangle.html},
+ YEAR = {Last Access: January, 2006},
+ }
+
+@MISC(Wikipedia,
+ AUTHOR = "Wikipedia",
+ TITLE = "Waterfall Model",
+
+ URL = {http://en.wikipedia.org/wiki/Waterfall\_model},
+ YEAR = {Last Access: January, 2006},
+ )
+
+@MISC{OpenMesh2006,
+ AUTHOR = "OpenMesh",
+ TITLE = "OpenMesh",
+
+ URL = {http://www.openmesh.org/},
+ YEAR = {Last Access: January, 2006},
+ }
+
+@MISC{Franklin2006,
+ AUTHOR = "W. Randolph Franklin ",
+ TITLE = "PNPOLY - Point Inclusion in Polygon Test",
+
+ URL = {http://www.ecse.rpi.edu/Homepages/wrf/Research/Short\_Notes/ pnpoly.html},
+ YEAR = {Last Access: January, 2006},
+ }
+
+
+
+
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+%%CreationDate: 1991 Aug 18 21:06:53
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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+dup 46 /period put
+dup 51 /three put
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+currentdict end
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+ cid_BYTE_COUNT ct_CID_STR_SIZE mod string
+ 3 index exec
+ pop
+ 1 index exch
+ 1 index length 1 sub
+ exch put
+ }
+ ifelse
+ cid_CIDFONT exch /GlyphData exch put
+ 2 index null eq
+ {
+ pop pop pop
+ }
+ {
+ pop /readstring load
+ 1 string exch
+ {
+ 3 copy exec
+ pop
+ dup length 0 eq
+ {
+ pop pop pop pop pop
+ true exit
+ }
+ if
+ 4 index
+ eq
+ {
+ pop pop pop pop
+ false exit
+ }
+ if
+ }
+ loop
+ pop
+ }
+ ifelse
+ } bind def
+ /StartData
+ {
+ mark
+ {
+ currentdict
+ dup /FDArray get 0 get /FontMatrix get
+ 0 get 0.001 eq
+ {
+ dup /CDevProc known not
+ {
+ /CDevProc 1183615869 internaldict /stdCDevProc 2 copy known
+ { get }
+ {
+ pop pop
+ { pop pop pop pop pop 0 -1000 7 index 2 div 880 }
+ }
+ ifelse
+ def
+ }
+ if
+ }
+ {
+ /CDevProc
+ {
+ pop pop pop pop pop
+ 0
+ 1 cid_temp /cid_CIDFONT get
+ /FDArray get 0 get
+ /FontMatrix get 0 get div
+ 7 index 2 div
+ 1 index 0.88 mul
+ } def
+ }
+ ifelse
+ /cid_temp 15 dict def
+ cid_temp
+ begin
+ /cid_CIDFONT exch def
+ 3 copy pop
+ dup /cid_BYTE_COUNT exch def 0 gt
+ {
+ ct_cidfont_stream_init
+ FDArray
+ {
+ /Private get
+ dup /SubrMapOffset known
+ {
+ begin
+ /Subrs SubrCount array def
+ Subrs
+ SubrMapOffset
+ SubrCount
+ SDBytes
+ ct_Level2?
+ {
+ currentdict dup /SubrMapOffset undef
+ dup /SubrCount undef
+ /SDBytes undef
+ }
+ if
+ end
+ /cid_SD_BYTES exch def
+ /cid_SUBR_COUNT exch def
+ /cid_SUBR_MAP_OFFSET exch def
+ /cid_SUBRS exch def
+ cid_SUBR_COUNT 0 gt
+ {
+ GlyphData cid_SUBR_MAP_OFFSET cid_SD_BYTES ct_GetInterval
+ 0 cid_SD_BYTES ct_cvnsi
+ 0 1 cid_SUBR_COUNT 1 sub
+ {
+ exch 1 index
+ 1 add
+ cid_SD_BYTES mul cid_SUBR_MAP_OFFSET add
+ GlyphData exch cid_SD_BYTES ct_GetInterval
+ 0 cid_SD_BYTES ct_cvnsi
+ cid_SUBRS 4 2 roll
+ GlyphData exch
+ 4 index
+ 1 index
+ sub
+ ct_GetInterval
+ dup length string copy put
+ }
+ for
+ pop
+ }
+ if
+ }
+ { pop }
+ ifelse
+ }
+ forall
+ }
+ if
+ cleartomark pop pop
+ end
+ CIDFontName currentdict /CIDFont defineresource pop
+ end end
+ }
+ stopped
+ { cleartomark /StartData ct_reraise }
+ if
+ } bind def
+ currentdict
+ end def
+ /ct_saveCIDInit
+ {
+ /CIDInit /ProcSet ct_resourcestatus
+ { true }
+ { /CIDInitC /ProcSet ct_resourcestatus }
+ ifelse
+ {
+ pop pop
+ /CIDInit /ProcSet findresource
+ ct_UseNativeCapability?
+ { pop null }
+ { /CIDInit ct_CIDInit /ProcSet defineresource pop }
+ ifelse
+ }
+ { /CIDInit ct_CIDInit /ProcSet defineresource pop null }
+ ifelse
+ ct_Vars exch /ct_oldCIDInit exch put
+ } bind def
+ /ct_restoreCIDInit
+ {
+ ct_Vars /ct_oldCIDInit get dup null ne
+ { /CIDInit exch /ProcSet defineresource pop }
+ { pop }
+ ifelse
+ } bind def
+ /ct_BuildCharSetUp
+ {
+ 1 index
+ begin
+ CIDFont
+ begin
+ Adobe_CoolType_Utility /ct_BuildCharDict get
+ begin
+ /ct_dfCharCode exch def
+ /ct_dfDict exch def
+ CIDFirstByte ct_dfCharCode add
+ dup CIDCount ge
+ { pop 0 }
+ if
+ /cid exch def
+ {
+ GlyphDirectory cid 2 copy known
+ { get }
+ { pop pop nullstring }
+ ifelse
+ dup length FDBytes sub 0 gt
+ {
+ dup
+ FDBytes 0 ne
+ { 0 FDBytes ct_cvnsi }
+ { pop 0 }
+ ifelse
+ /fdIndex exch def
+ dup length FDBytes sub FDBytes exch getinterval
+ /charstring exch def
+ exit
+ }
+ {
+ pop
+ cid 0 eq
+ { /charstring nullstring def exit }
+ if
+ /cid 0 def
+ }
+ ifelse
+ }
+ loop
+ } def
+ /ct_SetCacheDevice
+ {
+ 0 0 moveto
+ dup stringwidth
+ 3 -1 roll
+ true charpath
+ pathbbox
+ 0 -1000
+ 7 index 2 div 880
+ setcachedevice2
+ 0 0 moveto
+ } def
+ /ct_CloneSetCacheProc
+ {
+ 1 eq
+ {
+ stringwidth
+ pop -2 div -880
+ 0 -1000 setcharwidth
+ moveto
+ }
+ {
+ usewidths?
+ {
+ currentfont /Widths get cid
+ 2 copy known
+ { get exch pop aload pop }
+ { pop pop stringwidth }
+ ifelse
+ }
+ { stringwidth }
+ ifelse
+ setcharwidth
+ 0 0 moveto
+ }
+ ifelse
+ } def
+ /ct_Type3ShowCharString
+ {
+ ct_FDDict fdIndex 2 copy known
+ { get }
+ {
+ currentglobal 3 1 roll
+ 1 index gcheck setglobal
+ ct_Type1FontTemplate dup maxlength dict copy
+ begin
+ FDArray fdIndex get
+ dup /FontMatrix 2 copy known
+ { get }
+ { pop pop ct_defaultFontMtx }
+ ifelse
+ /FontMatrix exch dup length array copy def
+ /Private get
+ /Private exch def
+ /Widths rootfont /Widths get def
+ /CharStrings 1 dict dup /.notdef
+ <d841272cf18f54fc13> dup length string copy put def
+ currentdict
+ end
+ /ct_Type1Font exch definefont
+ dup 5 1 roll put
+ setglobal
+ }
+ ifelse
+ dup /CharStrings get 1 index /Encoding get
+ ct_dfCharCode get charstring put
+ rootfont /WMode 2 copy known
+ { get }
+ { pop pop 0 }
+ ifelse
+ exch
+ 1000 scalefont setfont
+ ct_str1 0 ct_dfCharCode put
+ ct_str1 exch ct_dfSetCacheProc
+ ct_SyntheticBold
+ {
+ currentpoint
+ ct_str1 show
+ newpath
+ moveto
+ ct_str1 true charpath
+ ct_StrokeWidth setlinewidth
+ stroke
+ }
+ { ct_str1 show }
+ ifelse
+ } def
+ /ct_Type4ShowCharString
+ {
+ ct_dfDict ct_dfCharCode charstring
+ FDArray fdIndex get
+ dup /FontMatrix get dup ct_defaultFontMtx ct_matrixeq not
+ { ct_1000Mtx matrix concatmatrix concat }
+ { pop }
+ ifelse
+ /Private get
+ Adobe_CoolType_Utility /ct_Level2? get not
+ {
+ ct_dfDict /Private
+ 3 -1 roll
+ { put }
+ 1183615869 internaldict /superexec get exec
+ }
+ if
+ 1183615869 internaldict
+ Adobe_CoolType_Utility /ct_Level2? get
+ { 1 index }
+ { 3 index /Private get mark 6 1 roll }
+ ifelse
+ dup /RunInt known
+ { /RunInt get }
+ { pop /CCRun }
+ ifelse
+ get exec
+ Adobe_CoolType_Utility /ct_Level2? get not
+ { cleartomark }
+ if
+ } bind def
+ /ct_BuildCharIncremental
+ {
+ {
+ Adobe_CoolType_Utility /ct_MakeOCF get begin
+ ct_BuildCharSetUp
+ ct_ShowCharString
+ }
+ stopped
+ { stop }
+ if
+ end
+ end
+ end
+ end
+ } bind def
+ /BaseFontNameStr (BF00) def
+ /ct_Type1FontTemplate 14 dict
+ begin
+ /FontType 1 def
+ /FontMatrix [0.001 0 0 0.001 0 0] def
+ /FontBBox [-250 -250 1250 1250] def
+ /Encoding ct_cHexEncoding def
+ /PaintType 0 def
+ currentdict
+ end def
+ /BaseFontTemplate 11 dict
+ begin
+ /FontMatrix [0.001 0 0 0.001 0 0] def
+ /FontBBox [-250 -250 1250 1250] def
+ /Encoding ct_cHexEncoding def
+ /BuildChar /ct_BuildCharIncremental load def
+ ct_Clone?
+ {
+ /FontType 3 def
+ /ct_ShowCharString /ct_Type3ShowCharString load def
+ /ct_dfSetCacheProc /ct_CloneSetCacheProc load def
+ /ct_SyntheticBold false def
+ /ct_StrokeWidth 1 def
+ }
+ {
+ /FontType 4 def
+ /Private 1 dict dup /lenIV 4 put def
+ /CharStrings 1 dict dup /.notdef <d841272cf18f54fc13> put def
+ /PaintType 0 def
+ /ct_ShowCharString /ct_Type4ShowCharString load def
+ }
+ ifelse
+ /ct_str1 1 string def
+ currentdict
+ end def
+ /BaseFontDictSize BaseFontTemplate length 5 add def
+ /ct_matrixeq
+ {
+ true 0 1 5
+ {
+ dup 4 index exch get exch 3 index exch get eq and
+ dup not
+ { exit }
+ if
+ }
+ for
+ exch pop exch pop
+ } bind def
+ /ct_makeocf
+ {
+ 15 dict
+ begin
+ exch /WMode exch def
+ exch /FontName exch def
+ /FontType 0 def
+ /FMapType 2 def
+ /FontMatrix matrix def
+ /bfCount 1 index /CIDCount get 256 idiv 1 add
+ dup 256 gt { pop 256} if def
+ /Encoding
+ 256 array 0 1 bfCount 1 sub { 2 copy dup put pop } for
+ bfCount 1 255 { 2 copy bfCount put pop } for
+ def
+ /FDepVector bfCount dup 256 lt { 1 add } if array def
+ BaseFontTemplate BaseFontDictSize dict copy
+ begin
+ /CIDFont exch def
+ CIDFont /FontBBox known
+ { CIDFont /FontBBox get /FontBBox exch def }
+ if
+ CIDFont /CDevProc known
+ { CIDFont /CDevProc get /CDevProc exch def }
+ if
+ currentdict
+ end
+ BaseFontNameStr 3 (0) putinterval
+ 0 1 bfCount dup 256 eq { 1 sub } if
+ {
+ FDepVector exch
+ 2 index BaseFontDictSize dict copy
+ begin
+ dup /CIDFirstByte exch 256 mul def
+ FontType 3 eq
+ { /ct_FDDict 2 dict def }
+ if
+ currentdict
+ end
+ 1 index 16
+ BaseFontNameStr 2 2 getinterval cvrs pop
+ BaseFontNameStr exch definefont
+ put
+ }
+ for
+ ct_Clone?
+ { /Widths 1 index /CIDFont get /GlyphDirectory get length dict def }
+ if
+ FontName
+ currentdict
+ end
+ definefont
+ ct_Clone?
+ {
+ gsave
+ dup 1000 scalefont setfont
+ ct_BuildCharDict
+ begin
+ /usewidths? false def
+ currentfont /Widths get
+ begin
+ exch /CIDFont get /GlyphDirectory get
+ {
+ pop
+ dup charcode exch 1 index 0 2 index 256 idiv put
+ 1 index exch 1 exch 256 mod put
+ stringwidth 2 array astore def
+ }
+ forall
+ end
+ /usewidths? true def
+ end
+ grestore
+ }
+ { exch pop }
+ ifelse
+ } bind def
+ /ct_ComposeFont
+ {
+ ct_UseNativeCapability?
+ {
+ 2 index /CMap ct_resourcestatus
+ { pop pop exch pop }
+ {
+ /CIDInit /ProcSet findresource
+ begin
+ 12 dict
+ begin
+ begincmap
+ /CMapName 3 index def
+ /CMapVersion 1.000 def
+ /CMapType 1 def
+ exch /WMode exch def
+ /CIDSystemInfo 3 dict dup
+ begin
+ /Registry (Adobe) def
+ /Ordering
+ CMapName ct_mkocfStr100 cvs
+ (Adobe-) search
+ {
+ pop pop
+ (-) search
+ {
+ dup length string copy
+ exch pop exch pop
+ }
+ { pop (Identity)}
+ ifelse
+ }
+ { pop (Identity) }
+ ifelse
+ def
+ /Supplement 0 def
+ end def
+ 1 begincodespacerange
+ <0000> <FFFF>
+ endcodespacerange
+ 1 begincidrange
+ <0000> <FFFF> 0
+ endcidrange
+ endcmap
+ CMapName currentdict /CMap defineresource pop
+ end
+ end
+ }
+ ifelse
+ composefont
+ }
+ {
+ 3 2 roll pop
+ 0 get /CIDFont findresource
+ ct_makeocf
+ }
+ ifelse
+ } bind def
+ /ct_MakeIdentity
+ {
+ ct_UseNativeCapability?
+ {
+ 1 index /CMap ct_resourcestatus
+ { pop pop }
+ {
+ /CIDInit /ProcSet findresource begin
+ 12 dict begin
+ begincmap
+ /CMapName 2 index def
+ /CMapVersion 1.000 def
+ /CMapType 1 def
+ /CIDSystemInfo 3 dict dup
+ begin
+ /Registry (Adobe) def
+ /Ordering
+ CMapName ct_mkocfStr100 cvs
+ (Adobe-) search
+ {
+ pop pop
+ (-) search
+ { dup length string copy exch pop exch pop }
+ { pop (Identity) }
+ ifelse
+ }
+ { pop (Identity) }
+ ifelse
+ def
+ /Supplement 0 def
+ end def
+ 1 begincodespacerange
+ <0000> <FFFF>
+ endcodespacerange
+ 1 begincidrange
+ <0000> <FFFF> 0
+ endcidrange
+ endcmap
+ CMapName currentdict /CMap defineresource pop
+ end
+ end
+ }
+ ifelse
+ composefont
+ }
+ {
+ exch pop
+ 0 get /CIDFont findresource
+ ct_makeocf
+ }
+ ifelse
+ } bind def
+ currentdict readonly pop
+ end
+ end
+%%EndResource
+/currentpacking where{pop currentpacking true setpacking}if
+%%BeginResource: procset pdfvars 6.0 1
+%%Copyright: Copyright 1987-2002 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: definition of dictionary of variables used by PDF & PDFText procsets
+userdict /PDF 162 dict put
+userdict /PDFVars 89 dict dup begin put
+/docSetupDone false def
+/InitAll 0 def
+/TermAll 0 def
+/DocInitAll 0 def
+/DocTermAll 0 def
+/_pdfEncodings 2 array def
+/_pdf_str1 1 string def
+/_pdf_i 0 def
+/_pdf_na 0 def
+/_pdf_showproc 0 def
+/_italMtx [1 0 .212557 1 0 0] def
+/_italMtx_WMode1 [1 -.212557 0 1 0 0] def
+/_italMtxType0 [1 0 .1062785 1 0 0] def
+/_italMtx_WMode1Type0 [1 -.1062785 0 1 0 0] def
+/_basefont 0 def
+/_basefonto 0 def
+/_pdf_oldCIDInit null def
+/_pdf_FontDirectory 30 dict def
+/_categories 10 dict def
+/_sa? true def
+/_ColorSep5044? false def
+/nulldict 0 dict def
+/_processColors 0 def
+/overprintstack null def
+/_defaulttransfer currenttransfer def
+/_defaultflatness currentflat def
+/_defaulthalftone null def
+/_defaultcolortransfer null def
+/_defaultblackgeneration null def
+/_defaultundercolorremoval null def
+/_defaultcolortransfer null def
+PDF begin
+[/c/cs/cm/d/d0/f/h/i/j/J/l/m/M/n/q/Q/re/ri/S/sc/sh/Tf/w/W
+/applyInterpFunc/applystitchFunc/domainClip/encodeInput
+/initgs/int/limit/rangeClip
+/defineRes/undefineRes/findRes/setSA/pl
+/? /! /| /: /+ /GetGlyphDirectory
+/pdf_flushFilters /pdf_readstring /pdf_dictOp /pdf_image /pdf_maskedImage
+/pdf_shfill /pdf_sethalftone
+] {null def} bind forall
+end
+end
+%%EndResource
+PDFVars begin PDF begin
+%%BeginResource: procset pdfutil 6.0 1
+%%Copyright: Copyright 1993-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Basic utilities used by other PDF procsets
+/bd {bind def} bind def
+/ld {load def} bd
+/bld {
+dup length dict begin
+{ null def } forall
+bind
+end
+def
+} bd
+/dd { PDFVars 3 1 roll put } bd
+/xdd { exch dd } bd
+/Level2?
+systemdict /languagelevel known
+{ systemdict /languagelevel get 2 ge } { false } ifelse
+def
+/Level1? Level2? not def
+/Level3?
+systemdict /languagelevel known
+{systemdict /languagelevel get 3 eq } { false } ifelse
+def
+/getifknown {
+2 copy known { get true } { pop pop false } ifelse
+} bd
+/here {
+currentdict exch getifknown
+} bd
+/isdefined? { where { pop true } { false } ifelse } bd
+%%EndResource
+%%BeginResource: procset l2compat 6.0 1
+%%Copyright: Copyright 1987-2003 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Level 1 emulation of level 2 operators
+/setcmykcolor isdefined? not
+{
+/setcmykcolor {
+1 sub 4 1 roll
+3 {
+3 index add neg dup 0 lt { pop 0 } if
+3 1 roll
+} repeat
+setrgbcolor
+pop
+} bd
+} if
+/rectclip isdefined? not
+{
+/rectclip { newpath re clip newpath } bd
+} if
+/rectfill isdefined? not
+{
+/rectfill { gsave newpath re fill grestore } bd
+} if
+/sethalftone isdefined? not
+{
+/sethalftone {
+begin
+HalftoneType 1 eq
+{ Frequency Angle /SpotFunction load setscreen }
+if
+end
+} bd
+} if
+Level1?
+{
+/pdf_show {show} bd
+/xshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_xshow
+} bd
+/yshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_yshow
+} bd
+/xyshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_xyshow
+} bd
+} if
+/getrampcolor {
+cvi
+/indx exch def
+[
+0 1 NumComp 1 sub {
+dup
+Samples exch get
+dup type /stringtype eq { indx get } if
+exch
+Scaling exch get aload pop
+3 1 roll
+mul add
+} for
+]
+L1setcolor
+} bd
+/sssetbackground { L1setcolor } bd
+%%EndResource
+%%BeginResource: procset pdf 6.0 1
+%%Copyright: Copyright 1998-2003 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: General operators for PDF, common to all Language Levels.
+/cm { matrix astore concat } bd
+/d /setdash ld
+/f /fill ld
+/h /closepath ld
+/i {dup 0 eq {pop _defaultflatness} if setflat} bd
+/j /setlinejoin ld
+/J /setlinecap ld
+/M /setmiterlimit ld
+/n /newpath ld
+/S /stroke ld
+/w /setlinewidth ld
+/W /clip ld
+/sg /setgray ld
+/initgs {
+0 setgray
+[] 0 d
+0 j
+0 J
+10 M
+1 w
+false setSA
+/_defaulttransfer load settransfer
+0 i
+/RelativeColorimetric ri
+newpath
+} bd
+/int {
+dup 2 index sub 3 index 5 index sub div 6 -2 roll sub mul
+exch pop add exch pop
+} bd
+/limit {
+dup 2 index le { exch } if pop
+dup 2 index ge { exch } if pop
+} bd
+/domainClip {
+Domain aload pop 3 2 roll
+limit
+} [/Domain] bld
+/applyInterpFunc {
+0 1 DimOut 1 sub
+{
+dup C0 exch get exch
+dup C1 exch get exch
+3 1 roll
+1 index sub
+3 index
+N exp mul add
+exch
+currentdict /Range_lo known
+{
+dup Range_lo exch get exch
+Range_hi exch get
+3 2 roll limit
+}
+{
+pop
+}
+ifelse
+exch
+} for
+pop
+} [/DimOut /C0 /C1 /N /Range_lo /Range_hi] bld
+/encodeInput {
+NumParts 1 sub
+0 1 2 index
+{
+dup Bounds exch get
+2 index gt
+{ exit }
+{ dup
+3 index eq
+{ exit }
+{ pop } ifelse
+} ifelse
+} for
+3 2 roll pop
+dup Bounds exch get exch
+dup 1 add Bounds exch get exch
+2 mul
+dup Encode exch get exch
+1 add Encode exch get
+int
+} [/NumParts /Bounds /Encode] bld
+/rangeClip {
+exch dup Range_lo exch get
+exch Range_hi exch get
+3 2 roll
+limit
+} [/Range_lo /Range_hi] bld
+/applyStitchFunc {
+Functions exch get exec
+currentdict /Range_lo known {
+0 1 DimOut 1 sub {
+DimOut 1 add -1 roll
+rangeClip
+} for
+} if
+} [/Functions /Range_lo /DimOut] bld
+/pdf_flushfilters
+{
+aload length
+{ dup status
+1 index currentfile ne and
+{ dup flushfile closefile }
+{ pop }
+ifelse
+} repeat
+} bd
+/pdf_readstring
+{
+1 index dup length 1 sub get
+exch readstring pop
+exch pdf_flushfilters
+} bind def
+/pdf_dictOp
+{
+3 2 roll
+10 dict copy
+begin
+_Filters dup length 1 sub get def
+currentdict exch exec
+_Filters pdf_flushfilters
+end
+} [/_Filters] bld
+/pdf_image {{image} /DataSource pdf_dictOp} bd
+/pdf_imagemask {{imagemask} /DataSource pdf_dictOp} bd
+/pdf_shfill {{sh} /DataSource pdf_dictOp} bd
+/pdf_sethalftone {{sethalftone} /Thresholds pdf_dictOp} bd
+/pdf_maskedImage
+{
+10 dict copy begin
+/miDict currentdict def
+/DataDict DataDict 10 dict copy def
+DataDict begin
+/DataSource
+_Filters dup length 1 sub get
+def
+miDict image
+_Filters pdf_flushfilters
+end
+end
+} [/miDict /DataDict /_Filters] bld
+/RadialShade {
+40 dict begin
+/background exch def
+/ext1 exch def
+/ext0 exch def
+/BBox exch def
+/r2 exch def
+/c2y exch def
+/c2x exch def
+/r1 exch def
+/c1y exch def
+/c1x exch def
+/rampdict exch def
+gsave
+BBox length 0 gt {
+newpath
+BBox 0 get BBox 1 get moveto
+BBox 2 get BBox 0 get sub 0 rlineto
+0 BBox 3 get BBox 1 get sub rlineto
+BBox 2 get BBox 0 get sub neg 0 rlineto
+closepath
+clip
+newpath
+} if
+c1x c2x eq
+{
+c1y c2y lt {/theta 90 def}{/theta 270 def} ifelse
+}
+{
+/slope c2y c1y sub c2x c1x sub div def
+/theta slope 1 atan def
+c2x c1x lt c2y c1y ge and { /theta theta 180 sub def} if
+c2x c1x lt c2y c1y lt and { /theta theta 180 add def} if
+}
+ifelse
+gsave
+clippath
+c1x c1y translate
+theta rotate
+-90 rotate
+{ pathbbox } stopped
+{ 0 0 0 0 } if
+/yMax exch def
+/xMax exch def
+/yMin exch def
+/xMin exch def
+grestore
+xMax xMin eq yMax yMin eq or
+{
+grestore
+end
+}
+{
+/max { 2 copy gt { pop } {exch pop} ifelse } bind def
+/min { 2 copy lt { pop } {exch pop} ifelse } bind def
+rampdict begin
+40 dict begin
+background length 0 gt { background sssetbackground gsave clippath fill grestore } if
+gsave
+c1x c1y translate
+theta rotate
+-90 rotate
+/c2y c1x c2x sub dup mul c1y c2y sub dup mul add sqrt def
+/c1y 0 def
+/c1x 0 def
+/c2x 0 def
+ext0 {
+0 getrampcolor
+c2y r2 add r1 sub 0.0001 lt
+{
+c1x c1y r1 360 0 arcn
+pathbbox
+/aymax exch def
+/axmax exch def
+/aymin exch def
+/axmin exch def
+/bxMin xMin axmin min def
+/byMin yMin aymin min def
+/bxMax xMax axmax max def
+/byMax yMax aymax max def
+bxMin byMin moveto
+bxMax byMin lineto
+bxMax byMax lineto
+bxMin byMax lineto
+bxMin byMin lineto
+eofill
+}
+{
+c2y r1 add r2 le
+{
+c1x c1y r1 0 360 arc
+fill
+}
+{
+c2x c2y r2 0 360 arc fill
+r1 r2 eq
+{
+/p1x r1 neg def
+/p1y c1y def
+/p2x r1 def
+/p2y c1y def
+p1x p1y moveto p2x p2y lineto p2x yMin lineto p1x yMin lineto
+fill
+}
+{
+/AA r2 r1 sub c2y div def
+AA -1 eq
+{ /theta 89.99 def}
+{ /theta AA 1 AA dup mul sub sqrt div 1 atan def}
+ifelse
+/SS1 90 theta add dup sin exch cos div def
+/p1x r1 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def
+/p1y p1x SS1 div neg def
+/SS2 90 theta sub dup sin exch cos div def
+/p2x r1 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def
+/p2y p2x SS2 div neg def
+r1 r2 gt
+{
+/L1maxX p1x yMin p1y sub SS1 div add def
+/L2maxX p2x yMin p2y sub SS2 div add def
+}
+{
+/L1maxX 0 def
+/L2maxX 0 def
+}ifelse
+p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto
+L1maxX L1maxX p1x sub SS1 mul p1y add lineto
+fill
+}
+ifelse
+}
+ifelse
+} ifelse
+} if
+c1x c2x sub dup mul
+c1y c2y sub dup mul
+add 0.5 exp
+0 dtransform
+dup mul exch dup mul add 0.5 exp 72 div
+0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+1 index 1 index lt { exch } if pop
+/hires exch def
+hires mul
+/numpix exch def
+/numsteps NumSamples def
+/rampIndxInc 1 def
+/subsampling false def
+numpix 0 ne
+{
+NumSamples numpix div 0.5 gt
+{
+/numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def
+/rampIndxInc NumSamples 1 sub numsteps div def
+/subsampling true def
+} if
+} if
+/xInc c2x c1x sub numsteps div def
+/yInc c2y c1y sub numsteps div def
+/rInc r2 r1 sub numsteps div def
+/cx c1x def
+/cy c1y def
+/radius r1 def
+newpath
+xInc 0 eq yInc 0 eq rInc 0 eq and and
+{
+0 getrampcolor
+cx cy radius 0 360 arc
+stroke
+NumSamples 1 sub getrampcolor
+cx cy radius 72 hires div add 0 360 arc
+0 setlinewidth
+stroke
+}
+{
+0
+numsteps
+{
+dup
+subsampling { round } if
+getrampcolor
+cx cy radius 0 360 arc
+/cx cx xInc add def
+/cy cy yInc add def
+/radius radius rInc add def
+cx cy radius 360 0 arcn
+eofill
+rampIndxInc add
+}
+repeat
+pop
+} ifelse
+ext1 {
+c2y r2 add r1 lt
+{
+c2x c2y r2 0 360 arc
+fill
+}
+{
+c2y r1 add r2 sub 0.0001 le
+{
+c2x c2y r2 360 0 arcn
+pathbbox
+/aymax exch def
+/axmax exch def
+/aymin exch def
+/axmin exch def
+/bxMin xMin axmin min def
+/byMin yMin aymin min def
+/bxMax xMax axmax max def
+/byMax yMax aymax max def
+bxMin byMin moveto
+bxMax byMin lineto
+bxMax byMax lineto
+bxMin byMax lineto
+bxMin byMin lineto
+eofill
+}
+{
+c2x c2y r2 0 360 arc fill
+r1 r2 eq
+{
+/p1x r2 neg def
+/p1y c2y def
+/p2x r2 def
+/p2y c2y def
+p1x p1y moveto p2x p2y lineto p2x yMax lineto p1x yMax lineto
+fill
+}
+{
+/AA r2 r1 sub c2y div def
+AA -1 eq
+{ /theta 89.99 def}
+{ /theta AA 1 AA dup mul sub sqrt div 1 atan def}
+ifelse
+/SS1 90 theta add dup sin exch cos div def
+/p1x r2 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def
+/p1y c2y p1x SS1 div sub def
+/SS2 90 theta sub dup sin exch cos div def
+/p2x r2 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def
+/p2y c2y p2x SS2 div sub def
+r1 r2 lt
+{
+/L1maxX p1x yMax p1y sub SS1 div add def
+/L2maxX p2x yMax p2y sub SS2 div add def
+}
+{
+/L1maxX 0 def
+/L2maxX 0 def
+}ifelse
+p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto
+L1maxX L1maxX p1x sub SS1 mul p1y add lineto
+fill
+}
+ifelse
+}
+ifelse
+} ifelse
+} if
+grestore
+grestore
+end
+end
+end
+} ifelse
+} bd
+/GenStrips {
+40 dict begin
+/background exch def
+/ext1 exch def
+/ext0 exch def
+/BBox exch def
+/y2 exch def
+/x2 exch def
+/y1 exch def
+/x1 exch def
+/rampdict exch def
+gsave
+BBox length 0 gt {
+newpath
+BBox 0 get BBox 1 get moveto
+BBox 2 get BBox 0 get sub 0 rlineto
+0 BBox 3 get BBox 1 get sub rlineto
+BBox 2 get BBox 0 get sub neg 0 rlineto
+closepath
+clip
+newpath
+} if
+x1 x2 eq
+{
+y1 y2 lt {/theta 90 def}{/theta 270 def} ifelse
+}
+{
+/slope y2 y1 sub x2 x1 sub div def
+/theta slope 1 atan def
+x2 x1 lt y2 y1 ge and { /theta theta 180 sub def} if
+x2 x1 lt y2 y1 lt and { /theta theta 180 add def} if
+}
+ifelse
+gsave
+clippath
+x1 y1 translate
+theta rotate
+{ pathbbox } stopped
+{ 0 0 0 0 } if
+/yMax exch def
+/xMax exch def
+/yMin exch def
+/xMin exch def
+grestore
+xMax xMin eq yMax yMin eq or
+{
+grestore
+end
+}
+{
+rampdict begin
+20 dict begin
+background length 0 gt { background sssetbackground gsave clippath fill grestore } if
+gsave
+x1 y1 translate
+theta rotate
+/xStart 0 def
+/xEnd x2 x1 sub dup mul y2 y1 sub dup mul add 0.5 exp def
+/ySpan yMax yMin sub def
+/numsteps NumSamples def
+/rampIndxInc 1 def
+/subsampling false def
+xStart 0 transform
+xEnd 0 transform
+3 -1 roll
+sub dup mul
+3 1 roll
+sub dup mul
+add 0.5 exp 72 div
+0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+1 index 1 index lt { exch } if pop
+mul
+/numpix exch def
+numpix 0 ne
+{
+NumSamples numpix div 0.5 gt
+{
+/numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def
+/rampIndxInc NumSamples 1 sub numsteps div def
+/subsampling true def
+} if
+} if
+ext0 {
+0 getrampcolor
+xMin xStart lt
+{ xMin yMin xMin neg ySpan rectfill } if
+} if
+/xInc xEnd xStart sub numsteps div def
+/x xStart def
+0
+numsteps
+{
+dup
+subsampling { round } if
+getrampcolor
+x yMin xInc ySpan rectfill
+/x x xInc add def
+rampIndxInc add
+}
+repeat
+pop
+ext1 {
+xMax xEnd gt
+{ xEnd yMin xMax xEnd sub ySpan rectfill } if
+} if
+grestore
+grestore
+end
+end
+end
+} ifelse
+} bd
+/currentdistillerparams where { pop currentdistillerparams /CoreDistVersion get 5000 lt}{true}ifelse
+{
+/PDFMark5 {cleartomark} bd
+}
+{
+/PDFMark5 {pdfmark} bd
+}ifelse
+/ReadByPDFMark5
+{
+2 dict begin
+/makerString exch def string /tmpString exch def
+{
+currentfile tmpString readline pop
+makerString anchorsearch
+{
+pop pop cleartomark exit
+}
+{
+3 copy /PUT PDFMark5 pop 2 copy (\n) /PUT PDFMark5
+} ifelse
+}loop
+end
+}bd
+%%EndResource
+%%BeginResource: procset sep_ops 6.0 1
+%%Copyright: Copyright 1987-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Support for Separations in Level 1, following the conventions of Tech Note 5044
+userdict /sep_ops 50 dict dup begin put
+/bdef {bind def} bind def
+/xdef {exch def} bdef
+/colorimagebuffer {
+0 1 2 index length 1 sub {
+dup 2 index exch get 255 exch sub 2 index 3 1 roll put
+} for
+} bdef
+/addprocs {
+[ 3 1 roll
+/exec load
+dup 3 1 roll
+] cvx
+} bdef
+/L1? {
+systemdict /languagelevel known {
+systemdict /languagelevel get 2 lt
+}{
+true
+} ifelse
+} bdef
+/colorexists {
+statusdict /processcolors known {
+statusdict /processcolors get exec
+}{
+/deviceinfo where {
+pop deviceinfo /Colors known {
+deviceinfo /Colors get
+statusdict /processcolors {
+deviceinfo /Colors known {
+deviceinfo /Colors get
+}{
+1
+} ifelse
+} put
+}{
+1
+} ifelse
+}{
+1
+} ifelse
+} ifelse
+1 gt
+} bdef
+/colorplate colorexists { 0 } { 5 } ifelse def
+/negativecolorplate false def
+/setcmykcolor where {
+pop
+gsave
+1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub
+4 {4 copy} repeat
+grestore
+1 dict begin
+/foureq {
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+pop pop pop pop and and and
+} def
+1 0 0 0 foureq {/colorplate 1 store} if
+0 1 0 0 foureq {/colorplate 2 store} if
+0 0 1 0 foureq {/colorplate 3 store} if
+0 0 0 1 foureq {/colorplate 4 store} if
+0 0 0 0 foureq {/colorplate 6 store} if
+end
+} if
+0 systemdict /currenttransfer get exec exec
+1 systemdict /currenttransfer get exec exec
+2 copy
+eq
+{
+/colorplate 6 store
+pop
+/negativecolorplate exch 0.5 lt store
+}
+{
+gt /negativecolorplate exch store
+}
+ifelse
+/findcmykcustomcolor where { pop }
+{
+/findcmykcustomcolor {
+[ 6 1 roll ] readonly
+} bdef
+} ifelse
+/setoverprint where {
+pop
+}{
+/setoverprint {
+pop
+} bdef
+} ifelse
+/currentoverprint where {
+pop
+}{
+/currentoverprint {
+false
+} bdef
+} ifelse
+/setcustomcolor where {
+pop
+}{
+L1? {
+/setcustomcolor {
+exch
+aload pop pop
+4 { 4 index mul 4 1 roll } repeat
+5 -1 roll pop
+setcmykcolor
+} bdef
+}{
+/setcustomcolor {
+exch
+[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
+0 4 getinterval
+[ exch /dup load exch cvx {mul exch dup}
+/forall load /pop load dup] cvx
+] setcolorspace setcolor
+} bdef
+} ifelse
+} ifelse
+/ik 0 def
+/iy 0 def
+/im 0 def
+/ic 0 def
+/imagetint {
+ic .3 mul
+im .59 mul
+iy .11 mul
+ik add add add dup
+1 gt {pop 1} if
+} bdef
+/setcmykcolor where {
+pop
+}{
+/setcmykcolor {
+/ik xdef /iy xdef /im xdef /ic xdef
+imagetint
+1 exch sub setgray
+} bdef
+} ifelse
+/customcolorimage where {
+pop
+}{
+L1? {
+/customcolorimage{
+gsave
+colorexists {
+aload pop pop
+/ik xdef /iy xdef /im xdef /ic xdef
+currentcolortransfer
+{ik mul ik sub 1 add} addprocs
+4 1 roll {iy mul iy sub 1 add} addprocs
+4 1 roll {im mul im sub 1 add} addprocs
+4 1 roll {ic mul ic sub 1 add} addprocs
+4 1 roll setcolortransfer
+/magentabuf 0 string def
+/yellowbuf 0 string def
+/blackbuf 0 string def
+{
+colorimagebuffer dup length magentabuf length ne
+{
+dup length dup dup
+/magentabuf exch string def
+/yellowbuf exch string def
+/blackbuf exch string def
+} if
+dup magentabuf copy yellowbuf copy
+blackbuf copy pop
+} addprocs
+{magentabuf}{yellowbuf}{blackbuf} true 4 colorimage
+}{
+aload pop pop /ik xdef /iy xdef /im xdef /ic xdef /tint
+imagetint def
+currenttransfer
+{tint mul 1 tint sub add} addprocs settransfer image
+} ifelse
+grestore
+} bdef
+}{
+/customcolorimage {
+gsave
+[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
+0 4 getinterval
+[ exch /dup load exch cvx {mul exch dup}
+/forall load /pop load dup] cvx
+] setcolorspace
+10 dict begin
+/ImageType 1 def
+/DataSource exch def
+/ImageMatrix exch def
+/BitsPerComponent exch def
+/Height exch def
+/Width exch def
+/Decode [1 0] def
+currentdict end
+image
+grestore
+} bdef
+} ifelse
+} ifelse
+/setseparationgray where {
+pop
+}{
+L1? {
+/setseparationgray { 1 exch sub dup dup dup setcmykcolor } bdef
+}{
+/setseparationgray {
+[/Separation /All /DeviceCMYK {dup dup dup}] setcolorspace
+1 exch sub setcolor
+} bdef
+} ifelse
+} ifelse
+/separationimage where { pop }
+{
+/separationimage {
+gsave
+1 1 1 1 (All)
+findcmykcustomcolor customcolorimage
+grestore
+} bdef
+} ifelse
+currentdict readonly pop end
+%%EndResource
+%%BeginResource: procset pdflev15044 6.0 1
+%%Copyright: Copyright 1987-2002 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: PDF operators, Level 1, with emulated separations (TN 5044)
+/_ColorSep5044? true dd
+/docinitialize {
+PDF begin
+/_defaulthalftone
+/currenthalftone where
+{ pop currenthalftone }
+{ 4 dict dup begin
+currentscreen
+/SpotFunction exch def
+/Angle exch def
+/Frequency exch def
+/HalftoneType 1 def
+end }
+ifelse
+dd
+/currentcolortransfer where
+{ pop /_defaultcolortransfer [ currentcolortransfer ] dd }
+{ /_defaultcolortransfer [currenttransfer dup dup dup] dd }
+ifelse
+end
+} bd
+/initialize {
+/overprintstack null dd
+sep_ops begin
+50 dict begin
+_defaulthalftone sethalftone
+} bd
+/terminate {
+end end
+} bd
+/currentcolortransfer where
+{ pop }
+{
+/setcolortransfer
+{
+settransfer pop pop pop
+} bd
+} ifelse
+/pl {
+transform
+0.25 sub round 0.25 add exch
+0.25 sub round 0.25 add exch
+itransform
+} bd
+/m { _sa? { pl } if moveto } bd
+/l { _sa? { pl } if lineto } bd
+/c
+{
+_sa? {3 {pl 6 2 roll} repeat} if
+curveto
+} bd
+/ri/pop ld
+/setSA { /_sa? xdd } bd
+/re
+{
+_sa?
+{
+8 dict begin
+/:h exch def
+/:w exch def
+/:y exch def
+/:x exch def
+:x :y pl
+/:ymin exch def /:xmin exch def
+:x :w add :y :h add pl
+/:ymax exch def /:xmax exch def
+:xmin :ymin moveto
+:xmax :ymin lineto
+:xmax :ymax lineto
+:xmin :ymax lineto
+closepath
+end
+}
+{
+4 2 roll moveto
+1 index 0 rlineto
+0 exch rlineto
+neg 0 rlineto
+closepath
+} ifelse
+} bd
+/q
+{
+gsave
+[currentoverprint overprintstack] /overprintstack xdd
+}
+[/overprintstack] bld
+/Q
+{
+overprintstack aload pop /overprintstack xdd setoverprint
+grestore
+}
+[/overprintstack] bld
+/AlmostFull?
+{ dup maxlength exch length sub 2 le
+} bd
+/Expand
+{ 1 index maxlength mul cvi dict
+dup begin exch { def } forall end
+} bd
+/xput
+{ 3 2 roll
+dup 3 index known not
+{ dup AlmostFull? { 1.5 Expand } if
+} if
+dup 4 2 roll put
+} bd
+/defineRes
+{ _categories 1 index known not
+{ /_categories _categories 2 index 10 dict xput store
+} if
+_categories exch 2 copy get 5 -1 roll 4 index xput put
+} bd
+/undefineRes {
+null exch
+defineRes
+} bd
+/findRes {
+_categories exch get exch get
+} bd
+/L1setcolor {
+aload length
+dup 0 eq
+{ pop .5 setgray }
+{ dup 1 eq
+{ pop setgray }
+{ 3 eq
+{ setrgbcolor }
+{ setcmykcolor }
+ifelse }
+ifelse }
+ifelse
+} bind dd
+/concattransferfuncs {
+[ 3 1 roll /exec load exch /exec load ] cvx
+} bd
+/concatandsettransfer {
+/_defaulttransfer load concattransferfuncs settransfer
+} bd
+/concatandsetcolortransfer {
+colorplate 0 eq
+{
+_defaultcolortransfer aload pop
+8 -1 roll 5 -1 roll concattransferfuncs 7 1 roll
+6 -1 roll 4 -1 roll concattransferfuncs 5 1 roll
+4 -1 roll 3 -1 roll concattransferfuncs 3 1 roll
+concattransferfuncs
+setcolortransfer
+} if
+colorplate 1 ge colorplate 4 le and
+{
+4 colorplate sub index 4 { exch pop } repeat
+concatandsettransfer
+} if
+colorplate 5 ge
+{
+0 index 4 { exch pop } repeat
+concatandsettransfer
+} if
+} bd
+/tn5044sethalftone
+{
+begin
+HalftoneType 5 eq
+{ [/Default /Cyan /Magenta /Yellow /Black /Default /Default /Default]
+colorplate get
+here not {
+/Default here not { currentdict } if
+} if
+}
+{ currentdict }
+ifelse
+end
+begin
+/TransferFunction here
+{
+concatandsettransfer
+currentdict dup length dict
+begin
+{
+1 index /TransferFunction ne { def } { pop pop } ifelse
+} forall
+currentdict
+end
+}
+{
+currentdict
+} ifelse
+end
+sethalftone
+} bd
+/paintimage
+{
+colorplate 0 eq
+{
+{ {currentfile cyanstr readstring pop}
+{currentfile magentastr readstring pop}
+{currentfile yellowstr readstring pop}
+{currentfile blackstr readstring pop
+currentfile graystr readstring pop pop}
+}
+{ {currentfile cyanstr readhexstring pop}
+{currentfile magentastr readhexstring pop}
+{currentfile yellowstr readhexstring pop}
+{currentfile blackstr readhexstring pop
+currentfile graystr readhexstring pop pop}
+} ifelse
+true 4 colorimage
+}
+{
+3 dict begin
+/binaryOK exch def
+[
+1 1 5 {
+dup
+/currentfile cvx
+[ /cyanstr /magentastr /yellowstr /blackstr /graystr ]
+3 -1 roll 1 sub get cvx
+binaryOK { /readstring } { /readhexstring } ifelse cvx
+/pop cvx
+5 -1 roll
+colorplate dup 5 gt { pop 5 } if
+eq not { /pop cvx } if
+} for
+] cvx bind
+end
+[
+colorplate 6 eq {
+/pop cvx
+negativecolorplate { 0 } { 1 } ifelse
+} if
+colorplate 4 le
+{
+1 /exch cvx /sub cvx
+} if
+colorplate 6 ne
+{
+systemdict /currenttransfer get exec
+aload pop
+} if
+] cvx
+gsave
+systemdict /settransfer get exec
+systemdict /image get exec
+grestore
+} ifelse
+} bd
+%%EndResource
+%%BeginResource: procset pdftext 6.0 1
+%%Copyright: Copyright 1987-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Text operators for PDF
+PDF /PDFText 78 dict dup begin put
+/docinitialize
+{
+/resourcestatus where {
+pop
+/CIDParams /ProcSet resourcestatus {
+pop pop
+false /CIDParams /ProcSet findresource /SetBuildCompatible get exec
+} if
+} if
+PDF begin
+PDFText /_pdfDefineIdentity-H known
+{ PDFText /_pdfDefineIdentity-H get exec}
+if
+end
+} bd
+/initialize {
+PDFText begin
+} bd
+/terminate { end } bd
+Level2?
+{
+/_safeput
+{
+3 -1 roll load 3 1 roll put
+}
+bd
+}
+{
+/_safeput
+{
+2 index load dup dup length exch maxlength ge
+{ dup length 5 add dict copy
+3 index xdd
+}
+{ pop }
+ifelse
+3 -1 roll load 3 1 roll put
+}
+bd
+}
+ifelse
+/pdf_has_composefont? systemdict /composefont known def
+/CopyFont {
+{
+1 index /FID ne 2 index /UniqueID ne and
+{ def } { pop pop } ifelse
+} forall
+} bd
+/Type0CopyFont
+{
+exch
+dup length dict
+begin
+CopyFont
+[
+exch
+FDepVector
+{
+dup /FontType get 0 eq
+{
+1 index Type0CopyFont
+/_pdfType0 exch definefont
+}
+{
+/_pdfBaseFont exch
+2 index exec
+}
+ifelse
+exch
+}
+forall
+pop
+]
+/FDepVector exch def
+currentdict
+end
+} bd
+Level2? {currentglobal true setglobal} if
+/cHexEncoding
+[/c00/c01/c02/c03/c04/c05/c06/c07/c08/c09/c0A/c0B/c0C/c0D/c0E/c0F/c10/c11/c12
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+/c26/c27/c28/c29/c2A/c2B/c2C/c2D/c2E/c2F/c30/c31/c32/c33/c34/c35/c36/c37/c38
+/c39/c3A/c3B/c3C/c3D/c3E/c3F/c40/c41/c42/c43/c44/c45/c46/c47/c48/c49/c4A/c4B
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+/cBE/cBF/cC0/cC1/cC2/cC3/cC4/cC5/cC6/cC7/cC8/cC9/cCA/cCB/cCC/cCD/cCE/cCF/cD0
+/cD1/cD2/cD3/cD4/cD5/cD6/cD7/cD8/cD9/cDA/cDB/cDC/cDD/cDE/cDF/cE0/cE1/cE2/cE3
+/cE4/cE5/cE6/cE7/cE8/cE9/cEA/cEB/cEC/cED/cEE/cEF/cF0/cF1/cF2/cF3/cF4/cF5/cF6
+/cF7/cF8/cF9/cFA/cFB/cFC/cFD/cFE/cFF] def
+Level2? {setglobal} if
+/modEnc {
+/_enc xdd
+/_icode 0 dd
+counttomark 1 sub -1 0
+{
+index
+dup type /nametype eq
+{
+_enc _icode 3 -1 roll put
+_icode 1 add
+}
+if
+/_icode xdd
+} for
+cleartomark
+_enc
+} bd
+/trEnc {
+/_enc xdd
+255 -1 0 {
+exch dup -1 eq
+{ pop /.notdef }
+{ Encoding exch get }
+ifelse
+_enc 3 1 roll put
+} for
+pop
+_enc
+} bd
+/TE {
+/_i xdd
+StandardEncoding 256 array copy modEnc
+_pdfEncodings exch _i exch put
+} bd
+/TZ
+{
+/_usePDFEncoding xdd
+findfont
+dup length 6 add dict
+begin
+{
+1 index /FID ne { def } { pop pop } ifelse
+} forall
+/pdf_origFontName FontName def
+/FontName exch def
+currentdict /PaintType known
+{ PaintType 2 eq {/PaintType 0 def} if }
+if
+_usePDFEncoding 0 ge
+{
+/Encoding _pdfEncodings _usePDFEncoding get def
+pop
+}
+{
+_usePDFEncoding -1 eq
+{
+counttomark 0 eq
+{ pop }
+{
+Encoding 256 array copy
+modEnc /Encoding exch def
+}
+ifelse
+}
+{
+256 array
+trEnc /Encoding exch def
+}
+ifelse
+}
+ifelse
+pdf_EuroProcSet pdf_origFontName known
+{
+pdf_origFontName pdf_AddEuroGlyphProc
+} if
+Level2?
+{
+currentdict /pdf_origFontName undef
+} if
+FontName currentdict
+end
+definefont pop
+}
+bd
+Level2?
+{
+/TZG
+{
+currentglobal true setglobal
+2 index _pdfFontStatus
+{
+2 index findfont
+false setglobal
+3 index findfont
+true setglobal
+ne
+{
+2 index findfont dup rcheck
+{
+dup length dict begin
+{
+1 index /FID ne { def } { pop pop } ifelse
+} forall
+currentdict end
+}
+if
+3 index exch definefont pop
+}
+if
+} if
+setglobal
+TZ
+} bd
+}
+{
+/TZG {TZ} bd
+} ifelse
+Level2?
+{
+currentglobal false setglobal
+userdict /pdftext_data 5 dict put
+pdftext_data
+begin
+/saveStacks
+{
+pdftext_data
+begin
+/vmmode currentglobal def
+false setglobal
+count array astore /os exch def
+end
+countdictstack array dictstack pdftext_data exch /ds exch put
+cleardictstack pdftext_data /dscount countdictstack put
+pdftext_data /vmmode get setglobal
+} bind def
+/restoreStacks
+{
+pdftext_data /vmmode currentglobal put false setglobal
+clear cleardictstack
+pdftext_data /ds get dup
+pdftext_data /dscount get 1 2 index length 1 sub
+{ get begin dup } for
+pop pop
+pdftext_data /os get aload pop
+pdftext_data /vmmode get setglobal
+} bind def
+/testForClonePrinterBug
+{
+currentglobal true setglobal
+/undefinedCategory /Generic /Category findresource
+dup length dict copy /Category defineresource pop
+setglobal
+pdftext_data /saveStacks get exec
+pdftext_data /vmmode currentglobal put false setglobal
+/undefined /undefinedCategory { resourcestatus } stopped
+pdftext_data exch /bugFound exch put
+pdftext_data /vmmode get setglobal
+pdftext_data /restoreStacks get exec
+pdftext_data /bugFound get
+} bind def
+end
+setglobal
+/pdf_resourcestatus
+pdftext_data /testForClonePrinterBug get exec
+{
+{
+pdftext_data /saveStacks get exec
+pdftext_data /os get dup dup length 1 sub
+dup 1 sub dup 0 lt { pop 0 } if
+exch 1 exch { get exch dup } for
+pop pop
+{ resourcestatus }
+stopped
+{
+clear cleardictstack pdftext_data /restoreStacks get exec
+{ pop pop } stopped pop false
+}
+{
+count array astore pdftext_data exch /results exch put
+pdftext_data /restoreStacks get exec pop pop
+pdftext_data /results get aload pop
+}
+ifelse
+}
+}
+{ { resourcestatus } }
+ifelse
+bd
+}
+if
+Level2?
+{
+/_pdfUndefineResource
+{
+currentglobal 3 1 roll
+_pdf_FontDirectory 2 index 2 copy known
+{undef}
+{pop pop}
+ifelse
+1 index (pdf) exch _pdfConcatNames 1 index
+1 index 1 _pdfConcatNames 1 index
+5 index 1 _pdfConcatNames 1 index
+4
+{
+2 copy pdf_resourcestatus
+{
+pop 2 lt
+{2 copy findresource gcheck setglobal undefineresource}
+{pop pop}
+ifelse
+}
+{ pop pop}
+ifelse
+} repeat
+setglobal
+} bd
+}
+{
+/_pdfUndefineResource { pop pop} bd
+}
+ifelse
+Level2?
+{
+/_pdfFontStatus
+{
+currentglobal exch
+/Font pdf_resourcestatus
+{pop pop true}
+{false}
+ifelse
+exch setglobal
+} bd
+}
+{
+/_pdfFontStatusString 50 string def
+_pdfFontStatusString 0 (fonts/) putinterval
+/_pdfFontStatus
+{
+FontDirectory 1 index known
+{ pop true }
+{
+_pdfFontStatusString 6 42 getinterval
+cvs length 6 add
+_pdfFontStatusString exch 0 exch getinterval
+{ status } stopped
+{pop false}
+{
+{ pop pop pop pop true}
+{ false }
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+ifelse
+Level2?
+{
+/_pdfCIDFontStatus
+{
+/CIDFont /Category pdf_resourcestatus
+{
+pop pop
+/CIDFont pdf_resourcestatus
+{pop pop true}
+{false}
+ifelse
+}
+{ pop false }
+ifelse
+} bd
+}
+if
+/_pdfString100 100 string def
+/_pdfComposeFontName
+{
+dup length 1 eq
+{
+0 get
+1 index
+type /nametype eq
+{
+_pdfString100 cvs
+length dup dup _pdfString100 exch (-) putinterval
+_pdfString100 exch 1 add dup _pdfString100 length exch sub getinterval
+2 index exch cvs length
+add 1 add _pdfString100 exch 0 exch getinterval
+exch pop
+true
+}
+{
+pop pop
+false
+}
+ifelse
+}
+{
+false
+}
+ifelse
+dup {exch cvn exch} if
+} bd
+/_pdfConcatNames
+{
+exch
+_pdfString100 cvs
+length dup dup _pdfString100 exch (-) putinterval
+_pdfString100 exch 1 add dup _pdfString100 length exch sub getinterval
+3 -1 roll exch cvs length
+add 1 add _pdfString100 exch 0 exch getinterval
+cvn
+} bind def
+/_pdfTextTempString 50 string def
+/_pdfRegOrderingArray [(Adobe-Japan1) (Adobe-CNS1) (Adobe-Korea1) (Adobe-GB1)] def
+/_pdf_CheckCIDSystemInfo
+{
+1 index _pdfTextTempString cvs
+(Identity) anchorsearch
+{
+pop pop pop pop true
+}
+{
+false
+_pdfRegOrderingArray
+{
+2 index exch
+anchorsearch
+{ pop pop pop true exit}
+{ pop }
+ifelse
+}
+forall
+exch pop
+exch /CIDFont findresource
+/CIDSystemInfo get
+3 -1 roll /CMap findresource
+/CIDSystemInfo get
+exch
+3 -1 roll
+{
+2 copy
+/Supplement get
+exch
+dup type /dicttype eq
+{/Supplement get}
+{pop 0 }
+ifelse
+ge
+}
+{ true }
+ifelse
+{
+dup /Registry get
+2 index /Registry get eq
+{
+/Ordering get
+exch /Ordering get
+dup type /arraytype eq
+{
+1 index type /arraytype eq
+{
+true
+1 index length 1 sub -1 0
+{
+dup 2 index exch get exch 3 index exch get ne
+{ pop false exit}
+if
+} for
+exch pop exch pop
+}
+{ pop pop false }
+ifelse
+}
+{
+eq
+}
+ifelse
+}
+{ pop pop false }
+ifelse
+}
+{ pop pop false }
+ifelse
+}
+ifelse
+} bind def
+pdf_has_composefont?
+{
+/_pdfComposeFont
+{
+2 copy _pdfComposeFontName not
+{
+2 index
+}
+if
+(pdf) exch _pdfConcatNames
+dup _pdfFontStatus
+{ dup findfont 5 2 roll pop pop pop true}
+{
+4 1 roll
+1 index /CMap pdf_resourcestatus
+{
+pop pop
+true
+}
+{false}
+ifelse
+1 index true exch
+{
+_pdfCIDFontStatus not
+{pop false exit}
+if
+}
+forall
+and
+{
+1 index 1 index 0 get _pdf_CheckCIDSystemInfo
+{
+3 -1 roll pop
+2 index 3 1 roll
+composefont true
+}
+{
+pop pop exch pop false
+}
+ifelse
+}
+{
+_pdfComposeFontName
+{
+dup _pdfFontStatus
+{
+exch pop
+1 index exch
+findfont definefont true
+}
+{
+pop exch pop
+false
+}
+ifelse
+}
+{
+exch pop
+false
+}
+ifelse
+}
+ifelse
+{ true }
+{
+dup _pdfFontStatus
+{ dup findfont true }
+{ pop false }
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+{
+/_pdfComposeFont
+{
+_pdfComposeFontName not
+{
+dup
+}
+if
+dup
+_pdfFontStatus
+{exch pop dup findfont true}
+{
+1 index
+dup type /nametype eq
+{pop}
+{cvn}
+ifelse
+eq
+{pop false}
+{
+dup _pdfFontStatus
+{dup findfont true}
+{pop false}
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+ifelse
+/_pdfStyleDicts 4 dict dup begin
+/Adobe-Japan1 4 dict dup begin
+Level2?
+{
+/Serif
+/HeiseiMin-W3-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiMin-W3}
+{
+/HeiseiMin-W3 _pdfCIDFontStatus
+{/HeiseiMin-W3}
+{/Ryumin-Light}
+ifelse
+}
+ifelse
+def
+/SansSerif
+/HeiseiKakuGo-W5-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiKakuGo-W5}
+{
+/HeiseiKakuGo-W5 _pdfCIDFontStatus
+{/HeiseiKakuGo-W5}
+{/GothicBBB-Medium}
+ifelse
+}
+ifelse
+def
+/HeiseiMaruGo-W4-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiMaruGo-W4}
+{
+/HeiseiMaruGo-W4 _pdfCIDFontStatus
+{/HeiseiMaruGo-W4}
+{
+/Jun101-Light-RKSJ-H _pdfFontStatus
+{ /Jun101-Light }
+{ SansSerif }
+ifelse
+}
+ifelse
+}
+ifelse
+/RoundSansSerif exch def
+/Default Serif def
+}
+{
+/Serif /Ryumin-Light def
+/SansSerif /GothicBBB-Medium def
+{
+(fonts/Jun101-Light-83pv-RKSJ-H) status
+}stopped
+{pop}{
+{ pop pop pop pop /Jun101-Light }
+{ SansSerif }
+ifelse
+/RoundSansSerif exch def
+}ifelse
+/Default Serif def
+}
+ifelse
+end
+def
+/Adobe-Korea1 4 dict dup begin
+/Serif /HYSMyeongJo-Medium def
+/SansSerif /HYGoThic-Medium def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+/Adobe-GB1 4 dict dup begin
+/Serif /STSong-Light def
+/SansSerif /STHeiti-Regular def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+/Adobe-CNS1 4 dict dup begin
+/Serif /MKai-Medium def
+/SansSerif /MHei-Medium def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+end
+def
+/TZzero
+{
+/_wmode xdd
+/_styleArr xdd
+/_regOrdering xdd
+3 copy
+_pdfComposeFont
+{
+5 2 roll pop pop pop
+}
+{
+[
+0 1 _styleArr length 1 sub
+{
+_styleArr exch get
+_pdfStyleDicts _regOrdering 2 copy known
+{
+get
+exch 2 copy known not
+{ pop /Default }
+if
+get
+}
+{
+pop pop pop /Unknown
+}
+ifelse
+}
+for
+]
+exch pop
+2 index 3 1 roll
+_pdfComposeFont
+{3 -1 roll pop}
+{
+findfont dup /FontName get exch
+}
+ifelse
+}
+ifelse
+dup /WMode 2 copy known
+{ get _wmode ne }
+{ pop pop _wmode 1 eq}
+ifelse
+{
+exch _wmode _pdfConcatNames
+dup _pdfFontStatus
+{ exch pop dup findfont false}
+{ exch true }
+ifelse
+}
+{
+dup /FontType get 0 ne
+}
+ifelse
+{
+dup /FontType get 3 eq _wmode 1 eq and
+{
+_pdfVerticalRomanT3Font dup length 10 add dict copy
+begin
+/_basefont exch
+dup length 3 add dict
+begin
+{1 index /FID ne {def}{pop pop} ifelse }
+forall
+/Encoding Encoding dup length array copy
+dup 16#27 /quotesingle put
+dup 16#60 /grave put
+_regOrdering /Adobe-Japan1 eq
+{dup 16#5c /yen put dup 16#a5 /yen put dup 16#b4 /yen put}
+if
+def
+FontName
+currentdict
+end
+definefont
+def
+/Encoding _basefont /Encoding get def
+/_fauxfont true def
+}
+{
+dup length 3 add dict
+begin
+{1 index /FID ne {def}{pop pop} ifelse }
+forall
+FontType 0 ne
+{
+/Encoding Encoding dup length array copy
+dup 16#27 /quotesingle put
+dup 16#60 /grave put
+_regOrdering /Adobe-Japan1 eq
+{dup 16#5c /yen put}
+if
+def
+/_fauxfont true def
+} if
+} ifelse
+/WMode _wmode def
+dup dup /FontName exch def
+currentdict
+end
+definefont pop
+}
+{
+pop
+}
+ifelse
+/_pdf_FontDirectory 3 1 roll _safeput
+}
+bd
+Level2?
+{
+/Tf {
+_pdf_FontDirectory 2 index 2 copy known
+{get exch 3 -1 roll pop}
+{pop pop}
+ifelse
+selectfont
+} bd
+}
+{
+/Tf {
+_pdf_FontDirectory 2 index 2 copy known
+{get exch 3 -1 roll pop}
+{pop pop}
+ifelse
+exch findfont exch
+dup type /arraytype eq
+{makefont}
+{scalefont}
+ifelse
+setfont
+} bd
+}
+ifelse
+/cshow where
+{
+pop /pdf_cshow /cshow load dd
+/pdf_remove2 {pop pop} dd
+}
+{
+/pdf_cshow {exch forall} dd
+/pdf_remove2 {} dd
+} ifelse
+/pdf_xshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+_pdf_x _pdf_y moveto
+0
+rmoveto
+}
+ifelse
+_pdf_i 1 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdf_yshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+_pdf_x _pdf_y moveto
+0 exch
+rmoveto
+}
+ifelse
+_pdf_i 1 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdf_xyshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+{_pdf_na _pdf_i 1 add get} stopped
+{ pop pop pop}
+{
+_pdf_x _pdf_y moveto
+rmoveto
+}
+ifelse
+}
+ifelse
+_pdf_i 2 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdfl1xs {/_pdf_showproc /show load dd pdf_xshow} bd
+/pdfl1ys {/_pdf_showproc /show load dd pdf_yshow} bd
+/pdfl1xys {/_pdf_showproc /show load dd pdf_xyshow} bd
+Level2? _ColorSep5044? not and
+{
+/pdfxs {{xshow} stopped {pdfl1xs} if} bd
+/pdfys {{yshow} stopped {pdfl1ys} if} bd
+/pdfxys {{xyshow} stopped {pdfl1xys} if} bd
+}
+{
+/pdfxs /pdfl1xs load dd
+/pdfys /pdfl1ys load dd
+/pdfxys /pdfl1xys load dd
+} ifelse
+/pdf_charpath {false charpath} bd
+/pdf_xcharpath {/_pdf_showproc /pdf_charpath load dd pdf_xshow} bd
+/pdf_ycharpath {/_pdf_showproc /pdf_charpath load dd pdf_yshow} bd
+/pdf_xycharpath {/_pdf_showproc /pdf_charpath load dd pdf_xyshow} bd
+/pdf_strokepath
+{
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 false charpath
+currentpoint S moveto
+} bind
+exch pdf_cshow
+} bd
+/pdf_xstrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_xshow} bd
+/pdf_ystrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_yshow} bd
+/pdf_xystrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_xyshow} bd
+Level2? {currentglobal true setglobal} if
+/d0/setcharwidth ld
+/nND {{/.notdef} repeat} bd
+/T3Defs {
+/BuildChar
+{
+1 index /Encoding get exch get
+1 index /BuildGlyph get exec
+}
+def
+/BuildGlyph {
+exch begin
+GlyphProcs exch get exec
+end
+} def
+/_pdfT3Font true def
+} bd
+/_pdfBoldRomanWidthProc
+{
+stringwidth 1 index 0 ne { exch .03 add exch }if setcharwidth
+0 0
+} bd
+/_pdfType0WidthProc
+{
+dup stringwidth 0 0 moveto
+2 index true charpath pathbbox
+0 -1
+7 index 2 div .88
+setcachedevice2
+pop
+0 0
+} bd
+/_pdfType0WMode1WidthProc
+{
+dup stringwidth
+pop 2 div neg -0.88
+2 copy
+moveto
+0 -1
+5 -1 roll true charpath pathbbox
+setcachedevice
+} bd
+/_pdfBoldBaseFont
+11 dict begin
+/FontType 3 def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/Encoding cHexEncoding def
+/_setwidthProc /_pdfBoldRomanWidthProc load def
+/_bcstr1 1 string def
+/BuildChar
+{
+exch begin
+_basefont setfont
+_bcstr1 dup 0 4 -1 roll put
+dup
+_setwidthProc
+3 copy
+moveto
+show
+_basefonto setfont
+moveto
+show
+end
+}bd
+currentdict
+end
+def
+pdf_has_composefont?
+{
+/_pdfBoldBaseCIDFont
+11 dict begin
+/CIDFontType 1 def
+/CIDFontName /_pdfBoldBaseCIDFont def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/_setwidthProc /_pdfType0WidthProc load def
+/_bcstr2 2 string def
+/BuildGlyph
+{
+exch begin
+_basefont setfont
+_bcstr2 1 2 index 256 mod put
+_bcstr2 0 3 -1 roll 256 idiv put
+_bcstr2 dup _setwidthProc
+3 copy
+moveto
+show
+_basefonto setfont
+moveto
+show
+end
+}bd
+currentdict
+end
+def
+/_pdfDefineIdentity-H
+{
+/Identity-H /CMap PDFText /pdf_resourcestatus get exec
+{
+pop pop
+}
+{
+/CIDInit/ProcSet findresource begin 12 dict begin
+begincmap
+/CIDSystemInfo
+3 dict begin
+/Registry (Adobe) def
+/Ordering (Identity) def
+/Supplement 0 def
+currentdict
+end
+def
+/CMapName /Identity-H def
+/CMapVersion 1 def
+/CMapType 1 def
+1 begincodespacerange
+<0000> <ffff>
+endcodespacerange
+1 begincidrange
+<0000> <ffff> 0
+endcidrange
+endcmap
+CMapName currentdict/CMap defineresource pop
+end
+end
+} ifelse
+} def
+} if
+/_pdfVerticalRomanT3Font
+10 dict begin
+/FontType 3 def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/_bcstr1 1 string def
+/BuildChar
+{
+exch begin
+_basefont setfont
+_bcstr1 dup 0 4 -1 roll put
+dup
+_pdfType0WidthProc
+moveto
+show
+end
+}bd
+currentdict
+end
+def
+Level2? {setglobal} if
+/MakeBoldFont
+{
+dup /ct_SyntheticBold known
+{
+dup length 3 add dict begin
+CopyFont
+/ct_StrokeWidth .03 0 FontMatrix idtransform pop def
+/ct_SyntheticBold true def
+currentdict
+end
+definefont
+}
+{
+dup dup length 3 add dict
+begin
+CopyFont
+/PaintType 2 def
+/StrokeWidth .03 0 FontMatrix idtransform pop def
+/dummybold currentdict
+end
+definefont
+dup /FontType get dup 9 ge exch 11 le and
+{
+_pdfBoldBaseCIDFont
+dup length 3 add dict copy begin
+dup /CIDSystemInfo get /CIDSystemInfo exch def
+/_Type0Identity /Identity-H 3 -1 roll [ exch ] composefont
+/_basefont exch def
+/_Type0Identity /Identity-H 3 -1 roll [ exch ] composefont
+/_basefonto exch def
+currentdict
+end
+/CIDFont defineresource
+}
+{
+_pdfBoldBaseFont
+dup length 3 add dict copy begin
+/_basefont exch def
+/_basefonto exch def
+currentdict
+end
+definefont
+}
+ifelse
+}
+ifelse
+} bd
+/MakeBold {
+1 index
+_pdf_FontDirectory 2 index 2 copy known
+{get}
+{exch pop}
+ifelse
+findfont
+dup
+/FontType get 0 eq
+{
+dup /WMode known {dup /WMode get 1 eq }{false} ifelse
+version length 4 ge
+and
+{version 0 4 getinterval cvi 2015 ge }
+{true}
+ifelse
+{/_pdfType0WidthProc}
+{/_pdfType0WMode1WidthProc}
+ifelse
+_pdfBoldBaseFont /_setwidthProc 3 -1 roll load put
+{MakeBoldFont} Type0CopyFont definefont
+}
+{
+dup /_fauxfont known not 1 index /SubstMaster known not and
+{
+_pdfBoldBaseFont /_setwidthProc /_pdfBoldRomanWidthProc load put
+MakeBoldFont
+}
+{
+2 index 2 index eq
+{ exch pop }
+{
+dup length dict begin
+CopyFont
+currentdict
+end
+definefont
+}
+ifelse
+}
+ifelse
+}
+ifelse
+pop pop
+dup /dummybold ne
+{/_pdf_FontDirectory exch dup _safeput }
+{ pop }
+ifelse
+}bd
+/MakeItalic {
+_pdf_FontDirectory exch 2 copy known
+{get}
+{exch pop}
+ifelse
+dup findfont
+dup /FontInfo 2 copy known
+{
+get
+/ItalicAngle 2 copy known
+{get 0 eq }
+{ pop pop true}
+ifelse
+}
+{ pop pop true}
+ifelse
+{
+exch pop
+dup /FontType get 0 eq Level2? not and
+{ dup /FMapType get 6 eq }
+{ false }
+ifelse
+{
+dup /WMode 2 copy known
+{
+get 1 eq
+{ _italMtx_WMode1Type0 }
+{ _italMtxType0 }
+ifelse
+}
+{ pop pop _italMtxType0 }
+ifelse
+}
+{
+dup /WMode 2 copy known
+{
+get 1 eq
+{ _italMtx_WMode1 }
+{ _italMtx }
+ifelse
+}
+{ pop pop _italMtx }
+ifelse
+}
+ifelse
+makefont
+dup /FontType get 42 eq Level2? not or
+{
+dup length dict begin
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diff --git a/Examples/MeshGenToolbox/doc/mgApp.tex b/Examples/MeshGenToolbox/doc/mgApp.tex
new file mode 100644
index 0000000000000000000000000000000000000000..2830a3ff78503bb2c82557420d47b0bd90d985ce
--- /dev/null
+++ b/Examples/MeshGenToolbox/doc/mgApp.tex
@@ -0,0 +1,435 @@
+\documentclass[12pt,titlepage]{article}
+
+\include{Preamble}
+
+\author{Wen Yu}
+
+\begin{document}
+
+\begin{titlepage}
+
+% Fonts for the title page
+\newcommand{\texttl}{\textsf} %font for the title (Emil's version is \textsf)
+\newcommand{\textau}{\textsf} %font for the authors, date, etc. (Emils version is \textsc)
+
+\begin{center}
+
+\HRule \\[0.4cm]
+{ \huge \bfseries \texttl{Module Guide for a Parallel Mesh Generation Toolbox}}\\[0.4cm]
+
+\HRule \\[2cm]
+
+\textau{\LARGE Wen Yu}\\[2cm]
+
+\textau{\LARGE {September 2008}}
+
+\vfill
+
+% Bottom of the page
+%\includegraphics[width=0.27\textwidth]{logo.pdf}
+\hfill
+\textau{\LARGE
+\raisebox{2pt}{\begin{tabular}[b]{r}
+\raisebox{8pt}{Computing and Software} \\
+McMaster University \end{tabular}}
+}
+\end{center}
+
+\end{titlepage}
+
+\tableofcontents
+
+\newpage
+\section{Introduction}
+Decomposing a system into modules is a commonly accepted approach to developing software. A module is a work assignment for a programmer or programming team. The basic principle of the decomposition used here is the information hiding principle \citep{Parnas1984}. According to \citet{Parnas1984},
+\begin{itemize}
+\item System details that are likely to change independently should be the secrets of separate modules.
+\item Each data structure is used in only one module.
+\item Any other program that requires information stored in a module's data structures must obtain it by calling access programs belonging to that module.
+\end{itemize}
+
+After completing the first stage of the design, the Software Requirements Specification (SRS), the Module Guide (MG) for the PMGT was developed. The MG specifies the modular structure of the system and is intended to allow both designers and maintainers to easily identify the parts of the software.
+The potential readers of this document are as follows:
+\begin{itemize}
+\item New project members: This document can be a guide for a new project member to easily understand the overall structure of the PMGT and quickly find the relevant modules they are searching for.
+\item Maintainers: The hierarchical structure of the module guide improves the maintainers' understanding when they need to make changes to the system. It is important for a maintainer to update the relevant sections of the document after changes have been made.
+\item Designers: Once the module guide has been written, it is can be used to check for consistency, feasibility and flexibility. Designers can verify the system in various ways, such as consistency among modules, feasibility of the decomposition, and flexibility of the design.
+\end{itemize}
+
+The rest of the document is organized as described in the following. Section \ref{AmgSecChange} lists the anticipated and unlikely changes of the software requirements. Section \ref{AmgSecMH} summarizes the module decomposition that was constructed according to the likely changes. Section \ref{AmgSecConnection} specifies the connections between the software requirements and the modules. Section \ref{AmgSecMD} gives a detailed description of the modules. Section \ref{AmgSecTM} includes two traceability matrices. One checks the completeness of the design against the requirements provided in the SRS. The other shows the relation between anticipated changes and the modules. Section \ref{AmgSecUse} describes the use relation between modules.
+
+\section{Anticipated and Unlikely Changes \label{AmgSecChange}}
+This section lists possible changes to the system. According to the likeliness of the change, the possible changes are classified into two categories. Anticipated changes are listed in Section \ref{AmgSecAchange}, and unlikely changes are listed in Section \ref{AmgSecUchange}.
+
+\subsection{Anticipated Changes \label{AmgSecAchange}}
+Anticipated changes are the source of the information that is to be hidden inside the modules. Ideally, changing one of the anticipated changes will only require changing the one module that hides the associated decision. The approach adapted here is called design for change. %Anticipated changes are numbered by \textbf{AC} followed by a number.
+\begin{description}
+\item[\refstepcounter{acnum} \actheacnum \label{acMemory}:] The data structure and algorithms for implementing the virtual memory of the system.
+\item[\refstepcounter{acnum} \actheacnum \label{acFile}:] The data structure and algorithms for implementing the interface between the file and the system.
+\item[\refstepcounter{acnum} \actheacnum \label{acKeyboard}:]The data structure and algorithms for implementing the interface between the keyboard and the system.
+\item[\refstepcounter{acnum} \actheacnum \label{acScreen}:] The data structure and algorithms for screen display.
+\item[\refstepcounter{acnum} \actheacnum \label{acInput}:] The format and structure of the initial input mesh.
+\item[\refstepcounter{acnum} \actheacnum \label{acOutput}:] The format and structure of the output mesh.
+\item[\refstepcounter{acnum} \actheacnum \label{acValid}:] The mechanisms for validating the input and output meshes.
+\item[\refstepcounter{acnum} \actheacnum \label{acVertex}:] The data structure of a vertex.
+\item[\refstepcounter{acnum} \actheacnum \label{acEdge}:] The data structure of an edge.
+\item[\refstepcounter{acnum} \actheacnum \label{acCell}:] The data structure of a cell.
+\item[\refstepcounter{acnum} \actheacnum \label{acMesh}:] The data structure of a mesh.
+\item[\refstepcounter{acnum} \actheacnum \label{acRefining}:] The algorithms for refining a mesh.
+\item[\refstepcounter{acnum} \actheacnum \label{acCoarsening}:] The algorithms for coarsening a mesh.
+\item[\refstepcounter{acnum} \actheacnum \label{acTriangle}:] The shape of a cell, which is initially assumed to be a triangular.
+\end{description}
+
+\subsection{Unlikely Changes \label{AmgSecUchange}}
+The module design should be as general as possible. However, a general system is more complex. Sometimes this complexity is not necessary. Fixing some design decisions at the system architecture stage can simplify the software design. If these decision should later need to be changed, then many parts of the design will potentially need to be modified. Hence, it is not intended that these decisions will be changed.
+\begin{description}
+\item[\refstepcounter{ucnum} \uctheucnum \label{ucIO}:] Input/Output devices (Input: File and/or Keyboard, Output: File, Memory, and/or Screen).
+\item[\refstepcounter{ucnum} \uctheucnum \label{ucInput}:] There will always be a source of input data external to the PMGT software.
+\item[\refstepcounter{ucnum} \uctheucnum \label{ucOutput}:] Output data are displayed to the output device.
+\item[\refstepcounter{ucnum} \uctheucnum \label{ucGoal}:] The goal of the system is refining or coarsening a mesh.
+\item[\refstepcounter{ucnum} \uctheucnum \label{ucMeshType}:] The type of the mesh is unstructured.
+\item[\refstepcounter{ucnum} \uctheucnum \label{ucEdge}:] The representation of an edge is a set of vertices.
+\item[\refstepcounter{ucnum} \uctheucnum \label{ucCell}:] The representation of a cell is a set of vertices.
+\item[\refstepcounter{ucnum} \uctheucnum \label{ucCoordinate}:] A Cartesian coordinate system is used.
+\end{description}
+
+\section{Module Hierarchy \label{AmgSecMH}}
+
+This section provides an overview of the module design. Modules are summarized in a hierarchy decomposed by secrets in Table \ref{AmgMH}. The modules listed below, which are leaves in the hierarchy tree, are the modules that will actually be implemented.
+\begin{description}
+\item [\refstepcounter{mnum} \mthemnum \label{mMemory}:] Virtual Memory Module
+\item [\refstepcounter{mnum} \mthemnum \label{mFileRW}:] File Read/Write Module
+\item [\refstepcounter{mnum} \mthemnum \label{mKeyboard}:] Keyboard Input Module
+\item [\refstepcounter{mnum} \mthemnum \label{mScreen}:] Screen Display Module
+\item [\refstepcounter{mnum} \mthemnum \label{mInput}:] Input Format Module
+\item [\refstepcounter{mnum} \mthemnum \label{mOutput}:] Output Format Module
+\item [\refstepcounter{mnum} \mthemnum \label{mService}:] Service Module
+\item [\refstepcounter{mnum} \mthemnum \label{mVertex}:] Vertex Module
+\item [\refstepcounter{mnum} \mthemnum \label{mEdge}:] Edge Module
+\item [\refstepcounter{mnum} \mthemnum \label{mCell}:] Cell Module
+\item [\refstepcounter{mnum} \mthemnum \label{mMesh}:] Mesh Module
+\item [\refstepcounter{mnum} \mthemnum \label{mRefining}:] Refining Module
+\item [\refstepcounter{mnum} \mthemnum \label{mCoarsening}:] Coarsening Module
+\end{description}
+Note that \mref{mMemory}, \mref{mFileRW}, \mref{mKeyboard} and \mref{mScreen} are commonly used modules and are already implemented by the operating system. They will not need to be implemented again for PMGT.
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{p{0.15\textwidth}|p{0.25\textwidth}|p{0.25\textwidth}|p{0.2\textwidth}}
+\hline
+\textbf{Level 1} & \textbf{Level 2} & \textbf{Level 3} & \textbf{Level 4} \\ \hline
+
+\multirow{4}{0.15\textwidth}{Hardware-Hiding Module}
+& \multirow{2}{0.25\textwidth}{Extended Computer Module} & Virtual Memory Module& \\ \cline{3-3}
+& & File Read/Write Module & \\ \cline{2-3}
+& \multirow{2}{0.25\textwidth}{Device Interface Module} & Keyboard Input Module & \\\cline{3-3}
+& & Screen Display Module & \\\hline
+
+\multirow{3}{0.15\textwidth}{Behavior-Hiding Module} & Input Format Module & &\\ \cline{2-2}
+& Output Format Module & &\\ \cline{2-2}
+& Service Module & &\\\hline
+
+\multirow{5}{0.15\textwidth}{Software Decision Module}
+& \multirow{4}{0.25\textwidth}{Mesh Data Module} &
+\multirow{3}{0.25\textwidth}{Entity Module} & Vertex Module \\ \cline{4-4}
+& & & Edge Module \\ \cline{4-4}
+& & & Cell Module \\ \cline{3-4}
+& & Mesh Module & \\ \cline{2-4}
+& \multirow {2}{0.25\textwidth}{Algorithm Module} & Refining Module & \\ \cline{3-3}
+& & Coarsening Module & \\ \hline
+
+\end{tabular}
+\caption{Module Hierarchy}
+\label{AmgMH}
+\end{table}
+
+\section{Connection Between Requirements and Design \label{AmgSecConnection}}
+The design of the system is intended to satisfy the requirements developed in the SRS. In this stage, the system is decomposed into modules. The connection between requirements and modules is listed in Table \ref{AmgRT}. However, some connections are not obvious. The explanation below has the purpose of making these connections clear. The software requirements are documented in the SRS. They are also listed starting on page \pageref{pagereq} for convenience.
+
+The functionalities of refining a mesh (\fref{RefiningMesh}), and coarsening a mesh (\fref{CoarseningMesh}) are achieved directly by \mref{mRefining} and \mref{mCoarsening}, respectively. The functional requirement {\em MeshType} (\fref{MeshType}) is related to the representation of mesh, which is contained in \mref{mEdge}, \mref{mCell}, and \mref{mMesh}. The algorithms for refining (\mref{mRefining}) and coarsening (\mref{mCoarsening}) also depend on the {\em MeshType} requirement. Another connection worth mentioning relates to the \emph{DomainDimension} requirement (\fref{DomainDimension}). All geometric information for the mesh, including dimension information, is stored in \mref{mVertex}. Algorithms in \mref{mRefining} and \mref{mCoarsening} also relate to the dimension of the domain.
+
+Some nonfunctional requirements, such as \emph{Performance} (\nref{Performance}) and \emph{Maintainability} (\nref{Maintainability}), are related to the overall quality of the system. These qualities depend on the implementation of all of the modules. The \emph{Precision} requirement depends on modules related to calculation, which are the module \mref{mVertex}, \mref{mEdge}, \mref{mCell}, \mref{mMesh}, \mref{mRefining} and \mref{mCoarsening}.
+
+\section{Module Decomposition \label{AmgSecMD}}
+Modules are decomposed according to the principle of ``information hiding'' proposed by \citet{Parnas1984}. The \emph{Secrets} field in a module decomposition is a brief statement of the design decision hidden by the module. The \emph{Services} field specifies \emph{what} the module will do without documenting \emph{how} to do it. For each module, a suggestion for the implementing software is given under the \emph{Implemented By} title. If the entry is \emph{OS}, this means that the module is provided by the operating system or by standard programming language libraries. \emph{PMGT} means the module will be implemented by the PMGT software. Only leaf modules in the hierarchy have to be implemented. If a dash (\emph{--}) is shown, this means that the module is not a leaf and will not have to be implemented. Whether or not this module is implemented depends on the programming language selected. This decomposition is inspired by \citet{Chen2003}. The decomposition of the mesh data module is partly based on \citet{ElSheikh2004}. One difference between the current design and \citet{ElSheikh2004} is that \citet{ElSheikh2004} has an explicit module for incidence and adjacency information. However, it is believed that where and how to store this information is an implementation decision that should be abstracted away at the design stage.
+
+\subsection{Hardware-Hiding Module}
+\begin{description}
+\item[Secrets:]The data structure and algorithm used to implement the virtual hardware.
+\item[Services:]Serves as a virtual hardware used by the rest of the system. This module provides the interface between the hardware and the software. So, the system can use it to display outputs or to accept inputs.
+\item[Implemented By:] --
+\end{description}
+
+\subsubsection{Extended Computer Module}
+\begin{description}
+\item[Secrets:]The number of processors, the instruction set of the computer, and the computer's capacity for performing concurrent operations.
+\item[Services:]Provides an instruction set including the operations on application-independent data types, sequence control operations, and general I/O operations.
+\item[Implemented By:] --
+\end{description}
+
+\paragraph{Virtual Memory Module (\mref{mMemory})}
+\begin{description}
+\item[Secrets:]The hardware addressing methods for data and instructions in real memory.
+\item[Services:]Presents a uniformly addressable virtual memory.
+\item[Implemented By:] OS
+\end{description}
+
+\paragraph{File Read Write Module (\mref{mFileRW})}
+\begin{description}
+\item[Secrets:]The data structure and algorithms for implementing the interface between the file and the system.
+\item[Services:]Provides an interface between the storage of the system and the IO devices.
+\item[Implemented By:] OS
+\end{description}
+
+\subsubsection{Device Interface Module}
+\begin{description}
+\item[Secrets:]Characteristics of the present devices not likely to be shared by replacement devices.
+\item[Services:]Provides virtual devices to be used by the rest of software.
+\item[Implemented By:] --
+\end{description}
+
+\paragraph{Keyboard Input Module (\mref{mKeyboard})}
+\begin{description}
+\item[Secrets:]The data structure and algorithms for implementing the interface between the keyboard and the system.
+\item[Services:]Retrieves the user inputs from the keyboard and communicates the information with other parts of the system.
+\item[Implemented By:] OS
+\end{description}
+
+\paragraph{Screen Display Module (\mref{mScreen})}
+\begin{description}
+\item[Secrets:]The data structure and algorithms to display graphics and text on the screen.
+\item[Services:]Provides an interface between the system and the screen so the system can display information on the screen through the use of programs in the module.
+\item[Implemented By:] OS
+\end{description}
+
+
+\subsection{Behavior-Hiding Module}
+\begin{description}
+\item[Secrets:]The contents of the required behaviors.
+\item[Services:]Includes programs that provide externally visible behavior of the system as specified in the software requirements specification (SRS) documents. This module serves as a communication layer between the hardware-hiding module and the software decision module. The programs in this module will need to change if there are changes in the SRS.
+\item[Implemented By:] --
+\end{description}
+
+\subsubsection{Input Format Module (\mref{mInput})}
+\begin{description}
+\item[Secrets:]The format and structure of the initial input mesh.
+\item[Services:]Converts the input mesh to the data structured used in PMGT.
+\item[Implemented By:] PMGT
+\end{description}
+
+\subsubsection{Output Format Module (\mref{mOutput})}
+\begin{description}
+\item[Secrets:] The format and structure of the output mesh.
+\item[Services:] Converts the output mesh to an output file.
+\item[Implemented By:] PMGT
+\end{description}
+
+\subsubsection{Service Module (\mref{mService})}
+\begin{description}
+\item[Secrets:] The algorithm for validating meshes.
+\item[Services:] Checks if the input and output meshes are valid.
+\item[Implemented By:] PMGT
+\end{description}
+
+\subsection{Software Decision Module}
+\begin{description}
+\item[Secrets:] The design decision based on mathematical theorems, physical facts, or programming considerations. The secrets of this module are \emph{not} described in the SRS.
+\item[Services:] Includes data structure and algorithms used in the system that do not provide direct interaction with the user. %Changes in these modules are more likely to be motivated by a desire to improve performance than by externally imposed changes.
+\item[Implemented By:] --
+\end{description}
+
+\subsubsection{Entity Module}
+\begin{description}
+\item[Secrets:] The data structure of a mesh entity, including vertex, edge, and cell.
+\item[Services:] Stores the complete mesh information generated, and also provides programs to import and export the mesh information.
+\item[Implemented By:] --
+\end{description}
+
+\paragraph{Vertex Module (\mref{mVertex})}
+\begin{description}
+\item[Secrets:] The data structure of a vertex.
+\item[Services:] Stores the complete vertex information generated and provides programs to import and export the vertex information. The operations on vertices are also included in this module.
+\item[Implemented By:] PMGT
+\end{description}
+
+\paragraph{Edge Module (\mref{mEdge})}
+\begin{description}
+\item[Secrets:] The data structure of an edge.
+\item[Services:] Stores the complete edge information generated and provides programs to import and export the edge information. The operations on edges are also included in this module.
+\item[Implemented By:] PMGT
+\end{description}
+
+\paragraph{Cell Module (\mref{mCell})}
+\begin{description}
+\item[Secrets:] The data structure of a cell.
+\item[Services:] Stores the complete cell information generated and provides programs to import and export the cell information. The operations on cells are also included in this module.
+\item[Implemented By:] PMGT
+\end{description}
+
+\paragraph{Mesh Module (\mref{mMesh})}
+\begin{description}
+\item[Secrets:] The data structure of a mesh.
+\item[Services:] Stores the complete mesh information generated and provides programs to import and export the cell information. The operations on meshes are also included in this module.
+\item[Implemented By:] PMGT
+\end{description}
+
+\subsubsection{Mesh Algorithm Module}
+\begin{description}
+\item[Secrets:] Algorithms for refining and coarsening a mesh.
+\item[Services:] Refining and coarsening a mesh.
+\item[Implemented By:]--
+\end{description}
+
+\paragraph{Refining Module (\mref{mRefining})}
+\begin{description}
+\item[Secrets:] Algorithms for refining a mesh.
+\item[Services:] Refining a mesh.
+\item[Implemented By:] MPGT
+\end{description}
+
+\paragraph{Coarsening Module (\mref{mCoarsening})}
+\begin{description}
+\item[Secrets:] Algorithms for coarsening a mesh.
+\item[Services:] Coarsening a mesh.
+\item[Implemented By:] MPGT
+\end{description}
+
+\section{Traceability Matrix \label{AmgSecTM}}
+A traceability matrix can be used for checking the completeness of the current design. In this section, there are two matrices, the traceability matrix for requirements and the traceability matrix for anticipated changes. The module names and their corresponding numbers are can be found in Section \ref{AmgSecMH}\\
+
+\subsection{Traceability Matrix for Requirements \label{AmgSecRT}}
+The traceability matrix in Table \ref{AmgRT} makes a connection between the modules and the requirements. Modules are listed in the first row and requirements are listed in the first column. If a module, say A, satisfies a requirement, say B, and A is in j-th column and B in i-th row, then there is a check mark \checkmark in the cell of the i-th row and the j-th column. There is a special column ``Doc.'' It represents the documentation of PMGT. the ``Doc'' entry is used to fulfill the requirement {\em Help} (\fref{Help}).
+The names of the requirements and their corresponding numbers are listed below for convenience.
+\begin{description}\label{pagereq}
+\refstepcounter{funnum} \label{RefiningMesh}
+\item[\fref{RefiningMesh}:] RefiningMesh
+\refstepcounter{funnum} \label{CoarseningMesh}
+\item[\fref{CoarseningMesh}:] CoarseningMesh
+\refstepcounter{funnum} \label{RefiningOrCoarsening}
+\item[\fref{RefiningOrCoarsening}:] RefiningOrCoarsening
+\refstepcounter{funnum} \label{MeshType}
+\item[\fref{MeshType}:] MeshType
+\refstepcounter{funnum} \label{ElmShape}
+\item[\fref{ElmShape}:] ElmShape
+\refstepcounter{funnum} \label{DomainDimension}
+\item[\fref{DomainDimension}:] DomainDimension
+\refstepcounter{funnum} \label{Conformal}
+\item[\fref{Conformal}:] Conformal
+\refstepcounter{funnum} \label{InputDefinition}
+\item[\fref{InputDefinition}:] InputDefinition
+\refstepcounter{funnum} \label{RCInstruction}
+\item[\fref{RCInstruction}:] RCInstruction
+\refstepcounter{funnum} \label{OutputStorage}
+\item[\fref{OutputStorage}:] OutputStorage
+\refstepcounter{funnum} \label{VertexUniqueID}
+\item[\fref{VertexUniqueID}:] VertexUniqueID
+\refstepcounter{funnum} \label{ElmUniqueID}
+\item[\fref{ElmUniqueID}:] ElmUniqueID
+\refstepcounter{funnum} \label{ElmTopology}
+\item[\fref{ElmTopology}:] ElmTopology
+\refstepcounter{funnum} \label{OutElmOrder}
+\item[\fref{OutElmOrder}:] OutElmOrder
+\refstepcounter{funnum} \label{OutVertexOrder}
+\item[\fref{OutVertexOrder}:] OutVertexOrder
+\refstepcounter{funnum} \label{Help}
+\item[\fref{Help}:] Help
+\refstepcounter{nfnum} \label{Performance}
+\item[\nref{Performance}:] Performance
+\refstepcounter{nfnum} \label{Precision}
+\item[\nref{Precision}:] Precision
+\refstepcounter{nfnum} \label{Exception}
+\item[\nref{Exception}:] Exception
+\refstepcounter{nfnum} \label{Portability}
+\item[\nref{Portability}:] Portability
+\refstepcounter{nfnum} \label{LookAndFeel}
+\item[\nref{LookAndFeel}:] LookAndFeel
+\refstepcounter{nfnum} \label{Usability}
+\item[\nref{Usability}:] Usability
+\refstepcounter{nfnum} \label{Maintainability}
+\item[\nref{Maintainability}:] Maintainability
+
+\end{description}
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{|p{0.04\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|}
+\hline
+ &\mref{mMemory} & \mref{mFileRW} & \mref{mKeyboard} & \mref{mScreen} & \mref{mInput}&\mref{mOutput}&\mref{mService} & \mref{mVertex} &
+\mref{mEdge} & \mref{mCell} & \mref{mMesh} & \mref{mRefining} & \mref{mCoarsening} & Doc\\
+\hline\hline
+\fref{RefiningMesh}& & & & & & & & & & & & \checkmark & & \\\hline%f2
+\fref{CoarseningMesh}& & & & & & & & & & & & & \checkmark& \\\hline%f3
+\fref{RefiningOrCoarsening}& & & & & & & & & & & & \checkmark & \checkmark& \\\hline%f1
+\fref{MeshType}& & & & & & & & & \checkmark & \checkmark& \checkmark & \checkmark & \checkmark& \\\hline%f4
+\fref{ElmShape}& & & & & & & \checkmark & & & \checkmark & & && \\\hline%f5
+\fref{DomainDimension}& & & & & & & & \checkmark & & & & \checkmark &\checkmark & \\\hline%f6
+\fref{Conformal}& & & & & & & \checkmark & & & & &\checkmark & \checkmark& \\\hline%f7
+\fref{InputDefinition}& & \checkmark & & & \checkmark& & & & & & & & & \\\hline%f11
+\fref{RCInstruction}& & & & & & & & & & & & \checkmark & \checkmark& \\\hline%f12
+\fref{OutputStorage}& \checkmark & \checkmark & & & & \checkmark & & & & & & & & \\\hline%f13
+\fref{VertexUniqueID}& & & & & & \checkmark & & & & & & & & \\\hline%f8
+\fref{ElmUniqueID}& & & & & & \checkmark & & & & & & && \\\hline%f9
+\fref{ElmTopology}& & & & & & \checkmark & & & & & & & & \\\hline%f10
+\fref{OutElmOrder}& & & & && \checkmark & & & & & & & & \\\hline%f14
+\fref{OutVertexOrder}& & & & && \checkmark & & & & & & & & \\\hline%f15
+\fref{Help} & & & & & & & & & & & & & & \checkmark\\\hline%f16
+\nref{Performance} & \checkmark & \checkmark & \checkmark & \checkmark &\checkmark & \checkmark & \checkmark & \checkmark & \checkmark &\checkmark &\checkmark & \checkmark & \checkmark &\\\hline%n1
+\nref{Precision} & & & & &\checkmark & \checkmark& \checkmark & \checkmark & \checkmark &\checkmark & \checkmark& \checkmark &\checkmark &\\\hline%n2
+\nref{Exception} & \checkmark & \checkmark & & & \checkmark& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark& \checkmark& \checkmark & \checkmark &\\\hline%n3
+\nref{Portability} & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & & & & & & & \\\hline%n4
+\nref{LookAndFeel} & & & & &\checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark& \checkmark& \checkmark & \checkmark &\\\hline%n5
+\nref{Usability} & & & \checkmark & \checkmark & \checkmark& \checkmark & \checkmark & \checkmark & \checkmark &\checkmark &\checkmark & \checkmark & &\checkmark\\\hline%n6
+\nref{Maintainability} & \checkmark & \checkmark & \checkmark &\checkmark & \checkmark& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark& \checkmark& \checkmark & \checkmark &\checkmark\\\hline%n7
+\end{tabular}
+\caption{Traceability Matrix: Modules and Requirements}
+\label{AmgRT}
+\end{table}
+
+\subsection{Traceability Matrix for Anticipated Changes \label{AmgSecCT}}
+The traceability matrix in Table \ref{AmgCT} illustrates the relationship between modules and anticipated changes listed in Section \ref{AmgSecChange}. If there is a \checkmark in an entry of the matrix, the change specified in that row is hidden in the module of the corresponding column.
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{|p{0.06\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.025\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|}
+\hline
+& \mref{mMemory} &\mref{mFileRW} & \mref{mKeyboard} & \mref{mScreen} & \mref{mInput}&\mref{mOutput}& \mref{mService} & \mref{mVertex} &
+\mref{mEdge} & \mref{mCell} & \mref{mMesh} & \mref{mRefining} & \mref{mCoarsening} \\
+\hline\hline
+\acref{acMemory} &\checkmark & & & & & & & & & & & & \\\hline
+\acref{acFile} & & \checkmark & & & & & & & & & & & \\\hline
+\acref{acKeyboard} & & & \checkmark & & & & & & & & & & \\\hline
+\acref{acScreen} & & & & \checkmark & & & & & & & & & \\\hline
+\acref{acInput} & & & & & \checkmark & & & & & & & & \\\hline
+\acref{acOutput} & & & & & & \checkmark & & & & & & & \\\hline
+\acref{acValid} & & & & & & & \checkmark & & & & & & \\\hline
+\acref{acVertex} & & & & & & & & \checkmark & & & & & \\\hline
+\acref{acEdge} & & & & & & & & & \checkmark & & & & \\\hline
+\acref{acCell} & & & & && & & & & \checkmark & & & \\\hline
+%\acref{acIncidence} & & & & & & & & & \checkmark & & \\\hline
+%\acref{acAdjacency} & & & & & & & & & \checkmark & & \\\hline
+\acref{acMesh} & & & & & & & & & & & \checkmark & & \\\hline
+\acref{acRefining}& & & && & & & & & & & \checkmark & \\\hline
+\acref{acCoarsening}& & & & & & & & & & & & &\checkmark \\\hline
+\acref{acTriangle}& & & & & & & \checkmark & & & \checkmark & & & \\\hline
+
+\end{tabular}
+\caption{Traceability Matrix: Modules and Anticipated Changes}
+\label{AmgCT}
+\end{table}
+
+
+\section{Use Hierarchy between Modules \label{AmgSecUse}}
+In this section, the uses hierarchy between modules is provided. \citet{Parnas1978} said of two programs A and B that A {\em uses} B if correct execution of B may be necessary for A to complete the task described in its specification. That is, A {\em uses} B if there exist situations in which the correct functioning of A depends upon the availability of a correct implementation of B. Figure \ref{fig:uh} illustrates the use relation between the modules. It can be seen that the graph is a directed acyclic graph (DAG). Each level of the hierarchy offers a testable and usable subset of the system, and modules in the higher level of the hierarchy are essentially simpler because they use modules from the lower levels.
+\begin{figure}[htbp]
+\centering
+\includegraphics[width=0.90\textwidth]{uh.eps}
+\caption{Use Hierarchy among Modules}
+\label{fig:uh}
+\end{figure}
+
+\newpage
+
+\bibliography{WenRef}
+\bibliographystyle{plainnat}
+
+\end{document}
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
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+%%CreationDate: 1991 Aug 20 16:45:46
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
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+%!PS-AdobeFont-1.1: CMSY10 1.0
+%%CreationDate: 1991 Aug 15 07:20:57
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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+/Weight (Medium) readonly def
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+/isFixedPitch false def
+end readonly def
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+readonly def
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+currentdict end
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+cleartomark
+%%EndFont
+%%BeginFont: CMR12
+%!PS-AdobeFont-1.1: CMR12 1.0
+%%CreationDate: 1991 Aug 20 16:38:05
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMR12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMR12 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 6 /Sigma put
+dup 11 /ff put
+dup 12 /fi put
+dup 34 /quotedblright put
+dup 35 /numbersign put
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 43 /plus put
+dup 44 /comma put
+dup 45 /hyphen put
+dup 46 /period put
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+readonly def
+/FontBBox{-34 -251 988 750}readonly def
+/UniqueID 5000794 def
+currentdict end
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+%%CreationDate: 1991 Aug 20 17:33:59
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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+/Weight (Medium) readonly def
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+userdict /end-hook known{end-hook}if
+%%EOF
diff --git a/Examples/MeshGenToolbox/doc/misApp.tex b/Examples/MeshGenToolbox/doc/misApp.tex
new file mode 100644
index 0000000000000000000000000000000000000000..ac76fa35c0cd34806ea1489a7fa7a8a6a2e6503d
--- /dev/null
+++ b/Examples/MeshGenToolbox/doc/misApp.tex
@@ -0,0 +1,771 @@
+\documentclass[12pt,titlepage]{article}
+
+\include{Preamble}
+
+\author{Wen Yu}
+
+\begin{document}
+
+\begin{titlepage}
+
+% Fonts for the title page
+\newcommand{\texttl}{\textsf} %font for the title (Emil's version is \textsf)
+\newcommand{\textau}{\textsf} %font for the authors, date, etc. (Emils version is \textsc)
+
+\begin{center}
+
+\HRule \\[0.4cm]
+{ \huge \bfseries \texttl{Module Interface Specification for a Parallel Mesh Generation Toolbox}}\\[0.4cm]
+
+\HRule \\[2cm]
+
+\textau{\LARGE Wen Yu}\\[2cm]
+
+\textau{\LARGE {September 2008}}
+
+\vfill
+
+% Bottom of the page
+%\includegraphics[width=0.27\textwidth]{logo.pdf}
+\hfill
+\textau{\LARGE
+\raisebox{2pt}{\begin{tabular}[b]{r}
+\raisebox{8pt}{Computing and Software} \\
+McMaster University \end{tabular}}
+}
+\end{center}
+
+\end{titlepage}
+
+\tableofcontents
+
+\newpage
+
+\section{Introduction \label{AmisSecIntro}}
+One of the advantages of decomposing the system into modules is that each module can be developed independently. However, the secret and services of each module does not provide enough information for parallel coding. A document specifying the interface of each module, called the Module Interface Specification (MIS), is needed. An MIS of a particular module is not only used as a guide by the programmers that are responsible for coding this module, but also by programmers that will use this module. An MIS is abstract because it describes \emph{what} the module will do, but not \emph{how} to do it.
+
+This MIS describes the services of the corresponding modules specified in the document ``Module Guide for a Mesh Generator.'' A state machine MIS is used. Note that some of the modules have multiple projections. In this case, variables listed in section \emph{state variables} give the format of all states for all of the created objects. The idea of multiple projection is also used in \citet{Bauer1995}. By using projections, the change of state variables is applicable to the particular object associated with this module. In this system, this particular kind of modules includes the module Vertex, Edge, Cell, and Mesh.
+
+The rest of the document is organized as follows. Section \ref{AmisSecTemplate} describes the MIS template used in this document. Section \ref{AmisSecMD} copies the module hierarchy from \emph{Module Guide} document for convenience. Section \ref{AmisSecV}, Section \ref{AmisSecE}, Section \ref{AmisSecC}, Section \ref{AmisSecM}, Section \ref{AmisSecSer}, Section \ref{AmisSecRef}, Section \ref{AmisSecCoa} give the MISs for the Vertex Module, Edge Module, Cell Module, Mesh Module, Service Module, Refining Module, and Coarsening Module, respectively.
+
+
+\section{Template \label{AmisSecTemplate}}
+This section gives the template used in this document. This template is modified version of the MIS template presented in \citet{Ghezzi2003} and \citet{Hoffman1999}. According to this template, each module is modeled as a finite state machine. It has a set of state variables, inputs, outputs, and transitions. In the case that an exception conditions become true, an exception is raised by the associated access program. If an access program has an output, then \emph{Output} is specified. If an access program changes states variables, a \emph{Transition} is specified. The inputs of the access program are listed as arguments.
+
+The discrete mathematics notation used here follows that introduced by \citet{Gries1993}. This notation is explained in the SRS. A dot notation is used in two cases. One is for referring to a field in a tuple, and the other is for referencing the access program of a module.
+
+The whole template is composed of four parts. First, the name of the module is given. Second, constants, data types, and access programs that are used by this module, but defined outside of this module, are listed. Third, the syntax of the interface is specified. Finally, the semantics of the interface is described. The template is described in the rest of this section.
+
+\subsection{Module Name}
+If ``{\bf (MP)}'' is appended to the name of the module, it means that this module has multiple projections.
+\subsection{Uses}
+This section lists constants, data types, and access programs that are defined outside of this module. The format of each imported item is specified after each header.
+
+\subsubsection{Imported Constants}
+{\bf Uses} $\langle$ \emph{module name} $\rangle$ {\bf Imports} $\langle$ \emph{resource constants list} $\rangle$
+
+\subsubsection{Imported Data Types}
+{\bf Uses} $\langle$ \emph{module name} $\rangle$ {\bf Imports} $\langle$ \emph{resource data type list}$\rangle$
+
+\subsubsection{Imported Access Programs}
+{\bf Uses} $\langle$ \emph{module name} $\rangle$ {\bf Imports} $\langle$ \emph{resource access program list}$\rangle$
+
+\subsection{Interface Syntax}
+This section defines the syntax of the module interface. The interface indicates the services that the module provides. Other modules can only access this module through this interface. Other information inside the module is the secret that it hides from other modules. Changing the internal design of a module will not affect the way that other modules use this module. The format of each exported items is specified after each header.
+
+\subsubsection{Exported Constants}
+ \emph{constant name : type of the constant}
+
+\subsubsection{Exported Data Types}
+ \emph{data type name := structure of the data type}
+
+\subsubsection{Exported Access Programs}
+The exported access programs are listed in the tabular format shown below. In this software, exceptions are handled inside the access routine by displaying error messages and terminating the program.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{|c|c|c|c|}
+\hline
+Routine Name & Input & Output & Exceptions \\
+\hline
+\end{tabular}
+\end{table}
+
+\subsection{Interface Semantics}
+The semantics of the interface is introduced in this section. The components of this section include state variables, state invariants, access program semantics, \emph{etc}.
+\subsubsection{State Variables}
+This section lists the state variables in the format of \emph{variable name}: \emph{type}
+\subsubsection{Assumption}
+Any assumption about this module are specified here.
+\subsubsection{Invariant}
+Predicates that should always hold before and after each access routine in the module.
+\subsubsection{Access Program Semantics} This section includes possible exceptions, possible outputs, and possible transitions. The contents of this section should be as formal as possible. When necessary and appropriate, an English explanation is included to help readers understand the meaning of some the mathematical notations.
+\subsubsection{Local Functions} Functions used to facilitate the expression of the interface semantics.
+\subsubsection{Local Data Types} Data types used to facilitate the expression of the interface semantics.
+\subsubsection{Local Constants} Constants used to facilitate the expression of interface semantics.
+\subsubsection{Considerations} Other issues related to the MIS of this module, but not covered in the other parts of the document.
+
+\section{Module Decomposition \label{AmisSecMD}}
+\begin{table}[ht]
+\centering
+\begin{tabular}{p{0.15\textwidth}|p{0.25\textwidth}|p{0.25\textwidth}|p{0.2\textwidth}}
+\hline
+\textbf{Level 1} & \textbf{Level 2} & \textbf{Level 3} & \textbf{Level 4} \\ \hline
+
+\multirow{4}{0.15\textwidth}{Hardware-Hiding Module}
+& \multirow{2}{0.25\textwidth}{Extended Computer Module} & Virtual Memory Module& \\ \cline{3-3}
+& & File Read/Write Module & \\ \cline{2-3}
+& \multirow{2}{0.25\textwidth}{Device Interface Module} & Keyboard Input Module & \\\cline{3-3}
+& & Screen Display Module & \\\hline
+
+\multirow{3}{0.15\textwidth}{Behavior-Hiding Module} & Input Format Module & &\\ \cline{2-2}
+& Output Format Module & &\\ \cline{2-2}
+& Service Module & &\\\hline
+
+\multirow{5}{0.15\textwidth}{Software Decision Module}
+& \multirow{4}{0.25\textwidth}{Mesh Data Module} &
+\multirow{3}{0.25\textwidth}{Entity Module} & Vertex Module \\ \cline{4-4}
+& & & Edge Module \\ \cline{4-4}
+& & & Cell Module \\ \cline{3-4}
+& & Mesh Module & \\ \cline{2-4}
+& \multirow {2}{0.25\textwidth}{Algorithm Module} & Refining Module & \\ \cline{3-3}
+& & Coarsening Module & \\ \hline
+
+\end{tabular}
+\caption{Module Hierarchy}
+\label{AmisMH}
+\end{table}
+
+PMGT is decomposited into the modules listed in Table \ref{AmisMH}. Note that only the leaf modules are implemented. The \emph{Virtual Memory Module}, \emph{File Read/Write Module}, \emph{Keyboard Input Module}, and \emph{Screen Display Module} are implemented by the operating system and programming language libraries. More information on the modular decomposition of the PMGT can be found in the MG document.
+
+
+\section{MIS of Vertex Module \label{AmisSecV}}
+
+\subsection{Module Name: Vertex (MP)}
+
+\subsection{Uses}
+\subsubsection{Imported Constants} None
+\subsubsection{Imported Data Types} None
+\subsubsection{Imported Access Programs}None
+
+\subsection{Interface Syntax}
+\subsubsection{Exported constants} None
+\subsubsection{Exported Data Types}
+{\tt VertexT} := tuple of ($x: \mathbb{R},\ y: \mathbb{R}$)
+\subsubsection{Exported Access Programs}
+The exported access programs for the vertex module are listed in Table \ref{AmisVEAP}.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{|c|c|c|c|}
+\hline
+Routine Name & Input & Output & Exceptions \\
+\hline
+initVertex & $\mathbb{R}$, $\mathbb{R}$ & & \\
+\hline
+getVertex & & {\tt VertexT} & \\
+\hline
+\end{tabular}
+\caption{Exported Access Programs of the Vertex Module}
+\label{AmisVEAP}
+\end{table}
+
+\subsection{Interface Semantics}
+\subsubsection{State Variables}
+$x: \mathbb{R}$\\
+$y: \mathbb{R}$
+\subsubsection{Invariant} None
+\subsubsection{Assumptions}initVertex() is called before any other access routine.
+\subsubsection{Access Program Semantics}
+\paragraph{initVertex($x1: \mathbb{R}, \ y1: \mathbb{R}$)}
+\begin{itemize}
+\item \textbf{Transition}\\
+$x := x1$ \\
+$y := y1$
+\end{itemize}
+
+\paragraph{getVertex()}
+\begin{itemize}
+\item \textbf{Output}\\ $( x, y)$
+\end{itemize}
+
+\subsubsection{Local Functions} None
+\subsubsection{Local Data Types} None
+\subsubsection{Local Constants} None
+\subsubsection{Considerations} None
+
+
+\section{MIS of Edge Module \label{AmisSecE}}
+
+\subsection{Module Name: Edge (MP)}
+
+\subsection{Uses}
+\subsubsection{Imported Constants} None
+\subsubsection{Imported Data Types}
+{\bf Uses} \emph{Vertex Module} {\bf Imports} \texttt{VertexT}
+\subsubsection{Imported Access Programs}None
+
+\subsection{Interface Syntax}
+\subsubsection{Exported constants} None
+\subsubsection{Exported Data Types}
+{\tt EdgeT} := set of {\tt VertexT}
+\subsubsection{Exported Access Programs}
+The exported access programs for the Edge module are listed in Table \ref{AmisEEAP}.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{|c|c|c|c|}
+\hline
+Routine Name & Input & Output & Exceptions \\
+\hline
+initEdge & {\tt VertexT, VertexT}& & EqualVertices\\
+\hline
+getEdge & & {\tt EdgeT} & \\
+\hline
+\end{tabular}
+\caption{Exported Access Programs of the Edge Module}
+\label{AmisEEAP}
+\end{table}
+
+\subsection{Interface Semantics}
+\subsubsection{State Variables}
+$e$: set of {\tt VertexT}
+\subsubsection{Invariant} $\# e = 2$
+\subsubsection{Assumptions}initEdge() is called before any other access routine.
+\subsubsection{Access Program Semantics} None
+\paragraph{initEdge({\it start}: {\tt VertexT}, {\it end}: {\tt VertexT})}
+\begin{itemize}
+\item \textbf{Exception}\\ {\it start = end} $\Longrightarrow$ EqualVertices
+\item \textbf{Transition}\\ {\it e: = \{start, end\}}
+\end{itemize}
+
+\paragraph{getEdge()}
+\begin{itemize}
+\item \textbf{Output}\\ $e$
+\end{itemize}
+\subsubsection{Local Functions} None
+\subsubsection{Local Data Types} None
+\subsubsection{Local Constants} None
+\subsubsection{Considerations} None
+
+
+
+\section{MIS of Cell Module \label{AmisSecC}}
+
+\subsection{Module Name: Cell (MP)}
+
+\subsection{Uses}
+\subsubsection{Imported Constants} None
+\subsubsection{Imported Data Types}
+{\bf Uses} \emph{Vertex Module} {\bf Imports} \texttt{VertexT}
+\subsubsection{Imported Access Programs}None
+
+\subsection{Interface Syntax}
+\subsubsection{Exported constants} None
+\subsubsection{Exported Data Types}
+{\tt CellT} := set of {\tt VertexT}
+\subsubsection{Exported Access Programs}
+The exported access programs for the cell module are listed in Table \ref{AmisCEAP}.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{|c|c|c|c|}
+\hline
+Routine Name & Input & Output & Exceptions \\
+\hline
+initCell & {\tt VertexT, VertexT, VertexT} & & EqualVertices\\
+\hline
+getCell & & {\tt CellT} & \\
+\hline
+\end{tabular}
+\caption{Exported Access Programs of the Cell Module}
+\label{AmisCEAP}
+\end{table}
+
+\subsection{Interface Semantics}
+\subsubsection{State Variables}
+$c$: set of {\tt VertexT}
+\subsubsection{Invariant} $\# c = 3$
+\subsubsection{Assumptions}initCell() is called before any other access routine.
+\subsubsection{Access Program Semantics}None
+\paragraph{initCell($v1$: {\tt VertexT}, $v2$: {\tt VertexT}, $v3$: {\tt VertexT})}
+\begin{itemize}
+\item \textbf{Exception}\\ $v1=v2 \vee v2=v3 \vee v3=v1 \Longrightarrow$ EqualVertices
+\item \textbf{Transition}\\
+$c := \{v1, v2, v3\}$
+\end{itemize}
+
+\paragraph{getCell()}
+\begin{itemize}
+\item \textbf{Output}\\ $c$
+\end{itemize}
+
+\subsubsection{Local Functions} None
+\subsubsection{Local Data Types} None
+\subsubsection{Local Constants} None
+\subsubsection{Considerations} None
+
+
+\section{MIS of Mesh Module \label{AmisSecM}}
+
+\subsection{Module Name: Mesh (MP)}
+
+\subsection{Uses}
+\subsubsection{Imported Constants} None
+\subsubsection{Imported Data Types}
+{\bf Uses} \emph{Vertex Module} {\bf Imports} \texttt{VertexT} \\
+{\bf Uses} \emph{Edge Module} {\bf Imports} \texttt{EdgeT} \\
+{\bf Uses} \emph{Cell Module} {\bf Imports} \texttt{CellT}
+\subsubsection{Imported Access Programs}None
+
+\subsection{Interface Syntax}
+\subsubsection{Exported constants} None
+\subsubsection{Exported Data Types}
+{\tt MeshT} := set of {\tt CellT}
+\subsubsection{Exported Access Programs}
+The exported access programs for the mesh module are listed in Table \ref{AmisMEAP}.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{|c|c|c|c|}
+\hline
+Routine Name & Input & Output & Exceptions \\
+\hline
+initMesh & & & \\
+\hline
+getMesh & & {\tt MeshT} & \\
+\hline
+numOfCells & & $\mathbb{N}$ & \\
+\hline
+addCell & {\tt CellT} & & CellExist\\
+\hline
+deleteCell & {\tt CellT} & & CellNotExist\\
+\hline
+onEdge & {\tt VertexT, EdgeT}& $\mathbb{B}$ & \\
+\hline
+belongToCell &{\tt EdgeT , CellT}&$ \mathbb{B}$&\\
+\hline
+inside &{\tt VertexT , CellT}&$ \mathbb{B}$&\\
+\hline
+vertices & & set of {\tt VertexT}&\\
+\hline
+edges & & set of {\tt EdgeT}&\\
+\hline
+boundaryEdges & & set of {\tt EdgeT}&\\
+\hline
+boundaryVertices & &set of {\tt VertexT}&\\
+\hline
+\end{tabular}
+\caption{Exported Access Programs of the Mesh Module}
+\label{AmisMEAP}
+\end{table}
+
+\subsection{Interface Semantics}
+\subsubsection{State Variables}
+$m$: set of {\tt CellT}
+\subsubsection{Invariant}
+$\# m\geq 0$
+\subsubsection{Assumptions}initCell() is called before any other access routine.
+\subsubsection{Access Program Semantics}
+\paragraph{initMesh()}
+\begin{itemize}
+\item \textbf{Transition}\\
+$ m := \emptyset$
+\end{itemize}
+
+\paragraph{getMesh()}
+\begin{itemize}
+\item \textbf{Output}\\ $m$
+\end{itemize}
+
+\paragraph{numOfCells()}
+\begin{itemize}
+\item \textbf{Output} \\
+$\# m$
+\end{itemize}
+
+\paragraph{addCell($c$: {\tt CellT})}
+\begin{itemize}
+\item \textbf{Exception}\\
+$c \in m \Longrightarrow$ CellExist
+\item \textbf{Transition} \\
+$m := m \cup \{c\}$
+\end{itemize}
+
+\paragraph{deleteCell($c$: {\tt CellT})}
+\begin{itemize}
+\item \textbf{Exception}\\
+$c \notin m \Longrightarrow$ CellNotExist
+\item \textbf{Transition} \\
+$m := m \backslash \{c\}$
+\end{itemize}
+
+\paragraph{onEdge($v$: {\tt VertexT}, $e$: {\tt EdgeT})}
+\begin{itemize}
+\item \textbf{Description}\\
+Returns true if a vertex $v$ is on the line segment between two vertices (exclusive) of the edge $e$.
+\item \textbf{Output} \\
+$ \exists v1,v2$: {\tt VertexT} $|\\
+ v1\in e \wedge v2\in e \wedge v1\neq v2 \wedge v\neq v1 \wedge v\neq v2:\\
+(v1.x < v.x\leq v2.x \wedge \\(v.y-v1.y)/(v.x-v1.x)=(v2.y-v1.y)/(v2.x-v1.x))$
+\end{itemize}
+
+\paragraph{belongToCell($e$: {\tt EdgeT}, $c$: {\tt CellT})}
+\begin{itemize}
+\item \textbf{Description}\\
+Returns true if an edge $e$ belongs to a cell $c$.
+\item \textbf{Output} \\
+$\forall v$: {\tt VertexT} $|\ v\in e: v\in c$
+\end{itemize}
+
+\paragraph{inside($v$: {\tt VertexT}, $c$: {\tt CellT})}
+\begin{itemize}
+\item \textbf{Description}\\
+Returns true if a vertex $v$ is inside a cell $c$. (The algorithm is adopt from \citet{Franklin2006}.)
+\item \textbf{Output} \\
+$\exists v1, v2, v3$: {\tt VertexT} $|\\
+v1\in c \wedge v2\in c \wedge v3\in c \wedge v1\neq v2 \wedge v2\neq v3 \wedge v3 \neq v1:\\
+((v.y-v1.y)*(v2.x-v1.x)-(v.x-v1.x)*(v2.y-v1.y))*\\
+((v.y-v2.y)*(v3.x-v2.x)-(v.x-v2.x)*(v3.y-v2.y)) > 0 \wedge \\
+((v.y-v2.y)*(v3.x-v2.x)-(v.x-v2.x)*(v3.y-v2.y))*\\
+((v.y-v3.y)*(v1.x-v3.x)-(v.x-v3.x)*(v1.y-v3.y)) > 0$
+\end{itemize}
+
+\paragraph{vertices()}
+\begin{itemize}
+\item \textbf{Description}\\
+Returns the set of all the vertices of the mesh.
+\item \textbf{Output} \\
+$\{v$: {\tt VertexT} $|\ (\forall c$: {\tt CellT} $|\ c\in m:v\in c):v\}$
+\end{itemize}
+
+\paragraph{edges()}
+\begin{itemize}
+\item \textbf{Description}\\
+Returns the set of all the edges of the mesh
+\item \textbf{Output} \\
+$\{v1,v2$: {\tt VertexT} $|\ (\forall c$: {\tt CellT} $|\ c\in m:v1\in c \wedge v2\in c \wedge v1 \neq v2):\{v1, v2\}\}$
+\end{itemize}
+
+\paragraph{boundaryEdges()}
+\begin{itemize}
+\item \textbf{Description}\\
+Returns a set of boundary edges of the mesh
+\item \textbf{Output} \\
+$ \{ b$: {\tt EdgeT} $|\ b\in$ Edges() $\wedge\\ (\# \{c$: {\tt CellT} $|\ c\in m\ \wedge$ belongToCell{\it (b, c): c\}=1):b\}}
+\end{itemize}
+
+\paragraph{boundaryVertices()}
+\begin{itemize}
+\item \textbf{Description}\\
+Returns a set of boundary vertices of the mesh.
+\item \textbf{Output} \\
+$ \{v$: {\tt VertexT} $|\ v\in$ boundaryEdges{\it(): v\}}
+\end{itemize}
+\subsubsection{Local Functions}
+\subsubsection{Local Data Types} None
+\subsubsection{Local Constants} None
+\subsubsection{Considerations} None
+
+\section{MIS of Service Module \label{AmisSecSer}}
+
+\subsection{Module Name: Service}
+
+\subsection{Uses}
+\subsubsection{Imported Constants} None
+\subsubsection{Imported Data Types}
+{\bf Uses} \emph{Vertex Module} {\bf Imports} \texttt{VertexT} \\
+{\bf Uses} \emph{Edge Module} {\bf Imports} \texttt{EdgeT} \\
+{\bf Uses} \emph{Cell Module} {\bf Imports} \texttt{CellT} \\
+{\bf Uses} \emph{Mesh Module} {\bf Imports} \texttt{MeshT}
+
+\subsubsection{Imported Access Programs}
+{\bf Uses} \emph{Mesh Module} {\bf Imports}
+\emph{onEdge(), inside(), \\vertices(), edges(), boundaryEdges(), boundaryVertices()}
+
+\subsection{Interface Syntax}
+\subsubsection{Exported constants} None
+\subsubsection{Exported Data Types}
+{\tt InstructionT} := \{{\tt REFINE, COARSEN, NOCHANGE}\}\\
+{\tt CellInstructionT}:= tuple of ({\it cell}: {\tt CellT}, {\it instr}: {\tt InstructionT})\\
+{\tt RCinstructionT} := tuple of \\({\it rORc}: {\tt InstructionT}, {\it cInstru}: set of {\tt CellInstructionT})
+\subsubsection{Exported Access Programs}
+The exported access programs for the services module are listed in Table \ref{AmisSerEAP}.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{|c|c|c|c|}
+\hline
+Routine Name & Input & Output & Exceptions \\
+\hline
+isValidMesh & {\tt MeshT} & $\mathbb{B}$ & \\
+\hline
+coveringUp & {\tt MeshT} $\times$ {\tt MeshT}& $\mathbb{B}$ & \\
+\hline
+\end{tabular}
+\caption{Exported Access Programs of the Services Module}
+\label{AmisSerEAP}
+\end{table}
+
+\subsection{Interface Semantics}
+\subsubsection{State Variables}None
+\subsubsection{Invariant} None
+\subsubsection{Assumptions} None
+\subsubsection{Access Program Semantics}
+
+\paragraph{isValidMesh($m$: {\tt MeshT})}
+\begin{itemize}
+\item \textbf{Description}\\
+Returns true if cells of the mesh are bounded, conformal, and non overlapping.
+\item \textbf{Output}\\ Bounded$(m)\ \wedge$ Conformal$(m)\ \wedge$ NoInteriorIntersect$(m)$
+\end{itemize}
+
+\paragraph{coveringUp($m1$:{\tt MeshT}, $m2$: {\tt MeshT})}
+\begin{itemize}
+\item \textbf{Description} \\
+Returns false if any boundary vertex of one mesh is not on a boundary edge of another mesh.
+Otherwise, return true.
+\item \textbf{Output} \\
+$\forall v1, v2$: {\tt VertexT} $| \\
+ v1\in$ boundaryVertice($m1)\ \wedge\ v2\in$ boundaryVertices$(m2): \\
+ (\exists\ b1, b2$: {\tt EdgeT} $|\ b1 \in$ boundaryEdges$(m1)\ \wedge\ b2 \in$ boundaryEdges$(m2)$:
+ (onEdge$(v1,b2)\ \vee\ v1\in b2)\ \wedge$ (onEdge$(v2, b1)\ \vee\ v2\in b1))$
+\end{itemize}
+
+\subsubsection{Local Functions}
+\begin{itemize}
+
+\item ValidEdge: {\tt EdgeT} $\rightarrow \mathbb{B}$\\
+ValidEdge($e$: {\tt EdgeT}) $\equiv \# e = 2$
+\item Area: {\tt CellT} $\rightarrow \mathbb{R}$\\
+Area($c$: {\tt CellT}) $\equiv \Sigma v1,v2,v3$: {\tt VertexT} $|\ v1\in c \wedge v2\in c \wedge v3\in c \\
+\wedge v1\neq v2 \wedge v2\neq v3 \wedge v3\neq v1:\\
+\frac{1}{12}* |v1.x*v2.y - v2.x*v1.y +\\
+v2.x*v3.y - v3.x*v2.y +\\
+v1.x*v3.y - v3.x*v1.y |$
+\item ValidCell: {\tt CellT} $\rightarrow \mathbb{B}$\\
+ValidCell($c$: {\tt CellT}) $\equiv \# c = 3\ \wedge$ Area$(c) \geq 0$
+\item Bounded: {\tt MeshT} $\rightarrow \mathbb{B}$\\
+Bounded($m$: {\tt MeshT}) $\equiv \forall v$: {\tt VertexT} $|\ v\in$ boundaryVertices($m$): \\
+$(\# \{e$: {\tt EdgeT} $|\ e\in$ boundaryEdge($m$) $\wedge v\in e: e\}=2)$
+
+\item Conformal: {\tt MeshT} $\rightarrow \mathbb{B}$\\
+Conformal($m$: {\tt MeshT}) $\equiv \forall c1, c2$: {\tt CellT} $|\ c1\in m \wedge c2\in m \wedge c1\neq c2 : \\
+(\exists e$: {\tt EdgeT} $|\ e\in$ edges($m):(\exists v:$ {\tt VertexT} $|\ v\in$ vertices($m):\\
+(c1\cap c2 = e \vee c1\cap c2 = v \vee c1\cap c2 = \emptyset) \wedge (\neg$ onEdge($v,\ e)) ))$
+
+\item NoInteriorIntersect: {\tt MeshT} $\rightarrow \mathbb{B}$\\
+NoInteriorIntersect($m$: {\tt MeshT}) $\equiv \forall c1, c2$: {\tt CellT} $|\\ c1\in m \wedge c2\in m \wedge c1 \neq c2:
+(\forall v$: {\tt VertexT} $|$ inside($v,\ c1): \neg$ inside($v,\ c2))$
+
+\end{itemize}
+\subsubsection{Local Data Types} None
+\subsubsection{Local Constants} None
+\subsubsection{Considerations} None
+
+
+\section{MIS of Input Format Module \label{AmisSecInput}}
+
+\subsection{Module Name: Input Format}
+
+\subsection{Uses}
+\subsubsection{Imported Constants} None
+\subsubsection{Imported Data Types}
+{\bf Uses} \emph{Embedding Application} {\bf Imports} \texttt{InputFormatT}
+
+\subsubsection{Imported Access Programs}
+None
+\subsection{Interface Syntax}
+\subsubsection{Exported constants} None
+\subsubsection{Exported Data Types}None
+\subsubsection{Exported Access Programs}
+The exported access programs for the input format module are listed in Table \ref{AmisInputEAP}.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{|c|c|c|c|}
+\hline
+Routine Name & Input & Output & Exceptions \\
+\hline
+convertInput & {\tt InputFormatT} &{\tt MeshT} & \\
+\hline
+\end{tabular}
+\caption{Exported Access Programs of the Input Format Module}
+\label{AmisInputEAP}
+\end{table}
+
+\subsection{Interface Semantics}
+\subsubsection{State Variables}None
+\subsubsection{Invariant} None
+\subsubsection{Assumptions} None
+\subsubsection{Access Program Semantics}
+\paragraph{convertInput($m$: {\tt InputFormatT})}
+\begin{itemize}
+\item \textbf{Output}\\
+$m'$ such that\\
+$m'$ is of type {\tt MeshT} and $m$ and $m'$ are equivalent.
+\end{itemize}
+
+\subsubsection{Local Functions}
+None
+\subsubsection{Local Data Types} None
+\subsubsection{Local Constants} None
+\subsubsection{Considerations}
+\begin{itemize}
+\item Semantics of access programs in this module heavily depend on the format of the input mesh. At this stage, this information is missing. Unknown data types {\tt InputFormatT} is used to represent the data structures of input mesh. English is used to describe the semantics.
+\end{itemize}
+
+
+\section{MIS of Output Format Module \label{AmisSecOutput}}
+
+\subsection{Module Name: Output Format}
+
+\subsection{Uses}
+\subsubsection{Imported Constants} None
+\subsubsection{Imported Data Types}
+{\bf Uses} \emph{Embedding Application} {\bf Imports} \texttt{OutputFormatT}
+
+\subsubsection{Imported Access Programs}None
+\subsection{Interface Syntax}
+\subsubsection{Exported constants} None
+\subsubsection{Exported Data Types} None
+\subsubsection{Exported Access Programs}
+The exported access programs for the output format module are listed in Table \ref{AmisOutputEAP}.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{|c|c|c|c|}
+\hline
+Routine Name & Input & Output & Exceptions \\
+\hline
+convertOutput & {\tt MeshT} & {\tt OutputFormatT} & \\
+\hline
+\end{tabular}
+\caption{Exported Access Programs of the Output Format Module}
+\label{AmisOutputEAP}
+\end{table}
+
+\subsection{Interface Semantics}
+\subsubsection{State Variables}None
+\subsubsection{Invariant} None
+\subsubsection{Assumptions} None
+\subsubsection{Access Program Semantics}
+
+\paragraph{convertOutput($m$: {\tt MeshT})}
+\begin{itemize}
+\item \textbf{Output}\\
+$m'$ such that\\
+$m'$ is of type {\tt OutputFormatT} and $m$ and $m'$ are equivalent.
+\end{itemize}
+
+\subsubsection{Local Functions}
+None
+\subsubsection{Local Data Types} None
+\subsubsection{Local Constants} None
+\subsubsection{Considerations}
+\begin{itemize}
+\item Semantics of access programs in this module heavily depend on the format of the requirements of the output. At this stage, this information is missing. Unknown data type {\tt OutputFormatT} are used to represent the data structures of input and output. English is used to describe the semantics.
+\end{itemize}
+
+
+\section{MIS of Refining Module \label{AmisSecRef}}
+
+\subsection{Module Name: Refining}
+
+\subsection{Uses}
+\subsubsection{Imported Constants} None
+\subsubsection{Imported Data Types}
+{\bf Uses} \emph{Mesh Module} {\bf Imports} \texttt{MeshT} \\
+{\bf Uses} \emph{Service Module} {\bf Imports} \\
+\texttt{InstructionT, CellInstructionT, RCinstructionT}
+
+\subsubsection{Imported Access Programs}
+{\bf Uses} \emph{Service Module} {\bf Imports} \emph{isValidMesh(), coveringUp()}
+
+\subsection{Interface Syntax}
+\subsubsection{Exported constants} None
+\subsubsection{Exported Data Types} None
+\subsubsection{Exported Access Programs}
+The exported access programs for the refining module are listed in Table \ref{AmisRefEAP}.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{|c|c|c|c|}
+\hline
+Routine Name & Input & Output & Exceptions \\
+\hline
+refining & {\tt MeshT, RCinstructionT} &{\tt MeshT} & \\
+\hline
+\end{tabular}
+\caption{Exported Access Programs of the Refining Module}
+\label{AmisRefEAP}
+\end{table}
+
+\subsection{Interface Semantics}
+\subsubsection{State Variables}None
+\subsubsection{Invariant} None
+\subsubsection{Assumptions} isValidMesh$(m)$ and {\it i.rORc} = {\tt REFINE} \\for input $m$: {\tt MeshT} and $i$: {\tt RCinstructionT}
+\subsubsection{Access Program Semantics}
+\paragraph{refining($m$: {\tt MeshT}, $i$: {\tt RCinstructionT})}
+\begin{itemize}
+\item \textbf{Output}\\
+$m'$ \\such that\\
+ValidMesh$(m)\ \wedge$ ValidMesh$(m')\ \wedge$ CoveringUp$(m', m)\ \wedge \# m' \geq \#m$
+\end{itemize}
+
+\subsubsection{Local Functions} None
+\subsubsection{Local Data Types} None
+\subsubsection{Local Constants} None
+\subsubsection{Considerations} None
+
+
+\section{MIS of Coarsening Module \label{AmisSecCoa}}
+
+\subsection{Module Name: Coarsening}
+
+\subsection{Uses}
+\subsubsection{Imported Constants} None
+\subsubsection{Imported Data Types}
+{\bf Uses} \emph{Mesh Module} {\bf Imports} \texttt{MeshT} \\
+{\bf Uses} \emph{Service Module} {\bf Imports} \\
+\texttt{InstructionT, CellInstructionT, RCinstructionT}
+
+\subsubsection{Imported Access Programs}
+{\bf Uses} \emph{Service Module} {\bf Imports} \emph{isValidMesh(), coveringUp()}
+
+\subsection{Interface Syntax}
+\subsubsection{Exported constants} None
+\subsubsection{Exported Data Types} None
+\subsubsection{Exported Access Programs}
+The exported access programs for the coarsening module are listed in Table \ref{AmisCoaEAP}.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{|c|c|c|c|}
+\hline
+Routine Name & Input & Output & Exceptions \\
+\hline
+coarsening & {\tt MeshT, RCinstructionT} &{\tt MeshT} & \\
+\hline
+\end{tabular}
+\caption{Exported Access Programs of the Coarsening Module}
+\label{AmisCoaEAP}
+\end{table}
+
+\subsection{Interface Semantics}
+\subsubsection{State Variables}None
+\subsubsection{Invariant} None
+\subsubsection{Assumptions} isValidMesh$(m)$ and {\it i.rORc} = {\tt COARSEN} \\for input $m$: {\tt MeshT} and $i$: {\tt RCinstructionT}
+\subsubsection{Access Program Semantics}
+\paragraph{coarsening($m$: {\tt MeshT})}
+\begin{itemize}
+\item \textbf{Output}\\
+$m'$ \\such that\\
+ValidMesh$(m)\ \wedge$ ValidMesh$(m')\ \wedge$ CoveringUp$(m',\ m)\ \wedge \# m' \leq \# m$
+\end{itemize}
+
+\subsubsection{Local Functions} None
+\subsubsection{Local Data Types} None
+\subsubsection{Local Constants} None
+\subsubsection{Considerations} None
+
+\newpage
+
+\bibliography{WenRef}
+\bibliographystyle{plainnat}
+
+\end{document}
+
+
+
+
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
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+% Math Symbol fonts were designed by the American Mathematical Society.
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+%%CreationDate: 1991 Aug 20 16:34:54
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
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+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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+%%CreationDate: 1991 Aug 18 21:06:53
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+%%CreationDate: 1991 Aug 20 17:33:59
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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+ endcodespacerange
+ 1 begincidrange
+ <0000> <FFFF> 0
+ endcidrange
+ endcmap
+ CMapName currentdict /CMap defineresource pop
+ end
+ end
+ }
+ if
+ }
+ {
+ /ct_Category 2 dict begin
+ /CIDFont 10 dict def
+ /ProcSet 2 dict def
+ currentdict
+ end
+ def
+ /defineresource
+ {
+ ct_Category 1 index 2 copy known
+ {
+ get
+ dup dup maxlength exch length eq
+ {
+ dup length 10 add dict copy
+ ct_Category 2 index 2 index put
+ }
+ if
+ 3 index 3 index put
+ pop exch pop
+ }
+ { pop pop /defineresource /undefined ct_raise }
+ ifelse
+ } bind def
+ /findresource
+ {
+ ct_Category 1 index 2 copy known
+ {
+ get
+ 2 index 2 copy known
+ { get 3 1 roll pop pop}
+ { pop pop /findresource /undefinedresource ct_raise }
+ ifelse
+ }
+ { pop pop /findresource /undefined ct_raise }
+ ifelse
+ } bind def
+ /resourcestatus
+ {
+ ct_Category 1 index 2 copy known
+ {
+ get
+ 2 index known
+ exch pop exch pop
+ {
+ 0 -1 true
+ }
+ {
+ false
+ }
+ ifelse
+ }
+ { pop pop /findresource /undefined ct_raise }
+ ifelse
+ } bind def
+ /ct_resourcestatus /resourcestatus load def
+ }
+ ifelse
+ /ct_CIDInit 2 dict
+ begin
+ /ct_cidfont_stream_init
+ {
+ {
+ dup (Binary) eq
+ {
+ pop
+ null
+ currentfile
+ ct_Level2?
+ {
+ { cid_BYTE_COUNT () /SubFileDecode filter }
+ stopped
+ { pop pop pop }
+ if
+ }
+ if
+ /readstring load
+ exit
+ }
+ if
+ dup (Hex) eq
+ {
+ pop
+ currentfile
+ ct_Level2?
+ {
+ { null exch /ASCIIHexDecode filter /readstring }
+ stopped
+ { pop exch pop (>) exch /readhexstring }
+ if
+ }
+ { (>) exch /readhexstring }
+ ifelse
+ load
+ exit
+ }
+ if
+ /StartData /typecheck ct_raise
+ }
+ loop
+ cid_BYTE_COUNT ct_CID_STR_SIZE le
+ {
+ 2 copy cid_BYTE_COUNT string exch exec
+ pop
+ 1 array dup
+ 3 -1 roll
+ 0 exch put
+ }
+ {
+ cid_BYTE_COUNT ct_CID_STR_SIZE div ceiling cvi
+ dup array exch 2 sub 0 exch 1 exch
+ {
+ 2 copy
+ 5 index
+ ct_CID_STR_SIZE
+ string
+ 6 index exec
+ pop
+ put
+ pop
+ }
+ for
+ 2 index
+ cid_BYTE_COUNT ct_CID_STR_SIZE mod string
+ 3 index exec
+ pop
+ 1 index exch
+ 1 index length 1 sub
+ exch put
+ }
+ ifelse
+ cid_CIDFONT exch /GlyphData exch put
+ 2 index null eq
+ {
+ pop pop pop
+ }
+ {
+ pop /readstring load
+ 1 string exch
+ {
+ 3 copy exec
+ pop
+ dup length 0 eq
+ {
+ pop pop pop pop pop
+ true exit
+ }
+ if
+ 4 index
+ eq
+ {
+ pop pop pop pop
+ false exit
+ }
+ if
+ }
+ loop
+ pop
+ }
+ ifelse
+ } bind def
+ /StartData
+ {
+ mark
+ {
+ currentdict
+ dup /FDArray get 0 get /FontMatrix get
+ 0 get 0.001 eq
+ {
+ dup /CDevProc known not
+ {
+ /CDevProc 1183615869 internaldict /stdCDevProc 2 copy known
+ { get }
+ {
+ pop pop
+ { pop pop pop pop pop 0 -1000 7 index 2 div 880 }
+ }
+ ifelse
+ def
+ }
+ if
+ }
+ {
+ /CDevProc
+ {
+ pop pop pop pop pop
+ 0
+ 1 cid_temp /cid_CIDFONT get
+ /FDArray get 0 get
+ /FontMatrix get 0 get div
+ 7 index 2 div
+ 1 index 0.88 mul
+ } def
+ }
+ ifelse
+ /cid_temp 15 dict def
+ cid_temp
+ begin
+ /cid_CIDFONT exch def
+ 3 copy pop
+ dup /cid_BYTE_COUNT exch def 0 gt
+ {
+ ct_cidfont_stream_init
+ FDArray
+ {
+ /Private get
+ dup /SubrMapOffset known
+ {
+ begin
+ /Subrs SubrCount array def
+ Subrs
+ SubrMapOffset
+ SubrCount
+ SDBytes
+ ct_Level2?
+ {
+ currentdict dup /SubrMapOffset undef
+ dup /SubrCount undef
+ /SDBytes undef
+ }
+ if
+ end
+ /cid_SD_BYTES exch def
+ /cid_SUBR_COUNT exch def
+ /cid_SUBR_MAP_OFFSET exch def
+ /cid_SUBRS exch def
+ cid_SUBR_COUNT 0 gt
+ {
+ GlyphData cid_SUBR_MAP_OFFSET cid_SD_BYTES ct_GetInterval
+ 0 cid_SD_BYTES ct_cvnsi
+ 0 1 cid_SUBR_COUNT 1 sub
+ {
+ exch 1 index
+ 1 add
+ cid_SD_BYTES mul cid_SUBR_MAP_OFFSET add
+ GlyphData exch cid_SD_BYTES ct_GetInterval
+ 0 cid_SD_BYTES ct_cvnsi
+ cid_SUBRS 4 2 roll
+ GlyphData exch
+ 4 index
+ 1 index
+ sub
+ ct_GetInterval
+ dup length string copy put
+ }
+ for
+ pop
+ }
+ if
+ }
+ { pop }
+ ifelse
+ }
+ forall
+ }
+ if
+ cleartomark pop pop
+ end
+ CIDFontName currentdict /CIDFont defineresource pop
+ end end
+ }
+ stopped
+ { cleartomark /StartData ct_reraise }
+ if
+ } bind def
+ currentdict
+ end def
+ /ct_saveCIDInit
+ {
+ /CIDInit /ProcSet ct_resourcestatus
+ { true }
+ { /CIDInitC /ProcSet ct_resourcestatus }
+ ifelse
+ {
+ pop pop
+ /CIDInit /ProcSet findresource
+ ct_UseNativeCapability?
+ { pop null }
+ { /CIDInit ct_CIDInit /ProcSet defineresource pop }
+ ifelse
+ }
+ { /CIDInit ct_CIDInit /ProcSet defineresource pop null }
+ ifelse
+ ct_Vars exch /ct_oldCIDInit exch put
+ } bind def
+ /ct_restoreCIDInit
+ {
+ ct_Vars /ct_oldCIDInit get dup null ne
+ { /CIDInit exch /ProcSet defineresource pop }
+ { pop }
+ ifelse
+ } bind def
+ /ct_BuildCharSetUp
+ {
+ 1 index
+ begin
+ CIDFont
+ begin
+ Adobe_CoolType_Utility /ct_BuildCharDict get
+ begin
+ /ct_dfCharCode exch def
+ /ct_dfDict exch def
+ CIDFirstByte ct_dfCharCode add
+ dup CIDCount ge
+ { pop 0 }
+ if
+ /cid exch def
+ {
+ GlyphDirectory cid 2 copy known
+ { get }
+ { pop pop nullstring }
+ ifelse
+ dup length FDBytes sub 0 gt
+ {
+ dup
+ FDBytes 0 ne
+ { 0 FDBytes ct_cvnsi }
+ { pop 0 }
+ ifelse
+ /fdIndex exch def
+ dup length FDBytes sub FDBytes exch getinterval
+ /charstring exch def
+ exit
+ }
+ {
+ pop
+ cid 0 eq
+ { /charstring nullstring def exit }
+ if
+ /cid 0 def
+ }
+ ifelse
+ }
+ loop
+ } def
+ /ct_SetCacheDevice
+ {
+ 0 0 moveto
+ dup stringwidth
+ 3 -1 roll
+ true charpath
+ pathbbox
+ 0 -1000
+ 7 index 2 div 880
+ setcachedevice2
+ 0 0 moveto
+ } def
+ /ct_CloneSetCacheProc
+ {
+ 1 eq
+ {
+ stringwidth
+ pop -2 div -880
+ 0 -1000 setcharwidth
+ moveto
+ }
+ {
+ usewidths?
+ {
+ currentfont /Widths get cid
+ 2 copy known
+ { get exch pop aload pop }
+ { pop pop stringwidth }
+ ifelse
+ }
+ { stringwidth }
+ ifelse
+ setcharwidth
+ 0 0 moveto
+ }
+ ifelse
+ } def
+ /ct_Type3ShowCharString
+ {
+ ct_FDDict fdIndex 2 copy known
+ { get }
+ {
+ currentglobal 3 1 roll
+ 1 index gcheck setglobal
+ ct_Type1FontTemplate dup maxlength dict copy
+ begin
+ FDArray fdIndex get
+ dup /FontMatrix 2 copy known
+ { get }
+ { pop pop ct_defaultFontMtx }
+ ifelse
+ /FontMatrix exch dup length array copy def
+ /Private get
+ /Private exch def
+ /Widths rootfont /Widths get def
+ /CharStrings 1 dict dup /.notdef
+ <d841272cf18f54fc13> dup length string copy put def
+ currentdict
+ end
+ /ct_Type1Font exch definefont
+ dup 5 1 roll put
+ setglobal
+ }
+ ifelse
+ dup /CharStrings get 1 index /Encoding get
+ ct_dfCharCode get charstring put
+ rootfont /WMode 2 copy known
+ { get }
+ { pop pop 0 }
+ ifelse
+ exch
+ 1000 scalefont setfont
+ ct_str1 0 ct_dfCharCode put
+ ct_str1 exch ct_dfSetCacheProc
+ ct_SyntheticBold
+ {
+ currentpoint
+ ct_str1 show
+ newpath
+ moveto
+ ct_str1 true charpath
+ ct_StrokeWidth setlinewidth
+ stroke
+ }
+ { ct_str1 show }
+ ifelse
+ } def
+ /ct_Type4ShowCharString
+ {
+ ct_dfDict ct_dfCharCode charstring
+ FDArray fdIndex get
+ dup /FontMatrix get dup ct_defaultFontMtx ct_matrixeq not
+ { ct_1000Mtx matrix concatmatrix concat }
+ { pop }
+ ifelse
+ /Private get
+ Adobe_CoolType_Utility /ct_Level2? get not
+ {
+ ct_dfDict /Private
+ 3 -1 roll
+ { put }
+ 1183615869 internaldict /superexec get exec
+ }
+ if
+ 1183615869 internaldict
+ Adobe_CoolType_Utility /ct_Level2? get
+ { 1 index }
+ { 3 index /Private get mark 6 1 roll }
+ ifelse
+ dup /RunInt known
+ { /RunInt get }
+ { pop /CCRun }
+ ifelse
+ get exec
+ Adobe_CoolType_Utility /ct_Level2? get not
+ { cleartomark }
+ if
+ } bind def
+ /ct_BuildCharIncremental
+ {
+ {
+ Adobe_CoolType_Utility /ct_MakeOCF get begin
+ ct_BuildCharSetUp
+ ct_ShowCharString
+ }
+ stopped
+ { stop }
+ if
+ end
+ end
+ end
+ end
+ } bind def
+ /BaseFontNameStr (BF00) def
+ /ct_Type1FontTemplate 14 dict
+ begin
+ /FontType 1 def
+ /FontMatrix [0.001 0 0 0.001 0 0] def
+ /FontBBox [-250 -250 1250 1250] def
+ /Encoding ct_cHexEncoding def
+ /PaintType 0 def
+ currentdict
+ end def
+ /BaseFontTemplate 11 dict
+ begin
+ /FontMatrix [0.001 0 0 0.001 0 0] def
+ /FontBBox [-250 -250 1250 1250] def
+ /Encoding ct_cHexEncoding def
+ /BuildChar /ct_BuildCharIncremental load def
+ ct_Clone?
+ {
+ /FontType 3 def
+ /ct_ShowCharString /ct_Type3ShowCharString load def
+ /ct_dfSetCacheProc /ct_CloneSetCacheProc load def
+ /ct_SyntheticBold false def
+ /ct_StrokeWidth 1 def
+ }
+ {
+ /FontType 4 def
+ /Private 1 dict dup /lenIV 4 put def
+ /CharStrings 1 dict dup /.notdef <d841272cf18f54fc13> put def
+ /PaintType 0 def
+ /ct_ShowCharString /ct_Type4ShowCharString load def
+ }
+ ifelse
+ /ct_str1 1 string def
+ currentdict
+ end def
+ /BaseFontDictSize BaseFontTemplate length 5 add def
+ /ct_matrixeq
+ {
+ true 0 1 5
+ {
+ dup 4 index exch get exch 3 index exch get eq and
+ dup not
+ { exit }
+ if
+ }
+ for
+ exch pop exch pop
+ } bind def
+ /ct_makeocf
+ {
+ 15 dict
+ begin
+ exch /WMode exch def
+ exch /FontName exch def
+ /FontType 0 def
+ /FMapType 2 def
+ /FontMatrix matrix def
+ /bfCount 1 index /CIDCount get 256 idiv 1 add
+ dup 256 gt { pop 256} if def
+ /Encoding
+ 256 array 0 1 bfCount 1 sub { 2 copy dup put pop } for
+ bfCount 1 255 { 2 copy bfCount put pop } for
+ def
+ /FDepVector bfCount dup 256 lt { 1 add } if array def
+ BaseFontTemplate BaseFontDictSize dict copy
+ begin
+ /CIDFont exch def
+ CIDFont /FontBBox known
+ { CIDFont /FontBBox get /FontBBox exch def }
+ if
+ CIDFont /CDevProc known
+ { CIDFont /CDevProc get /CDevProc exch def }
+ if
+ currentdict
+ end
+ BaseFontNameStr 3 (0) putinterval
+ 0 1 bfCount dup 256 eq { 1 sub } if
+ {
+ FDepVector exch
+ 2 index BaseFontDictSize dict copy
+ begin
+ dup /CIDFirstByte exch 256 mul def
+ FontType 3 eq
+ { /ct_FDDict 2 dict def }
+ if
+ currentdict
+ end
+ 1 index 16
+ BaseFontNameStr 2 2 getinterval cvrs pop
+ BaseFontNameStr exch definefont
+ put
+ }
+ for
+ ct_Clone?
+ { /Widths 1 index /CIDFont get /GlyphDirectory get length dict def }
+ if
+ FontName
+ currentdict
+ end
+ definefont
+ ct_Clone?
+ {
+ gsave
+ dup 1000 scalefont setfont
+ ct_BuildCharDict
+ begin
+ /usewidths? false def
+ currentfont /Widths get
+ begin
+ exch /CIDFont get /GlyphDirectory get
+ {
+ pop
+ dup charcode exch 1 index 0 2 index 256 idiv put
+ 1 index exch 1 exch 256 mod put
+ stringwidth 2 array astore def
+ }
+ forall
+ end
+ /usewidths? true def
+ end
+ grestore
+ }
+ { exch pop }
+ ifelse
+ } bind def
+ /ct_ComposeFont
+ {
+ ct_UseNativeCapability?
+ {
+ 2 index /CMap ct_resourcestatus
+ { pop pop exch pop }
+ {
+ /CIDInit /ProcSet findresource
+ begin
+ 12 dict
+ begin
+ begincmap
+ /CMapName 3 index def
+ /CMapVersion 1.000 def
+ /CMapType 1 def
+ exch /WMode exch def
+ /CIDSystemInfo 3 dict dup
+ begin
+ /Registry (Adobe) def
+ /Ordering
+ CMapName ct_mkocfStr100 cvs
+ (Adobe-) search
+ {
+ pop pop
+ (-) search
+ {
+ dup length string copy
+ exch pop exch pop
+ }
+ { pop (Identity)}
+ ifelse
+ }
+ { pop (Identity) }
+ ifelse
+ def
+ /Supplement 0 def
+ end def
+ 1 begincodespacerange
+ <0000> <FFFF>
+ endcodespacerange
+ 1 begincidrange
+ <0000> <FFFF> 0
+ endcidrange
+ endcmap
+ CMapName currentdict /CMap defineresource pop
+ end
+ end
+ }
+ ifelse
+ composefont
+ }
+ {
+ 3 2 roll pop
+ 0 get /CIDFont findresource
+ ct_makeocf
+ }
+ ifelse
+ } bind def
+ /ct_MakeIdentity
+ {
+ ct_UseNativeCapability?
+ {
+ 1 index /CMap ct_resourcestatus
+ { pop pop }
+ {
+ /CIDInit /ProcSet findresource begin
+ 12 dict begin
+ begincmap
+ /CMapName 2 index def
+ /CMapVersion 1.000 def
+ /CMapType 1 def
+ /CIDSystemInfo 3 dict dup
+ begin
+ /Registry (Adobe) def
+ /Ordering
+ CMapName ct_mkocfStr100 cvs
+ (Adobe-) search
+ {
+ pop pop
+ (-) search
+ { dup length string copy exch pop exch pop }
+ { pop (Identity) }
+ ifelse
+ }
+ { pop (Identity) }
+ ifelse
+ def
+ /Supplement 0 def
+ end def
+ 1 begincodespacerange
+ <0000> <FFFF>
+ endcodespacerange
+ 1 begincidrange
+ <0000> <FFFF> 0
+ endcidrange
+ endcmap
+ CMapName currentdict /CMap defineresource pop
+ end
+ end
+ }
+ ifelse
+ composefont
+ }
+ {
+ exch pop
+ 0 get /CIDFont findresource
+ ct_makeocf
+ }
+ ifelse
+ } bind def
+ currentdict readonly pop
+ end
+ end
+%%EndResource
+/currentpacking where{pop currentpacking true setpacking}if
+%%BeginResource: procset pdfvars 6.0 1
+%%Copyright: Copyright 1987-2002 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: definition of dictionary of variables used by PDF & PDFText procsets
+userdict /PDF 162 dict put
+userdict /PDFVars 89 dict dup begin put
+/docSetupDone false def
+/InitAll 0 def
+/TermAll 0 def
+/DocInitAll 0 def
+/DocTermAll 0 def
+/_pdfEncodings 2 array def
+/_pdf_str1 1 string def
+/_pdf_i 0 def
+/_pdf_na 0 def
+/_pdf_showproc 0 def
+/_italMtx [1 0 .212557 1 0 0] def
+/_italMtx_WMode1 [1 -.212557 0 1 0 0] def
+/_italMtxType0 [1 0 .1062785 1 0 0] def
+/_italMtx_WMode1Type0 [1 -.1062785 0 1 0 0] def
+/_basefont 0 def
+/_basefonto 0 def
+/_pdf_oldCIDInit null def
+/_pdf_FontDirectory 30 dict def
+/_categories 10 dict def
+/_sa? true def
+/_ColorSep5044? false def
+/nulldict 0 dict def
+/_processColors 0 def
+/overprintstack null def
+/_defaulttransfer currenttransfer def
+/_defaultflatness currentflat def
+/_defaulthalftone null def
+/_defaultcolortransfer null def
+/_defaultblackgeneration null def
+/_defaultundercolorremoval null def
+/_defaultcolortransfer null def
+PDF begin
+[/c/cs/cm/d/d0/f/h/i/j/J/l/m/M/n/q/Q/re/ri/S/sc/sh/Tf/w/W
+/applyInterpFunc/applystitchFunc/domainClip/encodeInput
+/initgs/int/limit/rangeClip
+/defineRes/undefineRes/findRes/setSA/pl
+/? /! /| /: /+ /GetGlyphDirectory
+/pdf_flushFilters /pdf_readstring /pdf_dictOp /pdf_image /pdf_maskedImage
+/pdf_shfill /pdf_sethalftone
+] {null def} bind forall
+end
+end
+%%EndResource
+PDFVars begin PDF begin
+%%BeginResource: procset pdfutil 6.0 1
+%%Copyright: Copyright 1993-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Basic utilities used by other PDF procsets
+/bd {bind def} bind def
+/ld {load def} bd
+/bld {
+dup length dict begin
+{ null def } forall
+bind
+end
+def
+} bd
+/dd { PDFVars 3 1 roll put } bd
+/xdd { exch dd } bd
+/Level2?
+systemdict /languagelevel known
+{ systemdict /languagelevel get 2 ge } { false } ifelse
+def
+/Level1? Level2? not def
+/Level3?
+systemdict /languagelevel known
+{systemdict /languagelevel get 3 eq } { false } ifelse
+def
+/getifknown {
+2 copy known { get true } { pop pop false } ifelse
+} bd
+/here {
+currentdict exch getifknown
+} bd
+/isdefined? { where { pop true } { false } ifelse } bd
+%%EndResource
+%%BeginResource: procset l2compat 6.0 1
+%%Copyright: Copyright 1987-2003 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Level 1 emulation of level 2 operators
+/setcmykcolor isdefined? not
+{
+/setcmykcolor {
+1 sub 4 1 roll
+3 {
+3 index add neg dup 0 lt { pop 0 } if
+3 1 roll
+} repeat
+setrgbcolor
+pop
+} bd
+} if
+/rectclip isdefined? not
+{
+/rectclip { newpath re clip newpath } bd
+} if
+/rectfill isdefined? not
+{
+/rectfill { gsave newpath re fill grestore } bd
+} if
+/sethalftone isdefined? not
+{
+/sethalftone {
+begin
+HalftoneType 1 eq
+{ Frequency Angle /SpotFunction load setscreen }
+if
+end
+} bd
+} if
+Level1?
+{
+/pdf_show {show} bd
+/xshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_xshow
+} bd
+/yshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_yshow
+} bd
+/xyshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_xyshow
+} bd
+} if
+/getrampcolor {
+cvi
+/indx exch def
+[
+0 1 NumComp 1 sub {
+dup
+Samples exch get
+dup type /stringtype eq { indx get } if
+exch
+Scaling exch get aload pop
+3 1 roll
+mul add
+} for
+]
+L1setcolor
+} bd
+/sssetbackground { L1setcolor } bd
+%%EndResource
+%%BeginResource: procset pdf 6.0 1
+%%Copyright: Copyright 1998-2003 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: General operators for PDF, common to all Language Levels.
+/cm { matrix astore concat } bd
+/d /setdash ld
+/f /fill ld
+/h /closepath ld
+/i {dup 0 eq {pop _defaultflatness} if setflat} bd
+/j /setlinejoin ld
+/J /setlinecap ld
+/M /setmiterlimit ld
+/n /newpath ld
+/S /stroke ld
+/w /setlinewidth ld
+/W /clip ld
+/sg /setgray ld
+/initgs {
+0 setgray
+[] 0 d
+0 j
+0 J
+10 M
+1 w
+false setSA
+/_defaulttransfer load settransfer
+0 i
+/RelativeColorimetric ri
+newpath
+} bd
+/int {
+dup 2 index sub 3 index 5 index sub div 6 -2 roll sub mul
+exch pop add exch pop
+} bd
+/limit {
+dup 2 index le { exch } if pop
+dup 2 index ge { exch } if pop
+} bd
+/domainClip {
+Domain aload pop 3 2 roll
+limit
+} [/Domain] bld
+/applyInterpFunc {
+0 1 DimOut 1 sub
+{
+dup C0 exch get exch
+dup C1 exch get exch
+3 1 roll
+1 index sub
+3 index
+N exp mul add
+exch
+currentdict /Range_lo known
+{
+dup Range_lo exch get exch
+Range_hi exch get
+3 2 roll limit
+}
+{
+pop
+}
+ifelse
+exch
+} for
+pop
+} [/DimOut /C0 /C1 /N /Range_lo /Range_hi] bld
+/encodeInput {
+NumParts 1 sub
+0 1 2 index
+{
+dup Bounds exch get
+2 index gt
+{ exit }
+{ dup
+3 index eq
+{ exit }
+{ pop } ifelse
+} ifelse
+} for
+3 2 roll pop
+dup Bounds exch get exch
+dup 1 add Bounds exch get exch
+2 mul
+dup Encode exch get exch
+1 add Encode exch get
+int
+} [/NumParts /Bounds /Encode] bld
+/rangeClip {
+exch dup Range_lo exch get
+exch Range_hi exch get
+3 2 roll
+limit
+} [/Range_lo /Range_hi] bld
+/applyStitchFunc {
+Functions exch get exec
+currentdict /Range_lo known {
+0 1 DimOut 1 sub {
+DimOut 1 add -1 roll
+rangeClip
+} for
+} if
+} [/Functions /Range_lo /DimOut] bld
+/pdf_flushfilters
+{
+aload length
+{ dup status
+1 index currentfile ne and
+{ dup flushfile closefile }
+{ pop }
+ifelse
+} repeat
+} bd
+/pdf_readstring
+{
+1 index dup length 1 sub get
+exch readstring pop
+exch pdf_flushfilters
+} bind def
+/pdf_dictOp
+{
+3 2 roll
+10 dict copy
+begin
+_Filters dup length 1 sub get def
+currentdict exch exec
+_Filters pdf_flushfilters
+end
+} [/_Filters] bld
+/pdf_image {{image} /DataSource pdf_dictOp} bd
+/pdf_imagemask {{imagemask} /DataSource pdf_dictOp} bd
+/pdf_shfill {{sh} /DataSource pdf_dictOp} bd
+/pdf_sethalftone {{sethalftone} /Thresholds pdf_dictOp} bd
+/pdf_maskedImage
+{
+10 dict copy begin
+/miDict currentdict def
+/DataDict DataDict 10 dict copy def
+DataDict begin
+/DataSource
+_Filters dup length 1 sub get
+def
+miDict image
+_Filters pdf_flushfilters
+end
+end
+} [/miDict /DataDict /_Filters] bld
+/RadialShade {
+40 dict begin
+/background exch def
+/ext1 exch def
+/ext0 exch def
+/BBox exch def
+/r2 exch def
+/c2y exch def
+/c2x exch def
+/r1 exch def
+/c1y exch def
+/c1x exch def
+/rampdict exch def
+gsave
+BBox length 0 gt {
+newpath
+BBox 0 get BBox 1 get moveto
+BBox 2 get BBox 0 get sub 0 rlineto
+0 BBox 3 get BBox 1 get sub rlineto
+BBox 2 get BBox 0 get sub neg 0 rlineto
+closepath
+clip
+newpath
+} if
+c1x c2x eq
+{
+c1y c2y lt {/theta 90 def}{/theta 270 def} ifelse
+}
+{
+/slope c2y c1y sub c2x c1x sub div def
+/theta slope 1 atan def
+c2x c1x lt c2y c1y ge and { /theta theta 180 sub def} if
+c2x c1x lt c2y c1y lt and { /theta theta 180 add def} if
+}
+ifelse
+gsave
+clippath
+c1x c1y translate
+theta rotate
+-90 rotate
+{ pathbbox } stopped
+{ 0 0 0 0 } if
+/yMax exch def
+/xMax exch def
+/yMin exch def
+/xMin exch def
+grestore
+xMax xMin eq yMax yMin eq or
+{
+grestore
+end
+}
+{
+/max { 2 copy gt { pop } {exch pop} ifelse } bind def
+/min { 2 copy lt { pop } {exch pop} ifelse } bind def
+rampdict begin
+40 dict begin
+background length 0 gt { background sssetbackground gsave clippath fill grestore } if
+gsave
+c1x c1y translate
+theta rotate
+-90 rotate
+/c2y c1x c2x sub dup mul c1y c2y sub dup mul add sqrt def
+/c1y 0 def
+/c1x 0 def
+/c2x 0 def
+ext0 {
+0 getrampcolor
+c2y r2 add r1 sub 0.0001 lt
+{
+c1x c1y r1 360 0 arcn
+pathbbox
+/aymax exch def
+/axmax exch def
+/aymin exch def
+/axmin exch def
+/bxMin xMin axmin min def
+/byMin yMin aymin min def
+/bxMax xMax axmax max def
+/byMax yMax aymax max def
+bxMin byMin moveto
+bxMax byMin lineto
+bxMax byMax lineto
+bxMin byMax lineto
+bxMin byMin lineto
+eofill
+}
+{
+c2y r1 add r2 le
+{
+c1x c1y r1 0 360 arc
+fill
+}
+{
+c2x c2y r2 0 360 arc fill
+r1 r2 eq
+{
+/p1x r1 neg def
+/p1y c1y def
+/p2x r1 def
+/p2y c1y def
+p1x p1y moveto p2x p2y lineto p2x yMin lineto p1x yMin lineto
+fill
+}
+{
+/AA r2 r1 sub c2y div def
+AA -1 eq
+{ /theta 89.99 def}
+{ /theta AA 1 AA dup mul sub sqrt div 1 atan def}
+ifelse
+/SS1 90 theta add dup sin exch cos div def
+/p1x r1 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def
+/p1y p1x SS1 div neg def
+/SS2 90 theta sub dup sin exch cos div def
+/p2x r1 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def
+/p2y p2x SS2 div neg def
+r1 r2 gt
+{
+/L1maxX p1x yMin p1y sub SS1 div add def
+/L2maxX p2x yMin p2y sub SS2 div add def
+}
+{
+/L1maxX 0 def
+/L2maxX 0 def
+}ifelse
+p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto
+L1maxX L1maxX p1x sub SS1 mul p1y add lineto
+fill
+}
+ifelse
+}
+ifelse
+} ifelse
+} if
+c1x c2x sub dup mul
+c1y c2y sub dup mul
+add 0.5 exp
+0 dtransform
+dup mul exch dup mul add 0.5 exp 72 div
+0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+1 index 1 index lt { exch } if pop
+/hires exch def
+hires mul
+/numpix exch def
+/numsteps NumSamples def
+/rampIndxInc 1 def
+/subsampling false def
+numpix 0 ne
+{
+NumSamples numpix div 0.5 gt
+{
+/numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def
+/rampIndxInc NumSamples 1 sub numsteps div def
+/subsampling true def
+} if
+} if
+/xInc c2x c1x sub numsteps div def
+/yInc c2y c1y sub numsteps div def
+/rInc r2 r1 sub numsteps div def
+/cx c1x def
+/cy c1y def
+/radius r1 def
+newpath
+xInc 0 eq yInc 0 eq rInc 0 eq and and
+{
+0 getrampcolor
+cx cy radius 0 360 arc
+stroke
+NumSamples 1 sub getrampcolor
+cx cy radius 72 hires div add 0 360 arc
+0 setlinewidth
+stroke
+}
+{
+0
+numsteps
+{
+dup
+subsampling { round } if
+getrampcolor
+cx cy radius 0 360 arc
+/cx cx xInc add def
+/cy cy yInc add def
+/radius radius rInc add def
+cx cy radius 360 0 arcn
+eofill
+rampIndxInc add
+}
+repeat
+pop
+} ifelse
+ext1 {
+c2y r2 add r1 lt
+{
+c2x c2y r2 0 360 arc
+fill
+}
+{
+c2y r1 add r2 sub 0.0001 le
+{
+c2x c2y r2 360 0 arcn
+pathbbox
+/aymax exch def
+/axmax exch def
+/aymin exch def
+/axmin exch def
+/bxMin xMin axmin min def
+/byMin yMin aymin min def
+/bxMax xMax axmax max def
+/byMax yMax aymax max def
+bxMin byMin moveto
+bxMax byMin lineto
+bxMax byMax lineto
+bxMin byMax lineto
+bxMin byMin lineto
+eofill
+}
+{
+c2x c2y r2 0 360 arc fill
+r1 r2 eq
+{
+/p1x r2 neg def
+/p1y c2y def
+/p2x r2 def
+/p2y c2y def
+p1x p1y moveto p2x p2y lineto p2x yMax lineto p1x yMax lineto
+fill
+}
+{
+/AA r2 r1 sub c2y div def
+AA -1 eq
+{ /theta 89.99 def}
+{ /theta AA 1 AA dup mul sub sqrt div 1 atan def}
+ifelse
+/SS1 90 theta add dup sin exch cos div def
+/p1x r2 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def
+/p1y c2y p1x SS1 div sub def
+/SS2 90 theta sub dup sin exch cos div def
+/p2x r2 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def
+/p2y c2y p2x SS2 div sub def
+r1 r2 lt
+{
+/L1maxX p1x yMax p1y sub SS1 div add def
+/L2maxX p2x yMax p2y sub SS2 div add def
+}
+{
+/L1maxX 0 def
+/L2maxX 0 def
+}ifelse
+p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto
+L1maxX L1maxX p1x sub SS1 mul p1y add lineto
+fill
+}
+ifelse
+}
+ifelse
+} ifelse
+} if
+grestore
+grestore
+end
+end
+end
+} ifelse
+} bd
+/GenStrips {
+40 dict begin
+/background exch def
+/ext1 exch def
+/ext0 exch def
+/BBox exch def
+/y2 exch def
+/x2 exch def
+/y1 exch def
+/x1 exch def
+/rampdict exch def
+gsave
+BBox length 0 gt {
+newpath
+BBox 0 get BBox 1 get moveto
+BBox 2 get BBox 0 get sub 0 rlineto
+0 BBox 3 get BBox 1 get sub rlineto
+BBox 2 get BBox 0 get sub neg 0 rlineto
+closepath
+clip
+newpath
+} if
+x1 x2 eq
+{
+y1 y2 lt {/theta 90 def}{/theta 270 def} ifelse
+}
+{
+/slope y2 y1 sub x2 x1 sub div def
+/theta slope 1 atan def
+x2 x1 lt y2 y1 ge and { /theta theta 180 sub def} if
+x2 x1 lt y2 y1 lt and { /theta theta 180 add def} if
+}
+ifelse
+gsave
+clippath
+x1 y1 translate
+theta rotate
+{ pathbbox } stopped
+{ 0 0 0 0 } if
+/yMax exch def
+/xMax exch def
+/yMin exch def
+/xMin exch def
+grestore
+xMax xMin eq yMax yMin eq or
+{
+grestore
+end
+}
+{
+rampdict begin
+20 dict begin
+background length 0 gt { background sssetbackground gsave clippath fill grestore } if
+gsave
+x1 y1 translate
+theta rotate
+/xStart 0 def
+/xEnd x2 x1 sub dup mul y2 y1 sub dup mul add 0.5 exp def
+/ySpan yMax yMin sub def
+/numsteps NumSamples def
+/rampIndxInc 1 def
+/subsampling false def
+xStart 0 transform
+xEnd 0 transform
+3 -1 roll
+sub dup mul
+3 1 roll
+sub dup mul
+add 0.5 exp 72 div
+0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+1 index 1 index lt { exch } if pop
+mul
+/numpix exch def
+numpix 0 ne
+{
+NumSamples numpix div 0.5 gt
+{
+/numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def
+/rampIndxInc NumSamples 1 sub numsteps div def
+/subsampling true def
+} if
+} if
+ext0 {
+0 getrampcolor
+xMin xStart lt
+{ xMin yMin xMin neg ySpan rectfill } if
+} if
+/xInc xEnd xStart sub numsteps div def
+/x xStart def
+0
+numsteps
+{
+dup
+subsampling { round } if
+getrampcolor
+x yMin xInc ySpan rectfill
+/x x xInc add def
+rampIndxInc add
+}
+repeat
+pop
+ext1 {
+xMax xEnd gt
+{ xEnd yMin xMax xEnd sub ySpan rectfill } if
+} if
+grestore
+grestore
+end
+end
+end
+} ifelse
+} bd
+/currentdistillerparams where { pop currentdistillerparams /CoreDistVersion get 5000 lt}{true}ifelse
+{
+/PDFMark5 {cleartomark} bd
+}
+{
+/PDFMark5 {pdfmark} bd
+}ifelse
+/ReadByPDFMark5
+{
+2 dict begin
+/makerString exch def string /tmpString exch def
+{
+currentfile tmpString readline pop
+makerString anchorsearch
+{
+pop pop cleartomark exit
+}
+{
+3 copy /PUT PDFMark5 pop 2 copy (\n) /PUT PDFMark5
+} ifelse
+}loop
+end
+}bd
+%%EndResource
+%%BeginResource: procset sep_ops 6.0 1
+%%Copyright: Copyright 1987-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Support for Separations in Level 1, following the conventions of Tech Note 5044
+userdict /sep_ops 50 dict dup begin put
+/bdef {bind def} bind def
+/xdef {exch def} bdef
+/colorimagebuffer {
+0 1 2 index length 1 sub {
+dup 2 index exch get 255 exch sub 2 index 3 1 roll put
+} for
+} bdef
+/addprocs {
+[ 3 1 roll
+/exec load
+dup 3 1 roll
+] cvx
+} bdef
+/L1? {
+systemdict /languagelevel known {
+systemdict /languagelevel get 2 lt
+}{
+true
+} ifelse
+} bdef
+/colorexists {
+statusdict /processcolors known {
+statusdict /processcolors get exec
+}{
+/deviceinfo where {
+pop deviceinfo /Colors known {
+deviceinfo /Colors get
+statusdict /processcolors {
+deviceinfo /Colors known {
+deviceinfo /Colors get
+}{
+1
+} ifelse
+} put
+}{
+1
+} ifelse
+}{
+1
+} ifelse
+} ifelse
+1 gt
+} bdef
+/colorplate colorexists { 0 } { 5 } ifelse def
+/negativecolorplate false def
+/setcmykcolor where {
+pop
+gsave
+1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub
+4 {4 copy} repeat
+grestore
+1 dict begin
+/foureq {
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+pop pop pop pop and and and
+} def
+1 0 0 0 foureq {/colorplate 1 store} if
+0 1 0 0 foureq {/colorplate 2 store} if
+0 0 1 0 foureq {/colorplate 3 store} if
+0 0 0 1 foureq {/colorplate 4 store} if
+0 0 0 0 foureq {/colorplate 6 store} if
+end
+} if
+0 systemdict /currenttransfer get exec exec
+1 systemdict /currenttransfer get exec exec
+2 copy
+eq
+{
+/colorplate 6 store
+pop
+/negativecolorplate exch 0.5 lt store
+}
+{
+gt /negativecolorplate exch store
+}
+ifelse
+/findcmykcustomcolor where { pop }
+{
+/findcmykcustomcolor {
+[ 6 1 roll ] readonly
+} bdef
+} ifelse
+/setoverprint where {
+pop
+}{
+/setoverprint {
+pop
+} bdef
+} ifelse
+/currentoverprint where {
+pop
+}{
+/currentoverprint {
+false
+} bdef
+} ifelse
+/setcustomcolor where {
+pop
+}{
+L1? {
+/setcustomcolor {
+exch
+aload pop pop
+4 { 4 index mul 4 1 roll } repeat
+5 -1 roll pop
+setcmykcolor
+} bdef
+}{
+/setcustomcolor {
+exch
+[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
+0 4 getinterval
+[ exch /dup load exch cvx {mul exch dup}
+/forall load /pop load dup] cvx
+] setcolorspace setcolor
+} bdef
+} ifelse
+} ifelse
+/ik 0 def
+/iy 0 def
+/im 0 def
+/ic 0 def
+/imagetint {
+ic .3 mul
+im .59 mul
+iy .11 mul
+ik add add add dup
+1 gt {pop 1} if
+} bdef
+/setcmykcolor where {
+pop
+}{
+/setcmykcolor {
+/ik xdef /iy xdef /im xdef /ic xdef
+imagetint
+1 exch sub setgray
+} bdef
+} ifelse
+/customcolorimage where {
+pop
+}{
+L1? {
+/customcolorimage{
+gsave
+colorexists {
+aload pop pop
+/ik xdef /iy xdef /im xdef /ic xdef
+currentcolortransfer
+{ik mul ik sub 1 add} addprocs
+4 1 roll {iy mul iy sub 1 add} addprocs
+4 1 roll {im mul im sub 1 add} addprocs
+4 1 roll {ic mul ic sub 1 add} addprocs
+4 1 roll setcolortransfer
+/magentabuf 0 string def
+/yellowbuf 0 string def
+/blackbuf 0 string def
+{
+colorimagebuffer dup length magentabuf length ne
+{
+dup length dup dup
+/magentabuf exch string def
+/yellowbuf exch string def
+/blackbuf exch string def
+} if
+dup magentabuf copy yellowbuf copy
+blackbuf copy pop
+} addprocs
+{magentabuf}{yellowbuf}{blackbuf} true 4 colorimage
+}{
+aload pop pop /ik xdef /iy xdef /im xdef /ic xdef /tint
+imagetint def
+currenttransfer
+{tint mul 1 tint sub add} addprocs settransfer image
+} ifelse
+grestore
+} bdef
+}{
+/customcolorimage {
+gsave
+[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
+0 4 getinterval
+[ exch /dup load exch cvx {mul exch dup}
+/forall load /pop load dup] cvx
+] setcolorspace
+10 dict begin
+/ImageType 1 def
+/DataSource exch def
+/ImageMatrix exch def
+/BitsPerComponent exch def
+/Height exch def
+/Width exch def
+/Decode [1 0] def
+currentdict end
+image
+grestore
+} bdef
+} ifelse
+} ifelse
+/setseparationgray where {
+pop
+}{
+L1? {
+/setseparationgray { 1 exch sub dup dup dup setcmykcolor } bdef
+}{
+/setseparationgray {
+[/Separation /All /DeviceCMYK {dup dup dup}] setcolorspace
+1 exch sub setcolor
+} bdef
+} ifelse
+} ifelse
+/separationimage where { pop }
+{
+/separationimage {
+gsave
+1 1 1 1 (All)
+findcmykcustomcolor customcolorimage
+grestore
+} bdef
+} ifelse
+currentdict readonly pop end
+%%EndResource
+%%BeginResource: procset pdflev15044 6.0 1
+%%Copyright: Copyright 1987-2002 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: PDF operators, Level 1, with emulated separations (TN 5044)
+/_ColorSep5044? true dd
+/docinitialize {
+PDF begin
+/_defaulthalftone
+/currenthalftone where
+{ pop currenthalftone }
+{ 4 dict dup begin
+currentscreen
+/SpotFunction exch def
+/Angle exch def
+/Frequency exch def
+/HalftoneType 1 def
+end }
+ifelse
+dd
+/currentcolortransfer where
+{ pop /_defaultcolortransfer [ currentcolortransfer ] dd }
+{ /_defaultcolortransfer [currenttransfer dup dup dup] dd }
+ifelse
+end
+} bd
+/initialize {
+/overprintstack null dd
+sep_ops begin
+50 dict begin
+_defaulthalftone sethalftone
+} bd
+/terminate {
+end end
+} bd
+/currentcolortransfer where
+{ pop }
+{
+/setcolortransfer
+{
+settransfer pop pop pop
+} bd
+} ifelse
+/pl {
+transform
+0.25 sub round 0.25 add exch
+0.25 sub round 0.25 add exch
+itransform
+} bd
+/m { _sa? { pl } if moveto } bd
+/l { _sa? { pl } if lineto } bd
+/c
+{
+_sa? {3 {pl 6 2 roll} repeat} if
+curveto
+} bd
+/ri/pop ld
+/setSA { /_sa? xdd } bd
+/re
+{
+_sa?
+{
+8 dict begin
+/:h exch def
+/:w exch def
+/:y exch def
+/:x exch def
+:x :y pl
+/:ymin exch def /:xmin exch def
+:x :w add :y :h add pl
+/:ymax exch def /:xmax exch def
+:xmin :ymin moveto
+:xmax :ymin lineto
+:xmax :ymax lineto
+:xmin :ymax lineto
+closepath
+end
+}
+{
+4 2 roll moveto
+1 index 0 rlineto
+0 exch rlineto
+neg 0 rlineto
+closepath
+} ifelse
+} bd
+/q
+{
+gsave
+[currentoverprint overprintstack] /overprintstack xdd
+}
+[/overprintstack] bld
+/Q
+{
+overprintstack aload pop /overprintstack xdd setoverprint
+grestore
+}
+[/overprintstack] bld
+/AlmostFull?
+{ dup maxlength exch length sub 2 le
+} bd
+/Expand
+{ 1 index maxlength mul cvi dict
+dup begin exch { def } forall end
+} bd
+/xput
+{ 3 2 roll
+dup 3 index known not
+{ dup AlmostFull? { 1.5 Expand } if
+} if
+dup 4 2 roll put
+} bd
+/defineRes
+{ _categories 1 index known not
+{ /_categories _categories 2 index 10 dict xput store
+} if
+_categories exch 2 copy get 5 -1 roll 4 index xput put
+} bd
+/undefineRes {
+null exch
+defineRes
+} bd
+/findRes {
+_categories exch get exch get
+} bd
+/L1setcolor {
+aload length
+dup 0 eq
+{ pop .5 setgray }
+{ dup 1 eq
+{ pop setgray }
+{ 3 eq
+{ setrgbcolor }
+{ setcmykcolor }
+ifelse }
+ifelse }
+ifelse
+} bind dd
+/concattransferfuncs {
+[ 3 1 roll /exec load exch /exec load ] cvx
+} bd
+/concatandsettransfer {
+/_defaulttransfer load concattransferfuncs settransfer
+} bd
+/concatandsetcolortransfer {
+colorplate 0 eq
+{
+_defaultcolortransfer aload pop
+8 -1 roll 5 -1 roll concattransferfuncs 7 1 roll
+6 -1 roll 4 -1 roll concattransferfuncs 5 1 roll
+4 -1 roll 3 -1 roll concattransferfuncs 3 1 roll
+concattransferfuncs
+setcolortransfer
+} if
+colorplate 1 ge colorplate 4 le and
+{
+4 colorplate sub index 4 { exch pop } repeat
+concatandsettransfer
+} if
+colorplate 5 ge
+{
+0 index 4 { exch pop } repeat
+concatandsettransfer
+} if
+} bd
+/tn5044sethalftone
+{
+begin
+HalftoneType 5 eq
+{ [/Default /Cyan /Magenta /Yellow /Black /Default /Default /Default]
+colorplate get
+here not {
+/Default here not { currentdict } if
+} if
+}
+{ currentdict }
+ifelse
+end
+begin
+/TransferFunction here
+{
+concatandsettransfer
+currentdict dup length dict
+begin
+{
+1 index /TransferFunction ne { def } { pop pop } ifelse
+} forall
+currentdict
+end
+}
+{
+currentdict
+} ifelse
+end
+sethalftone
+} bd
+/paintimage
+{
+colorplate 0 eq
+{
+{ {currentfile cyanstr readstring pop}
+{currentfile magentastr readstring pop}
+{currentfile yellowstr readstring pop}
+{currentfile blackstr readstring pop
+currentfile graystr readstring pop pop}
+}
+{ {currentfile cyanstr readhexstring pop}
+{currentfile magentastr readhexstring pop}
+{currentfile yellowstr readhexstring pop}
+{currentfile blackstr readhexstring pop
+currentfile graystr readhexstring pop pop}
+} ifelse
+true 4 colorimage
+}
+{
+3 dict begin
+/binaryOK exch def
+[
+1 1 5 {
+dup
+/currentfile cvx
+[ /cyanstr /magentastr /yellowstr /blackstr /graystr ]
+3 -1 roll 1 sub get cvx
+binaryOK { /readstring } { /readhexstring } ifelse cvx
+/pop cvx
+5 -1 roll
+colorplate dup 5 gt { pop 5 } if
+eq not { /pop cvx } if
+} for
+] cvx bind
+end
+[
+colorplate 6 eq {
+/pop cvx
+negativecolorplate { 0 } { 1 } ifelse
+} if
+colorplate 4 le
+{
+1 /exch cvx /sub cvx
+} if
+colorplate 6 ne
+{
+systemdict /currenttransfer get exec
+aload pop
+} if
+] cvx
+gsave
+systemdict /settransfer get exec
+systemdict /image get exec
+grestore
+} ifelse
+} bd
+%%EndResource
+%%BeginResource: procset pdftext 6.0 1
+%%Copyright: Copyright 1987-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Text operators for PDF
+PDF /PDFText 78 dict dup begin put
+/docinitialize
+{
+/resourcestatus where {
+pop
+/CIDParams /ProcSet resourcestatus {
+pop pop
+false /CIDParams /ProcSet findresource /SetBuildCompatible get exec
+} if
+} if
+PDF begin
+PDFText /_pdfDefineIdentity-H known
+{ PDFText /_pdfDefineIdentity-H get exec}
+if
+end
+} bd
+/initialize {
+PDFText begin
+} bd
+/terminate { end } bd
+Level2?
+{
+/_safeput
+{
+3 -1 roll load 3 1 roll put
+}
+bd
+}
+{
+/_safeput
+{
+2 index load dup dup length exch maxlength ge
+{ dup length 5 add dict copy
+3 index xdd
+}
+{ pop }
+ifelse
+3 -1 roll load 3 1 roll put
+}
+bd
+}
+ifelse
+/pdf_has_composefont? systemdict /composefont known def
+/CopyFont {
+{
+1 index /FID ne 2 index /UniqueID ne and
+{ def } { pop pop } ifelse
+} forall
+} bd
+/Type0CopyFont
+{
+exch
+dup length dict
+begin
+CopyFont
+[
+exch
+FDepVector
+{
+dup /FontType get 0 eq
+{
+1 index Type0CopyFont
+/_pdfType0 exch definefont
+}
+{
+/_pdfBaseFont exch
+2 index exec
+}
+ifelse
+exch
+}
+forall
+pop
+]
+/FDepVector exch def
+currentdict
+end
+} bd
+Level2? {currentglobal true setglobal} if
+/cHexEncoding
+[/c00/c01/c02/c03/c04/c05/c06/c07/c08/c09/c0A/c0B/c0C/c0D/c0E/c0F/c10/c11/c12
+/c13/c14/c15/c16/c17/c18/c19/c1A/c1B/c1C/c1D/c1E/c1F/c20/c21/c22/c23/c24/c25
+/c26/c27/c28/c29/c2A/c2B/c2C/c2D/c2E/c2F/c30/c31/c32/c33/c34/c35/c36/c37/c38
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+/cBE/cBF/cC0/cC1/cC2/cC3/cC4/cC5/cC6/cC7/cC8/cC9/cCA/cCB/cCC/cCD/cCE/cCF/cD0
+/cD1/cD2/cD3/cD4/cD5/cD6/cD7/cD8/cD9/cDA/cDB/cDC/cDD/cDE/cDF/cE0/cE1/cE2/cE3
+/cE4/cE5/cE6/cE7/cE8/cE9/cEA/cEB/cEC/cED/cEE/cEF/cF0/cF1/cF2/cF3/cF4/cF5/cF6
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+counttomark 1 sub -1 0
+{
+index
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+}
+if
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+} for
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+} bd
+/trEnc {
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+255 -1 0 {
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+{ pop /.notdef }
+{ Encoding exch get }
+ifelse
+_enc 3 1 roll put
+} for
+pop
+_enc
+} bd
+/TE {
+/_i xdd
+StandardEncoding 256 array copy modEnc
+_pdfEncodings exch _i exch put
+} bd
+/TZ
+{
+/_usePDFEncoding xdd
+findfont
+dup length 6 add dict
+begin
+{
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+} forall
+/pdf_origFontName FontName def
+/FontName exch def
+currentdict /PaintType known
+{ PaintType 2 eq {/PaintType 0 def} if }
+if
+_usePDFEncoding 0 ge
+{
+/Encoding _pdfEncodings _usePDFEncoding get def
+pop
+}
+{
+_usePDFEncoding -1 eq
+{
+counttomark 0 eq
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+{
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+}
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+}
+{
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+}
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+}
+ifelse
+pdf_EuroProcSet pdf_origFontName known
+{
+pdf_origFontName pdf_AddEuroGlyphProc
+} if
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+{
+currentdict /pdf_origFontName undef
+} if
+FontName currentdict
+end
+definefont pop
+}
+bd
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+{
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+{
+currentglobal true setglobal
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+{
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+ne
+{
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+{
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+} forall
+currentdict end
+}
+if
+3 index exch definefont pop
+}
+if
+} if
+setglobal
+TZ
+} bd
+}
+{
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+} ifelse
+Level2?
+{
+currentglobal false setglobal
+userdict /pdftext_data 5 dict put
+pdftext_data
+begin
+/saveStacks
+{
+pdftext_data
+begin
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+false setglobal
+count array astore /os exch def
+end
+countdictstack array dictstack pdftext_data exch /ds exch put
+cleardictstack pdftext_data /dscount countdictstack put
+pdftext_data /vmmode get setglobal
+} bind def
+/restoreStacks
+{
+pdftext_data /vmmode currentglobal put false setglobal
+clear cleardictstack
+pdftext_data /ds get dup
+pdftext_data /dscount get 1 2 index length 1 sub
+{ get begin dup } for
+pop pop
+pdftext_data /os get aload pop
+pdftext_data /vmmode get setglobal
+} bind def
+/testForClonePrinterBug
+{
+currentglobal true setglobal
+/undefinedCategory /Generic /Category findresource
+dup length dict copy /Category defineresource pop
+setglobal
+pdftext_data /saveStacks get exec
+pdftext_data /vmmode currentglobal put false setglobal
+/undefined /undefinedCategory { resourcestatus } stopped
+pdftext_data exch /bugFound exch put
+pdftext_data /vmmode get setglobal
+pdftext_data /restoreStacks get exec
+pdftext_data /bugFound get
+} bind def
+end
+setglobal
+/pdf_resourcestatus
+pdftext_data /testForClonePrinterBug get exec
+{
+{
+pdftext_data /saveStacks get exec
+pdftext_data /os get dup dup length 1 sub
+dup 1 sub dup 0 lt { pop 0 } if
+exch 1 exch { get exch dup } for
+pop pop
+{ resourcestatus }
+stopped
+{
+clear cleardictstack pdftext_data /restoreStacks get exec
+{ pop pop } stopped pop false
+}
+{
+count array astore pdftext_data exch /results exch put
+pdftext_data /restoreStacks get exec pop pop
+pdftext_data /results get aload pop
+}
+ifelse
+}
+}
+{ { resourcestatus } }
+ifelse
+bd
+}
+if
+Level2?
+{
+/_pdfUndefineResource
+{
+currentglobal 3 1 roll
+_pdf_FontDirectory 2 index 2 copy known
+{undef}
+{pop pop}
+ifelse
+1 index (pdf) exch _pdfConcatNames 1 index
+1 index 1 _pdfConcatNames 1 index
+5 index 1 _pdfConcatNames 1 index
+4
+{
+2 copy pdf_resourcestatus
+{
+pop 2 lt
+{2 copy findresource gcheck setglobal undefineresource}
+{pop pop}
+ifelse
+}
+{ pop pop}
+ifelse
+} repeat
+setglobal
+} bd
+}
+{
+/_pdfUndefineResource { pop pop} bd
+}
+ifelse
+Level2?
+{
+/_pdfFontStatus
+{
+currentglobal exch
+/Font pdf_resourcestatus
+{pop pop true}
+{false}
+ifelse
+exch setglobal
+} bd
+}
+{
+/_pdfFontStatusString 50 string def
+_pdfFontStatusString 0 (fonts/) putinterval
+/_pdfFontStatus
+{
+FontDirectory 1 index known
+{ pop true }
+{
+_pdfFontStatusString 6 42 getinterval
+cvs length 6 add
+_pdfFontStatusString exch 0 exch getinterval
+{ status } stopped
+{pop false}
+{
+{ pop pop pop pop true}
+{ false }
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+ifelse
+Level2?
+{
+/_pdfCIDFontStatus
+{
+/CIDFont /Category pdf_resourcestatus
+{
+pop pop
+/CIDFont pdf_resourcestatus
+{pop pop true}
+{false}
+ifelse
+}
+{ pop false }
+ifelse
+} bd
+}
+if
+/_pdfString100 100 string def
+/_pdfComposeFontName
+{
+dup length 1 eq
+{
+0 get
+1 index
+type /nametype eq
+{
+_pdfString100 cvs
+length dup dup _pdfString100 exch (-) putinterval
+_pdfString100 exch 1 add dup _pdfString100 length exch sub getinterval
+2 index exch cvs length
+add 1 add _pdfString100 exch 0 exch getinterval
+exch pop
+true
+}
+{
+pop pop
+false
+}
+ifelse
+}
+{
+false
+}
+ifelse
+dup {exch cvn exch} if
+} bd
+/_pdfConcatNames
+{
+exch
+_pdfString100 cvs
+length dup dup _pdfString100 exch (-) putinterval
+_pdfString100 exch 1 add dup _pdfString100 length exch sub getinterval
+3 -1 roll exch cvs length
+add 1 add _pdfString100 exch 0 exch getinterval
+cvn
+} bind def
+/_pdfTextTempString 50 string def
+/_pdfRegOrderingArray [(Adobe-Japan1) (Adobe-CNS1) (Adobe-Korea1) (Adobe-GB1)] def
+/_pdf_CheckCIDSystemInfo
+{
+1 index _pdfTextTempString cvs
+(Identity) anchorsearch
+{
+pop pop pop pop true
+}
+{
+false
+_pdfRegOrderingArray
+{
+2 index exch
+anchorsearch
+{ pop pop pop true exit}
+{ pop }
+ifelse
+}
+forall
+exch pop
+exch /CIDFont findresource
+/CIDSystemInfo get
+3 -1 roll /CMap findresource
+/CIDSystemInfo get
+exch
+3 -1 roll
+{
+2 copy
+/Supplement get
+exch
+dup type /dicttype eq
+{/Supplement get}
+{pop 0 }
+ifelse
+ge
+}
+{ true }
+ifelse
+{
+dup /Registry get
+2 index /Registry get eq
+{
+/Ordering get
+exch /Ordering get
+dup type /arraytype eq
+{
+1 index type /arraytype eq
+{
+true
+1 index length 1 sub -1 0
+{
+dup 2 index exch get exch 3 index exch get ne
+{ pop false exit}
+if
+} for
+exch pop exch pop
+}
+{ pop pop false }
+ifelse
+}
+{
+eq
+}
+ifelse
+}
+{ pop pop false }
+ifelse
+}
+{ pop pop false }
+ifelse
+}
+ifelse
+} bind def
+pdf_has_composefont?
+{
+/_pdfComposeFont
+{
+2 copy _pdfComposeFontName not
+{
+2 index
+}
+if
+(pdf) exch _pdfConcatNames
+dup _pdfFontStatus
+{ dup findfont 5 2 roll pop pop pop true}
+{
+4 1 roll
+1 index /CMap pdf_resourcestatus
+{
+pop pop
+true
+}
+{false}
+ifelse
+1 index true exch
+{
+_pdfCIDFontStatus not
+{pop false exit}
+if
+}
+forall
+and
+{
+1 index 1 index 0 get _pdf_CheckCIDSystemInfo
+{
+3 -1 roll pop
+2 index 3 1 roll
+composefont true
+}
+{
+pop pop exch pop false
+}
+ifelse
+}
+{
+_pdfComposeFontName
+{
+dup _pdfFontStatus
+{
+exch pop
+1 index exch
+findfont definefont true
+}
+{
+pop exch pop
+false
+}
+ifelse
+}
+{
+exch pop
+false
+}
+ifelse
+}
+ifelse
+{ true }
+{
+dup _pdfFontStatus
+{ dup findfont true }
+{ pop false }
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+{
+/_pdfComposeFont
+{
+_pdfComposeFontName not
+{
+dup
+}
+if
+dup
+_pdfFontStatus
+{exch pop dup findfont true}
+{
+1 index
+dup type /nametype eq
+{pop}
+{cvn}
+ifelse
+eq
+{pop false}
+{
+dup _pdfFontStatus
+{dup findfont true}
+{pop false}
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+ifelse
+/_pdfStyleDicts 4 dict dup begin
+/Adobe-Japan1 4 dict dup begin
+Level2?
+{
+/Serif
+/HeiseiMin-W3-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiMin-W3}
+{
+/HeiseiMin-W3 _pdfCIDFontStatus
+{/HeiseiMin-W3}
+{/Ryumin-Light}
+ifelse
+}
+ifelse
+def
+/SansSerif
+/HeiseiKakuGo-W5-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiKakuGo-W5}
+{
+/HeiseiKakuGo-W5 _pdfCIDFontStatus
+{/HeiseiKakuGo-W5}
+{/GothicBBB-Medium}
+ifelse
+}
+ifelse
+def
+/HeiseiMaruGo-W4-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiMaruGo-W4}
+{
+/HeiseiMaruGo-W4 _pdfCIDFontStatus
+{/HeiseiMaruGo-W4}
+{
+/Jun101-Light-RKSJ-H _pdfFontStatus
+{ /Jun101-Light }
+{ SansSerif }
+ifelse
+}
+ifelse
+}
+ifelse
+/RoundSansSerif exch def
+/Default Serif def
+}
+{
+/Serif /Ryumin-Light def
+/SansSerif /GothicBBB-Medium def
+{
+(fonts/Jun101-Light-83pv-RKSJ-H) status
+}stopped
+{pop}{
+{ pop pop pop pop /Jun101-Light }
+{ SansSerif }
+ifelse
+/RoundSansSerif exch def
+}ifelse
+/Default Serif def
+}
+ifelse
+end
+def
+/Adobe-Korea1 4 dict dup begin
+/Serif /HYSMyeongJo-Medium def
+/SansSerif /HYGoThic-Medium def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+/Adobe-GB1 4 dict dup begin
+/Serif /STSong-Light def
+/SansSerif /STHeiti-Regular def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+/Adobe-CNS1 4 dict dup begin
+/Serif /MKai-Medium def
+/SansSerif /MHei-Medium def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+end
+def
+/TZzero
+{
+/_wmode xdd
+/_styleArr xdd
+/_regOrdering xdd
+3 copy
+_pdfComposeFont
+{
+5 2 roll pop pop pop
+}
+{
+[
+0 1 _styleArr length 1 sub
+{
+_styleArr exch get
+_pdfStyleDicts _regOrdering 2 copy known
+{
+get
+exch 2 copy known not
+{ pop /Default }
+if
+get
+}
+{
+pop pop pop /Unknown
+}
+ifelse
+}
+for
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+exch pop
+2 index 3 1 roll
+_pdfComposeFont
+{3 -1 roll pop}
+{
+findfont dup /FontName get exch
+}
+ifelse
+}
+ifelse
+dup /WMode 2 copy known
+{ get _wmode ne }
+{ pop pop _wmode 1 eq}
+ifelse
+{
+exch _wmode _pdfConcatNames
+dup _pdfFontStatus
+{ exch pop dup findfont false}
+{ exch true }
+ifelse
+}
+{
+dup /FontType get 0 ne
+}
+ifelse
+{
+dup /FontType get 3 eq _wmode 1 eq and
+{
+_pdfVerticalRomanT3Font dup length 10 add dict copy
+begin
+/_basefont exch
+dup length 3 add dict
+begin
+{1 index /FID ne {def}{pop pop} ifelse }
+forall
+/Encoding Encoding dup length array copy
+dup 16#27 /quotesingle put
+dup 16#60 /grave put
+_regOrdering /Adobe-Japan1 eq
+{dup 16#5c /yen put dup 16#a5 /yen put dup 16#b4 /yen put}
+if
+def
+FontName
+currentdict
+end
+definefont
+def
+/Encoding _basefont /Encoding get def
+/_fauxfont true def
+}
+{
+dup length 3 add dict
+begin
+{1 index /FID ne {def}{pop pop} ifelse }
+forall
+FontType 0 ne
+{
+/Encoding Encoding dup length array copy
+dup 16#27 /quotesingle put
+dup 16#60 /grave put
+_regOrdering /Adobe-Japan1 eq
+{dup 16#5c /yen put}
+if
+def
+/_fauxfont true def
+} if
+} ifelse
+/WMode _wmode def
+dup dup /FontName exch def
+currentdict
+end
+definefont pop
+}
+{
+pop
+}
+ifelse
+/_pdf_FontDirectory 3 1 roll _safeput
+}
+bd
+Level2?
+{
+/Tf {
+_pdf_FontDirectory 2 index 2 copy known
+{get exch 3 -1 roll pop}
+{pop pop}
+ifelse
+selectfont
+} bd
+}
+{
+/Tf {
+_pdf_FontDirectory 2 index 2 copy known
+{get exch 3 -1 roll pop}
+{pop pop}
+ifelse
+exch findfont exch
+dup type /arraytype eq
+{makefont}
+{scalefont}
+ifelse
+setfont
+} bd
+}
+ifelse
+/cshow where
+{
+pop /pdf_cshow /cshow load dd
+/pdf_remove2 {pop pop} dd
+}
+{
+/pdf_cshow {exch forall} dd
+/pdf_remove2 {} dd
+} ifelse
+/pdf_xshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+_pdf_x _pdf_y moveto
+0
+rmoveto
+}
+ifelse
+_pdf_i 1 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdf_yshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+_pdf_x _pdf_y moveto
+0 exch
+rmoveto
+}
+ifelse
+_pdf_i 1 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdf_xyshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+{_pdf_na _pdf_i 1 add get} stopped
+{ pop pop pop}
+{
+_pdf_x _pdf_y moveto
+rmoveto
+}
+ifelse
+}
+ifelse
+_pdf_i 2 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdfl1xs {/_pdf_showproc /show load dd pdf_xshow} bd
+/pdfl1ys {/_pdf_showproc /show load dd pdf_yshow} bd
+/pdfl1xys {/_pdf_showproc /show load dd pdf_xyshow} bd
+Level2? _ColorSep5044? not and
+{
+/pdfxs {{xshow} stopped {pdfl1xs} if} bd
+/pdfys {{yshow} stopped {pdfl1ys} if} bd
+/pdfxys {{xyshow} stopped {pdfl1xys} if} bd
+}
+{
+/pdfxs /pdfl1xs load dd
+/pdfys /pdfl1ys load dd
+/pdfxys /pdfl1xys load dd
+} ifelse
+/pdf_charpath {false charpath} bd
+/pdf_xcharpath {/_pdf_showproc /pdf_charpath load dd pdf_xshow} bd
+/pdf_ycharpath {/_pdf_showproc /pdf_charpath load dd pdf_yshow} bd
+/pdf_xycharpath {/_pdf_showproc /pdf_charpath load dd pdf_xyshow} bd
+/pdf_strokepath
+{
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 false charpath
+currentpoint S moveto
+} bind
+exch pdf_cshow
+} bd
+/pdf_xstrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_xshow} bd
+/pdf_ystrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_yshow} bd
+/pdf_xystrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_xyshow} bd
+Level2? {currentglobal true setglobal} if
+/d0/setcharwidth ld
+/nND {{/.notdef} repeat} bd
+/T3Defs {
+/BuildChar
+{
+1 index /Encoding get exch get
+1 index /BuildGlyph get exec
+}
+def
+/BuildGlyph {
+exch begin
+GlyphProcs exch get exec
+end
+} def
+/_pdfT3Font true def
+} bd
+/_pdfBoldRomanWidthProc
+{
+stringwidth 1 index 0 ne { exch .03 add exch }if setcharwidth
+0 0
+} bd
+/_pdfType0WidthProc
+{
+dup stringwidth 0 0 moveto
+2 index true charpath pathbbox
+0 -1
+7 index 2 div .88
+setcachedevice2
+pop
+0 0
+} bd
+/_pdfType0WMode1WidthProc
+{
+dup stringwidth
+pop 2 div neg -0.88
+2 copy
+moveto
+0 -1
+5 -1 roll true charpath pathbbox
+setcachedevice
+} bd
+/_pdfBoldBaseFont
+11 dict begin
+/FontType 3 def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/Encoding cHexEncoding def
+/_setwidthProc /_pdfBoldRomanWidthProc load def
+/_bcstr1 1 string def
+/BuildChar
+{
+exch begin
+_basefont setfont
+_bcstr1 dup 0 4 -1 roll put
+dup
+_setwidthProc
+3 copy
+moveto
+show
+_basefonto setfont
+moveto
+show
+end
+}bd
+currentdict
+end
+def
+pdf_has_composefont?
+{
+/_pdfBoldBaseCIDFont
+11 dict begin
+/CIDFontType 1 def
+/CIDFontName /_pdfBoldBaseCIDFont def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/_setwidthProc /_pdfType0WidthProc load def
+/_bcstr2 2 string def
+/BuildGlyph
+{
+exch begin
+_basefont setfont
+_bcstr2 1 2 index 256 mod put
+_bcstr2 0 3 -1 roll 256 idiv put
+_bcstr2 dup _setwidthProc
+3 copy
+moveto
+show
+_basefonto setfont
+moveto
+show
+end
+}bd
+currentdict
+end
+def
+/_pdfDefineIdentity-H
+{
+/Identity-H /CMap PDFText /pdf_resourcestatus get exec
+{
+pop pop
+}
+{
+/CIDInit/ProcSet findresource begin 12 dict begin
+begincmap
+/CIDSystemInfo
+3 dict begin
+/Registry (Adobe) def
+/Ordering (Identity) def
+/Supplement 0 def
+currentdict
+end
+def
+/CMapName /Identity-H def
+/CMapVersion 1 def
+/CMapType 1 def
+1 begincodespacerange
+<0000> <ffff>
+endcodespacerange
+1 begincidrange
+<0000> <ffff> 0
+endcidrange
+endcmap
+CMapName currentdict/CMap defineresource pop
+end
+end
+} ifelse
+} def
+} if
+/_pdfVerticalRomanT3Font
+10 dict begin
+/FontType 3 def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/_bcstr1 1 string def
+/BuildChar
+{
+exch begin
+_basefont setfont
+_bcstr1 dup 0 4 -1 roll put
+dup
+_pdfType0WidthProc
+moveto
+show
+end
+}bd
+currentdict
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+(Requiremen)-36 b(ts)4000 68414 y(\(I\))25350 73598 y(36)p
+eop end
+%%Page: 37 38
+TeXDict begin 37 37 bop 9082 3028 a Fm(Wen)464 b(Y)-100
+b(u)465 b({)g(McMaster)g(University)d({)j(Computing)f(and)h(Softwar)-66
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+10407 V 21566 10407 V 24654 10407 V 27742 10407 V 30830
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+25252 V 46270 25252 V 5707 25296 40586 45 v 5685 26901
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+30421 V 27742 30421 V 30830 30421 V 33918 30421 V 37006
+30421 V 28540 w Fa(X)p 40094 30421 V 1981 w(X)p 43182
+30421 V 46270 30421 V 5707 30465 40586 45 v 5685 32071
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+V 15390 32071 V 18478 32071 V 21566 32071 V 24654 32071
+V 27742 32071 V 30830 32071 V 33918 32071 V 37006 32071
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+33941 V 27742 33941 V 30830 33941 V 23645 w Fa(X)p 33918
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+35591 V 15390 35591 V 18478 35591 V 21566 35591 V 24654
+35591 V 27742 35591 V 30830 35591 V 23645 w Fa(X)p 33918
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+V 24654 37240 V 27742 37240 V 30830 37240 V 23645 w Fa(X)p
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+(Requiremen)-36 b(ts)4000 47701 y(\(I)36 b(I\))p 13650
+50405 24700 45 v 13628 52010 45 1606 v 17157 52010 V
+17843 51529 a(F1)p 20685 52010 V 2029 w(F2)p 24214 52010
+V 2030 w(F6)p 27742 52010 V 2029 w(F8)p 31271 52010 V
+2030 w(F10)p 34799 52010 V 1379 w(N6)p 38328 52010 V
+13650 52055 24700 45 v 13650 52276 V 13628 53881 45 1606
+v 14314 53399 a(F3)p 17157 53881 V 2030 w Fa(X)p 20685
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+53881 V 34799 53881 V 38328 53881 V 13650 53925 24700
+45 v 13628 55530 45 1606 v 14314 55049 a Fj(F5)p 17157
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+55575 24700 45 v 13628 57180 45 1606 v 14314 56698 a
+Fj(F9)p 17157 57180 V 20685 57180 V 24214 57180 V 27742
+57180 V 12615 w Fa(X)p 31271 57180 V 34799 57180 V 38328
+57180 V 13650 57224 24700 45 v 13628 58829 45 1606 v
+14314 58348 a Fj(F11)p 17157 58829 V 20685 58829 V 24214
+58829 V 27742 58829 V 31271 58829 V 15494 w Fa(X)p 34799
+58829 V 38328 58829 V 13650 58873 24700 45 v 13628 60478
+45 1606 v 14314 59997 a Fj(F12)p 17157 60478 V 20685
+60478 V 24214 60478 V 27742 60478 V 31271 60478 V 15494
+w Fa(X)p 34799 60478 V 38328 60478 V 13650 60523 24700
+45 v 13628 62128 45 1606 v 14314 61646 a Fj(F13)p 17157
+62128 V 20685 62128 V 24214 62128 V 27742 62128 V 31271
+62128 V 15494 w Fa(X)p 34799 62128 V 38328 62128 V 13650
+62172 24700 45 v 13628 63777 45 1606 v 14314 63296 a
+Fj(F14)p 17157 63777 V 20685 63777 V 24214 63777 V 27742
+63777 V 31271 63777 V 15494 w Fa(X)p 34799 63777 V 38328
+63777 V 13650 63821 24700 45 v 13628 65427 45 1606 v
+14314 64945 a Fj(F15)p 17157 65427 V 20685 65427 V 24214
+65427 V 27742 65427 V 31271 65427 V 15494 w Fa(X)p 34799
+65427 V 38328 65427 V 13650 65471 24700 45 v 13628 67076
+45 1606 v 14314 66594 a Fj(F16)p 17157 67076 V 20685
+67076 V 24214 67076 V 27742 67076 V 31271 67076 V 34799
+67076 V 19022 w Fa(X)p 38328 67076 V 13650 67120 24700
+45 v 9929 69334 a Fj(T)-108 b(able)434 b(6:)579 b(T)-108
+b(raceabilit)-36 b(y)435 b(Matrix)f(\(P)-108 b(AR)g(T)433
+b(I)36 b(I)g(I\):)434 b(Requiremen)-36 b(ts)25350 73598
+y(37)p eop end
+%%Trailer
+
+userdict /end-hook known{end-hook}if
+%%EOF
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@@ -0,0 +1,1126 @@
+\documentclass[12pt,titlepage]{article}
+
+\include{Preamble}
+
+\author{Wen Yu}
+
+\begin{document}
+
+\begin{titlepage}
+
+% Fonts for the title page
+\newcommand{\texttl}{\textsf} %font for the title (Emil's version is \textsf)
+\newcommand{\textau}{\textsf} %font for the authors, date, etc. (Emils version is \textsc)
+
+\begin{center}
+
+\HRule \\[0.4cm]
+{ \huge \bfseries \texttl{Software Requirements Specification for a Parallel Mesh Generation Toolbox}}\\[0.4cm]
+
+\HRule \\[2cm]
+
+\textau{\LARGE Wen Yu}\\[2cm]
+
+\textau{\LARGE {September 2008}}
+
+\vfill
+
+% Bottom of the page
+%\includegraphics[width=0.27\textwidth]{logo.pdf}
+\hfill
+\textau{\LARGE
+\raisebox{2pt}{\begin{tabular}[b]{r}
+\raisebox{8pt}{Computing and Software} \\
+McMaster University \end{tabular}}
+}
+\end{center}
+
+\end{titlepage}
+
+\tableofcontents
+
+\newpage
+
+\section{Reference Material}
+\subsection{Table of Symbols, Abbreviations and Acronyms}
+
+\subsubsection{Symbols}
+\begin{tabular}{p{\firstCol}p{\secondCol}}
+$\Omega$ & a closed bounded domain in $\mathbb{R}^{2}$ \\
+$\Omega^{*}$ & a mesh covering the domain bounded by $\Omega$\\
+$K$ & a simple shape, such as a line segment in 1D, a triangle or a quadrilateral in 2D, or a tetrahedron or hexahedron
+in 3D\\
+$M^{\mbox{IN}}$ & an input mesh\\
+$M^{\mbox{OUT}}$ & an output mesh\\
+$I$ & instructions on how a mesh should be \\
+ & refined/coarsened
+\end{tabular}
+%\newpage
+
+\subsubsection{Abbreviations and Acronyms}
+\begin{tabular}{p{\firstCol}p{\secondCol}}
+1D & One Dimensional Space\\
+2D & Two Dimensional Space\\
+3D & Three Dimensional Space\\
+FEA & Finite Element Analysis\\
+HPC & High Performance Computing\\
+PDE & Partial Differential Equation\\
+PMGT & Parallel Mesh Generation Toolbox\\
+SHARCNET & Shared Hierarchical Academic Research Computing Network\\
+SRS & Software Requirements Specification\\
+AOMD & Algorithm Oriented Mesh Database\\
+\end{tabular}
+\newpage
+
+\subsection{Index of Requirements}
+CoarseningMesh, \pageref{CoarseningMesh}\\
+Conformal, \pageref{Conformal}\\\\
+DomainDimension, \pageref{DomainDimension}\\\\
+ElmShape, \pageref{ElmShape}\\
+ElmTopology, \pageref{ElmTopology}\\
+ElmUniqueID, \pageref{ElmUniqueID}\\
+Exception, \pageref{Exception}\\\\
+Help, \pageref{Help}\\\\
+InputDefinition, \pageref{InputDefinition}\\\\
+LookAndFeel, \pageref{LookAndFeel}\\\\
+Maintainability, \pageref{Maintainability}\\
+MeshType, \pageref{MeshType}\\\\
+OutElmOrder, \pageref{OutElmOrder}\\
+OutputStorage, \pageref{OutputStorage}\\
+OutVertexOrder, \pageref{OutVertexOrder}\\\\
+Performance, \pageref{Performance}\\
+Portability, \pageref{Portability}\\
+Precision, \pageref{Precision}\\\\
+RCInstruction, \pageref{RCInstruction}\\
+RefiningMesh, \pageref{RefiningMesh}\\
+RefiningOrCoarsening, \pageref{RefiningOrCoarsening}\\\\
+Usability, \pageref{Usability}\\\\
+VertexUniqueID, \pageref{VertexUniqueID}
+%\printindex
+\newpage
+
+\section{Introduction \label{AreqSecIntro}}
+
+This section gives an overview of the Software Requirements Specification (SRS) for a Parallel Mesh Generation Toolbox (PMGT). First, the purpose of the document is provided. Second, the scope of PMGT is identified. Third, some terminology for software engineering and mesh generation are defined. Finally, the organization of the document is summarized. The Table of Symbols, Abbreviation and Acronyms, and Index of Requirement are given at the beginning of the SRS.
+
+\subsection{Purpose of the Document}
+This SRS provides a black-box description of PMGT. The intended audience of the SRS is the development team and the users of PMGT.
+
+\subsection{Scope of the Software Product}
+PMGT provides a library that will be embedded into a larger application, such as a finite element analysis (FEA) program.
+\begin{itemize}
+\item The input of PMGT is an existing mesh $M^{\mbox{IN}}$ with instructions $I$ provided by the user on how the mesh should be refined/coarsened.
+\item PMGT refines/coarsens $M^{\mbox{IN}}$ according to the supplied instructions $I$ on how the mesh should be refined/coarsened.
+\item PMGT will take advantage of parallel computation.
+\item The output of PMGT is a refined/coarsened mesh $M^{\mbox{OUT}}$.
+\end{itemize}
+Note that depending on the given instruction, PMGT can either refine or coarsen the given mesh, but cannot do both at the same time. That is, any individual transition from $M^{\mbox{IN}}$ to $M^{\mbox{OUT}}$ will only do one of refining or coarsening. The embedding application will have access to reading the mesh information, such as information on the position of vertices and on the vertices that define a given element. However, the application cannot directly change any mesh data, except for the information indicating which elements should be refined/coarsened.
+
+\subsection{Terminology Definition}
+This subsection provides the definitions for terminology used in the SRS. There are two classes of terminology. One relates to software engineering, and the other relates to mesh generation. The definitions are listed in alphabetical order.
+\subsubsection{Software Engineering Related Terminology\label{AreqSEterm}}
+\begin{description}
+
+\item[Constraint:] A statement that expresses measurable bounds for an element or function of the system. That is, a constraint is a factor that is imposed on the solution by force or compulsion and may limit or modify the design changes. \citep{IEEE1998}
+
+\item[Context:] The boundaries between the system that we intend to build and the people, organizations, other system and pieces of technology that have a direct interface with the system. \citep{Volere2001}
+
+\item[Functional Requirements:] Functional requirements define precisely what input are expected by the software, what outputs will be generated by the software, and the details of relationships that exist between those inputs and outputs. In short, functional requirements describe all aspects of interface between the software and its environment (that is, hardware, humans, and other software). \citep{Davis1990}
+
+\item[Goal:] Goals capture, at different levels of abstraction, the various objectives the system under
+consideration should achieve. \citep{Lamsweerde2001}
+
+\item[Non-functional Requirements:] Non-functional requirements define the overall qualities or attributes to be exhibited by the resulting software system. \citep{Davis1990}
+
+\item[Requirements:] A software requirement is: \begin {inparaenum}[\itshape i\upshape)]
+\item a condition or capability needed by a user to solve a problem or achieve an objective;
+\item a condition or capability that must be met or possessed by a system or system component to satisfy a contract,
+standard, specification, or other formally imposed document; or,
+\item a documented representation of a condition or capability as in the above two definitions.
+\end{inparaenum} \citep{IEEE2000}
+
+\item[Software Engineering:] Software Engineering is the application of a systematic, disciplined, quantifiable approach to the development, operation, and maintenance of software. \citep{IEEE1990}
+
+\item[Software Requirements Specification:] A Software Requirements Specification (SRS) is a document containing a complete description of what the software will do without describing how it will do it. \citep{Davis1990}
+
+\item[System:] An interdependent group of people, objects, and procedures constituted to achieve defined objectives or some operational role by performing specified functions. \citep{IEEE1998}
+
+\item[System Context:] System Context documents the relationships between the system being specified and other human and computer systems. \citep{Sommerville1992}
+
+\item[User:]The person, or persons, who operate or interact directly with the product. \citep{IEEE2000}
+
+\end{description}
+
+\subsubsection{Mesh Generation Related Terminology\label{AreqMGterm}}
+\begin{description}
+
+%\item [Aspect Ratio:] The aspect ratio of a simplex is defined as its maximum side length divided by its minimum altitude. \citep{Mitchell2000}
+%The aspect ratio of a convex body is the ratio between its longest dimension and its shortest dimension.
+
+\item [Cell:] Another name for an element, as defined in page \pageref{AreqElmDef}.
+
+\item[Conformal Mesh:] A conformal mesh is a mesh (defined on page \pageref{def_mesh}) following the definition of a mesh, with the addition of the
+following property:\\
+The intersection of two elements in the mesh $\Omega^{*}$ is either the empty set, a vertex, an edge or a face (when the
+dimension is 3). \citep{FreyAndGeorge2000}
+
+\item [Connectivity:] There are two types of connectivity, one for the mesh and one for a mesh element:
+\begin{enumerate}
+\item ``The connectivity of a mesh is the definition of the connection between its vertices.''~\citep{FreyAndGeorge2000}
+\item ``The connectivity of a mesh element is the definition of the connections between the vertices at the element
+level.''~\citep{FreyAndGeorge2000}
+\end{enumerate}
+
+\item [Domain:] The area or volume that is to be discretized. The domain is sometimes referred to as the
+computational domain. \citep{Smith2004}
+
+
+\item [Edge:] An edge is a line segment between two vertices.
+
+\item [Element \label{AreqElmDef}:] The original domain is discretized into smaller, usually simpler, shapes called elements.
+The typical shapes for elements in 1D is a line, in 2D is a triangle or a quadrilateral, and in 3D a tetrahedron or a
+hexahedron. Elements are also called cells. \citep{Smith2004}
+
+\item [Embedding Application:] The software that uses PMGT.
+
+\item [Face:] A face is a maximal connected subset of the plane without vertices inside the subset. In 2D, a face is a cell.\citep{FreyAndGeorge2000}
+
+\item [Hybrid Mesh:] A mesh is said to be hybrid if it includes some elements with a different spatial dimension. \citep{FreyAndGeorge2000}
+
+\item[Mesh:] \label{def_mesh}
+In \citet{Smith2004}, a mesh is defined as follows:\\
+Let $\Omega$ be a closed bounded domain in $\mathbb{R}$ or $\mathbb{R}^2$ or $\mathbb{R}^3$
+and let $K$ be an element. A mesh of $\Omega$, denoted by $\Omega^{*}$, has the following properties:
+\begin{enumerate}
+\item $\Omega \approx \cup(K | K \in \Omega^{*} : K)$, where $\cup$ is first closed and then opened
+\item the length of every element $K$, of dimension 1, in $\Omega^{*}$ is greater than zero
+\item the interior of every element $K$, of dimension 2 or greater, in $\Omega^{*}$ is nonempty
+\item the intersection of the interior of two elements is empty
+\end{enumerate}
+The only difference between above definition and the definition given by \citet{FreyAndGeorge2000} is that equality (=) had been changed to approximate equality ($\approx$).
+
+\item [Mesh Generation:] The automatic mesh generation problem is that of attempting to define a set of elements to best describe a geometric domain, subject to various element size and shape criteria. \citep{Smith2004}
+
+\item [Mixed Mesh:] A mesh is said to be mixed if it includes some elements of a different geometric nature. \citep{FreyAndGeorge2000}
+
+\item [Structured Mesh:] The mesh in which the local organization of the grid points and the form of the grid cells do not depend on their position but are defined by a general rule. There is a pattern to the topology that repeats.
+\citet{FreyAndGeorge2000} say, ``a mesh is called structured if its connectivity is of the finite difference type.''
+They go on to remark, ``Peculiar meshes other than quad or hex meshes could have a structured connectivity. For
+instance, one can consider a classical grid of quads where each of them are subdivided into two triangles using the same
+subdivision pattern.''
+
+\item [Topology:] ``The topology of a mesh element is the definition of this element in terms of its faces and edges,
+these last two being defined in terms of the element's vertices.''~\citep{FreyAndGeorge2000}\\
+The topology of a mesh is the set of topologies of its constitute mesh elements.
+
+\item [Unstructured Mesh:] The mesh whose element connectivity of the neighbouring grid vertices varies from point to
+point. Any mesh that is not structured is an unstructured mesh. \citep{Smith2004}
+
+\item [Vertices:] The locations that define the shape of the cells. In 1D the vertices are the end-points of the
+elements. For 2D and 3D elements the vertices correspond to the location in space that defines the intersection of
+the edges of an element. \citep{Smith2004}
+
+\end{description}
+
+
+\subsection{Organization of the Document}
+This SRS follows the template introduced by~\cite{Lai2004}. Lai's template targets an SRS for scientific computing software. In particular, the example shown is for engineering mechanics software, such as software to analyze beams. In the current work, Lai's template is modified to fit PMGT, which is a more general purpose software. For example, the instanced model section of Lai's template is removed since PMGT is not designed for solving a specific physical problem.
+
+Section \ref{AreqSecIntro} (this section) is an introduction to the SRS.
+The rest of the document is arranged as follows. Section \ref{AreqSecGSD} provides the general information about the system. Section \ref{AreqSecSSR} is the major part of the SRS. All functional requirements and non-functional requirements of the software are presented in this section. Section \ref{AreqSecOSI} discusses some other system issues. Section \ref{AreqSecTM} gives a traceability matrix that summaries the association of each requirement with goals, assumptions, theoretical models and data definitions introduced in \ref{AreqSecSSR}. This SRS also contains the list of possible changes in the requirements and values of auxiliary constants. The references are listed at the end of this document.
+
+\section{General System Description \label{AreqSecGSD}}
+
+This section describes the general information about the system. The interfaces between the system and its environment are defined first. Then the characteristics of potential users are discussed. At end of this section, some system constraints are described.
+
+\subsection{System Context}
+The software to be built is a library tool that will be called by other applications. There is no direct interaction between the system and the end users. Users of the embedding application, such as an FEA program, provide some parameters directly to the FEA program. Some of these parameters are passed to PMGT by the FEA program. The interface between PMGT and the embedding application should only show what PMGT can do and hide the information about how to do it. Therefore, users who are not experts in mesh generation or in parallel processing will be able to use this toolbox. %The characteristics of users of PMGT will be described in the Section \ref{userchar}.
+\begin{figure}[ht]
+\centering
+\epsfig{file=syscon.eps, width=\textwidth}
+\caption{System Context Diagram}
+\label{AreqSyscon}
+\end{figure}
+
+Figure~\ref{AreqSyscon} shows the context that PMGT will normally fit into.
+A circle represents an external entity outside the system, an embedding application in this case. The rectangle is the system itself. Arrows represent the data flows between them.
+
+The \emph{input}: $M^{\mbox{IN}}\times I$
+
+The \emph{output}: $M^{\mbox{OUT}}$.
+
+PMGT has the following function:
+\begin{quote}
+A mesh $M^{\mbox{IN}}$ and some refining/coarsening instructions $I$ are given. PMGT generates a refined/coarsened mesh $M^{\mbox{OUT}}$ according to the instructions $I$.
+\end{quote}
+%\begin{quotation}
+
+%\end{quotation}
+
+\subsection {User Characteristics}\label{AreqUserchar}
+The target user group of PMGT includes both software designers, who intend to embed this library in their applications, and theoreticians, who are involved in parallel mesh generation. A user of PMGT is expected to be familiar with the notion/knowledge of mesh creation. PMGT is a library used by other applications. Therefore, users should not be novices in terms of software design. The prerequisite software design knowledge are equivalent to that of a senior undergraduate student in science or engineering who took an introductory course on programming. For example, they should be comfortable with compilation of the programming language in which PMGT is written, be familiar with embedding a library in their software, $etc.$
+
+\subsection{System Constraints}
+This system is intended to be built on the Shared Hierarchical Academic Research Computing Network (SHARCNET).
+SHARCNET is structured as a ``cluster of clusters'' across South Central Ontario, designed to meet the computational needs of researchers in a diverse number of research areas and to facilitate the development of leading-edge tools for high performance computing (HPC) grids.
+
+Large production clusters, located at the Universities of Western Ontario, Guelph and McMaster, house over 400 HP/Compaq
+Alpha processors and large symmetric multiprocessor computers. Windsor and Wilfrid Laurier host smaller development
+clusters (8 processors), which enable researchers to develop and test code before moving to one of the larger clusters.
+A glance of SHARCNET systems is shown in Table \ref{AreqSharcnet}. Note that the network is constantly being updated. Detailed information can be found at \citet{sharcnet2006}.
+\begin{table}[htbp]
+\centering
+\begin{tabular}{p{0.2\textwidth}|p{0.2\textwidth}|p{0.1\textwidth}|p{0.1\textwidth}|p{0.25\textwidth}}
+\hline \hline
+System & Make & Type & CPUs & OS \\
+\hline
+bala & Compaq & Cluster & 8 & Red Hat Linux 7.2\\
+cat & Unknown & Cluster & 162 & Red Hat Linux 8 \\
+goblin & Sun & Cluster & 56 & Fedora Core 2 \\
+hammerhead & Compaq & Cluster & 112 & Red Hat Linux 7.2 \\
+idra & Compaq SC & Cluster & 128 & Tru64 \\
+mako & HP & Cluster & 16 & Fedora Core 2 \\
+tiger & Compaq & Cluster & 8 & Red Hat Linux 7.2 \\
+typhon & Compaq & SMP & 16 & Tru64 \\
+wobbe & Unknown & Cluster & 193 & Red Hat Linux 8 \\
+TOTALS & & & 699 \\
+\hline \hline
+\end{tabular}
+\caption{A Glance at the SHARCNET System}
+\label{AreqSharcnet}
+\end{table}
+
+\section{Specific System Requirements \label{AreqSecSSR}}
+
+This section describes the system requirements in detail. After the problem is clearly and unambiguously stated, some solution characteristics are specified. Non-functional requirements are also included in this section. The symbol $:=$ is used to indicate type definition. The notation for set building and expressions used in this section follows \citet{Gries1993}. To define the notation, first let $x$ be a list of dummies, $t$ a type, $R$ a predicate, $E$ an expression, $*$ an operator, and $P$ a predicate. Notation $\{ x:t\ |\ R:E\}$ represents a set of values that result from evaluating $E[x:=v]$ in the state for each value $v$ in $t$ such that $R[x:=v]$ holds in that state. Expression $(*x:t\ |\ R:P)$ denotes the application of operator $*$ to the values $P$ for all $x$ in $t$ for which range $R$ is true.
+
+\subsection{Problem Description \label{AreqSecPD}}
+The problems (goals) specified in this subsection represent ideal general models. The problems are simplified by introducing some assumptions, which are listed in Section \ref{AreqSolution}.
+
+\subsubsection{Background Overview}
+Many physical problems of importance to scientists and engineers are modeled as a set of Partial Differential Equations (PDEs). In most practical cases, it is necessary to solve the PDEs numerally. Numerical methods to solve PDEs frequently require that the domain of interest be divided into a mesh, which is a set of small, simple elements that cover the computational domain. In some applications, a single mesh is generated and used many times; in this case the processing time spent on mesh construction is not critical and a relatively slow, sequential algorithm suffices \citep{Ruppert1993}. However, some applications need adaptive meshing, which requires that the meshes be generated once and then modified many times. For instance, adaptive meshing is used for reliable Finite Element Analysis (FEA) using a posterrori error estimation \citep{Zienkiewicz2005}. The increased mesh interaction for adaptive meshing means an increased need for speed of managing the mesh data which suggest employing parallel processing techniques. Although generating a mesh using multiple processors is complicated, it can offer considerable speed-up over sequential processing. In addition, some FEA applications are implemented on multiple processors. If the adaptive mesh can be generated in multiple processors as well, the mesh data can remain on the local processors. Potentially, time to be used will be significantly reduced.
+
+\subsubsection{Goal Statements}
+There are two related goals for PMGT.
+\begin{description}
+\item[\refstepcounter{goalnum}\gthegoalnum \label{gRefining}:] Given a mesh $M^{\mbox{IN}}$ and instructions $I$ on how to refine the mesh, PMGT should generate a refined mesh $M^{\mbox{OUT}}$ according to the instructions $I$.
+\item[\refstepcounter{goalnum}\gthegoalnum \label{gCoarsening}:]Given a mesh $M^{\mbox{IN}}$ and instructions $I$ on how to coarsen the mesh, PMGT should generate a coarsened mesh $M^{\mbox{OUT}}$ according to the instructions $I$.
+\end{description}
+
+\subsection{Solution Characteristics Specification\label{AreqSolution}}
+The goals stated in the last section are too general to achieve. In this section, the assumptions are specified first to reduce the scope of the software. Second, the theoretical models for the goals are described. Third, data definitions are given to assist with defining the theoretical models. Finally, the system behaviour is summarized.
+\subsubsection{Assumptions}
+\begin{description}
+\item [\refstepcounter{assnum} \atheassnum \label{aDimension}:]PMGT focuses on a 2D domain.
+\item[\refstepcounter{assnum} \atheassnum \label{aClosed}:]The input and output meshes are bounded.
+\item [\refstepcounter{assnum} \atheassnum \label{aUnstructured}:]The input and output meshes are unstructured.
+\item[\refstepcounter{assnum} \atheassnum \label{aConformal}:]The input and output meshes are conformal.
+\item[\refstepcounter{assnum} \atheassnum \label{aElmShape}:]The elements of input and output meshes are triangles.
+\item[\refstepcounter{assnum} \atheassnum \label{aValidMesh}:] The initial mesh is valid.
+\end{description}
+
+\subsubsection{Theoretical Model}
+The theoretical models corresponding to the goals given in Section \ref{AreqSecPD} describes the relationship between the input mesh ($M^{\mbox{IN}}$) and the output mesh ($M^{\mbox{OUT}}$). The meshes are assumed to be embedded in a 2D space.
+\begin{description}
+\item[\refstepcounter{tmnum} \tmthetmnum \label{tmRefining}:] Refining Mesh
+\begin{description}
+\item [\emph{Input}:] $M^{\mbox{IN}}$: {\tt MeshT}, $I$: {\tt RCinstructionT}
+\item [\emph{Output}:] $M^{\mbox{OUT}}$: {\tt MeshT}
+\end{description}
+The following behavior is specified:
+\begin{itemize}
+\item {\it Refined}($M^{\mbox{OUT}},\ M^{\mbox{IN}}$)
+\end{itemize}
+That is, the output mesh is a refined version of the input mesh.
+\item[\refstepcounter{tmnum} \tmthetmnum \label{tmCoarsening}:] Coarsening Mesh
+\begin{description}
+\item [\emph{Input}:] $M^{\mbox{IN}}$: {\tt MeshT}, $I$: {\tt RCinstructionT}
+\item [\emph{Output}:] $M^{\mbox{OUT}}$: {\tt MeshT}
+\end{description}
+The following behavior is specified:
+\begin{itemize}
+\item {\it Coarsened}($M^{\mbox{OUT}},\ M^{\mbox{IN}}$)
+\end{itemize}
+That is, the output mesh is a coarsened version of the input mesh.
+\end{description}
+
+\subsubsection{Data Definitions}
+The data definitions below are organized so that a definition listed in the beginning may be used to define a data item listed after it.
+\begin{description}
+\item [VertexT (\refstepcounter{ddnum} \dtheddnum \label{dVertexT}):] A vertex is represented by two real numbers, which are its $x$ coordinate and $y$ coordinate. More formally,\\
+{\tt VertexT} := tuple of ($x: \mathbb{R},\ y: \mathbb{R}$).
+
+\item [EdgeT (\refstepcounter{ddnum} \dtheddnum \label{dEdgeT}):] An edge is represented by a set of {\tt VertexT}. More formally,\\
+{\tt EdgeT} := set of {\tt VertexT}.
+
+\item [ValidEdge (\refstepcounter{ddnum} \dtheddnum \label{dValidEdge}):] An edge is valid if the edge is a line segment (that is, the set has two elements). More formally, \\
+{\it ValidEdge}: {\tt EdgeT} $\rightarrow \mathbb{B}$\\
+{\it ValidEdge}($e$: {\tt EdgeT}) $\equiv \# e = 2$
+
+\item [CellT (\refstepcounter{ddnum} \dtheddnum \label{dCellT}):] A cell is represented by a set of $VertexT$. More formally, \\
+{\tt CellT} := set of {\tt VertexT}
+
+\item [Area (\refstepcounter{ddnum} \dtheddnum \label{dArea}):] The area of a triangle whose apexes are elements of a cell. More formally, \\
+{\it Area}: {\tt CellT} $\rightarrow \mathbb{R}$\\
+{\it Area}($c$: {\tt CellT}) $\equiv \Sigma v1,v2,v3$: {\tt VertexT} $|\ v1\in c \wedge v2\in c \wedge v3\in c \\
+\wedge v1\neq v2 \wedge v2\neq v3 \wedge v3\neq v1:\\
+\frac{1}{12}* |v1.x*v2.y - v2.x*v1.y +\\
+v2.x*v3.y - v3.x*v2.y +\\
+v1.x*v3.y - v3.x*v1.y |$
+
+\item [ValidCell (\refstepcounter{ddnum} \dtheddnum \label{dValidCell}):] A cell is valid if the cell is a triangle (that is , the set has three elements) and the area of the triangle is greater than zero. More formally, \\
+{\it ValidCell}: {\tt CellT} $\rightarrow \mathbb{B}$\\
+{\it ValidCell}($c$: {\tt CellT}) $\equiv \# c = 3 \wedge$ {\it Area}($c$) $\geq 0$
+
+\item [MeshT (\refstepcounter{ddnum} \dtheddnum \label{dMeshT}):] A mesh is represented by a set of cells. More formally,\\
+{\tt MeshT} := set of {\tt CellT}.
+
+\item [OnEdge (\refstepcounter{ddnum} \dtheddnum \label{dOnEdge}):] Checks if a vertex is on the line segment between two vertices (exclusive) of an edge. More formally,\\
+{\it OnEdge}: {\tt VertexT} $\times$ {\tt EdgeT} $\rightarrow \mathbb{B}$\\
+{\it OnEdge}($v$: {\tt VertexT}, $e$: {\tt EdgeT}) $\equiv \exists\ v1,\ v2$: {\tt VertexT} $|\\
+ v1 \in e \wedge v2 \in e \wedge v1 \neq v2 \wedge v \neq v1 \wedge v \neq v2:\\
+(v1.x < v.x \leq v2.x \wedge \\(v.y-v1.y)/(v.x-v1.x)=(v2.y-v1.y)/(v2.x-v1.x))$
+
+\item [BelongToCell (\refstepcounter{ddnum} \dtheddnum \label{dBelongToCell}):] Checks if an edge belongs to a cell. More formally, \\
+{\it BelongToCell}: {\tt VertexT} $\times$ {\tt CellT} $\rightarrow \mathbb{B}$\\
+{\it BelongeToCell}($e$: {\tt EdgeT}, $c$: {\tt CellT}) $\equiv \forall\ v$: {\tt VertexT} $|\ v\in e: v\in c$
+
+\item [Inside (\refstepcounter{ddnum} \dtheddnum \label{dInside}):] Checks if a point (of type VertexT) is inside of a cell. The {\em inside} checking is false if the point is on an edge of the cell or the point is a vertex of the cell. (The algorithm to check if a point is inside a polygon is from \citet{Blackpawn}.) More formally,\\
+{\it Inside}: {\tt VertexT} $\times$ {\tt CellT} $\rightarrow \mathbb{B}$\\
+{\it Inside}($v$: {\tt VertexT}, $c$: {\tt CellT}) $\equiv \exists\ v1,\ v2,\ v3$: {\tt VertexT} $|\\
+v1\in c \wedge v2\in c \wedge v3\in c \wedge v1\neq v2 \wedge v2\neq v3 \wedge v3 \neq v1:\\
+((v.y-v1.y)*(v2.x-v1.x)-(v.x-v1.x)*(v2.y-v1.y))*\\
+((v.y-v2.y)*(v3.x-v2.x)-(v.x-v2.x)*(v3.y-v2.y)) > 0 \wedge \\
+((v.y-v2.y)*(v3.x-v2.x)-(v.x-v2.x)*(v3.y-v2.y))*\\
+((v.y-v3.y)*(v1.x-v3.x)-(v.x-v3.x)*(v1.y-v3.y)) > 0$
+
+\item [Vertices (\refstepcounter{ddnum} \dtheddnum \label{dVertices}):] A set of all vetices of the mesh. More formally,\\
+{\it Vertices}: {\tt MeshT} $\rightarrow$ set of {\tt VertexT}\\
+{\it Vertices}($m$: {\tt MeshT}) $\equiv$ \{$v$: {\tt VertexT} $|$ ($\forall\ c$: {\tt CellT} $|\ c\ \in m :v\ \in c):v\}$
+
+\item [Edges (\refstepcounter{ddnum} \dtheddnum \label{dEdges}):] A set of all edges of the mesh. More formally, \\
+{\it Edges}: {\tt MeshT} $\rightarrow $ set of $EdgeT$\\
+{\it Edges}($m$: {\tt MeshT}) $\equiv \{v1,\ v2$: {\tt VertexT} $|\ (\forall c$: {\tt CellT} $|\ c \in m:\\ v1 \in c \wedge v2 \in c \wedge v1 \neq v2):\{v1, v2\}\}$
+
+\item [BoundaryEdges (\refstepcounter{ddnum} \dtheddnum \label{dBoundaryEdges}):]A set of edges are boundary edges if they form a boundary of a mesh. More formally,\\
+{\it BoundaryEdges}: {\tt MeshT} $\rightarrow $ set of $EdgeT$\\
+{\it BoundaryEdges}($m$: {\tt MeshT}) $\equiv \{ b$: {\tt EdgeT} $|\ b\in$ {\it Edges}($m$) $\wedge \\
+(\# \{c$: {\tt CellT} $|\ c\in m \wedge$ {\it BelongToCell}({\it b, c}): $c\}=1$): $b\}$
+
+\item [BoundaryVertices (\refstepcounter{ddnum} \dtheddnum \label{dBoundaryVertices}):] A set of boundary vertices of the mesh. More formally,\\
+{\it BoundaryVertices}: {\tt MeshT} $\rightarrow$ set of {\tt VertexT}\\
+{\it BoundaryVertices}($m$: {\tt MeshT}) $\equiv \\
+\{v$: {\tt VertexT} $|\ v \in$ {\it BoundaryEdges}($m$): $v\}$
+
+\item [Bounded (\refstepcounter{ddnum} \dtheddnum \label{dBounded}):] A mesh is bounded if the boundary edges form a closed polygon(all vertices of boundary edges belong to exactly two boundary edges). More formally, \\
+{\it Bounded}: {\tt MeshT} $\rightarrow \mathbb{B}$\\
+{\it Bounded}($m$: {\tt MeshT}) $\equiv \forall v$: {\tt VertexT} $|\ v\in$ {\it BoundaryVertices}($m$): \\
+($\# \{e$: {\tt EdgeT} $|\ e \in$ {\it BoundaryEdge}($m$) $\wedge v\in e: e\}=2)$
+
+\item [Conformal (\refstepcounter{ddnum} \dtheddnum \label{dConformal}):] In 2D, a mesh is conformal if the intersection of any two cells is either a vertex or an edge or empty. More formally,\\
+{\it Conformal}: {\tt MeshT} $\rightarrow \mathbb{B}$\\
+{\it Conformal}($m$: {\tt MeshT}) $\equiv \forall c1, c2$: {\tt CellT} $|\ c1\in m \wedge c2\in m \wedge c1\neq c2 : \\
+(\exists e$: {\tt EdgeT} $|\ e\in$ {\it Eeges}($m$): $(\exists v:$ {\tt VertexT} $|\ v\in$ {\it Vertices}($m$):\\
+$(c1\cap c2 = e \vee c1\cap c2 = v \vee c1\cap c2 = \emptyset) \wedge (\neg$ {\it OnEdge(v, e)) ))}
+
+\item [NoInteriorIntersect (\refstepcounter{ddnum} \dtheddnum \label{dNoInteriorIntersect}):] NoInteriorIntersect is true if a point in space (of type VertexT) is inside only one cell of the mesh. More formally,\\
+{\it NoInteriorIntersect}: {\tt MeshT} $\rightarrow \mathbb{B}$\\
+{\it NoInteriorIntersect}($m$: {\tt MeshT}) $\equiv \forall c1, c2$: {\tt CellT} $|\\ c1\in m \wedge c2\in m \wedge c1 \neq c2:
+ (\forall v$: {\tt VertexT} $|$ {\it Inside(v, c1)}: $\neg$ {\it Inside(v,c2))}
+
+\item [ValidMesh (\refstepcounter{ddnum} \dtheddnum \label{dValidMesh}):] A mesh is valid if the mesh is bounded, conformal, and any point is only inside one cell. More formally, \\
+{\it ValidMesh}: {\tt MeshT} $\rightarrow \mathbb{B}$\\
+{\it ValidMesh}($m$: {\tt MeshT}) $\equiv (\forall e$: {\tt EdgeT} $|\ e\in$ {\it Edges(m): ValidEdge(e))} \\
+$\wedge\ (\forall c$: {\tt CellT} $|\ c\in m$: {\it ValidCell(c))} $\wedge$\\
+{\it Bounded(m)} $\wedge$ {\it Conformal(m)} $\wedge$ {\it NoInteriorIntersect(m)}
+
+\item [CoveringUp (\refstepcounter{ddnum} \dtheddnum \label{dCoveringUp}):] True if two meshes covering up each other, that is, if all endpoints of the boundary edges of one mesh are on the boundary edges or are end points of the boundary edges of another mesh. More formally, \\
+{\it CoveringUp}: {\tt MeshT} $\times$ {\tt MeshT} $\rightarrow \mathbb{B}$\\
+{\it CoveringUp}($m1,\ m2$: {\tt MeshT}) $\equiv \forall v1,\ v2$: {\tt VertexT}, $| \\
+ v1 \in$ {\it BoundaryVertice(m1)} $\wedge\ v2\in$ {\it BoundaryVertices(m2)}: \\
+ $(\exists b1,\ b2$: {\tt EdgeT} $|\ b1\in$ {\it BoundaryEdges(m1)} $\wedge b2\in$ {\it BoundaryEdges(m2):
+ (OnEdge(v1, b2)} $\vee v1\in b2) \wedge$ {\it (OnEdge(v2, b1)} $\vee v2\in b1))$
+
+\item [InstructionT (\refstepcounter{ddnum} \dtheddnum \label{dInstructionT}):] The type of instructions is defined as:\\
+{\tt InstructionT} := \{{\tt REFINE, COARSEN, NOCHANGE}\}
+
+\item [CellInstructionT (\refstepcounter{ddnum} \dtheddnum \label{dCellInstructionT}):] The type of instructions on a cell is defined as:\\
+{\tt CellInstructionT}:= tuple of ({\it cell}: {\tt CellT}, {\it instr}: {\tt InstructionT})\\
+(For each cell, there is an instruction for refining, coarsening, or nochange.)
+
+\item [RCinstructionT (\refstepcounter{ddnum} \dtheddnum \label{dRCInstructionT}):] The type of instructions on a mesh is defined as:\\
+{\tt RCinstructionT}:= tuple of ({\it rORc}: {\tt InstructionT}, {\it cInstr}: set of {\tt CellInstructionT})\\
+(For each mesh, there is an instruction on whole mesh, and there are set of instruction on each cell.)
+
+\item [Refined (\refstepcounter{ddnum} \dtheddnum \label{dRefined}):] True if a mesh $M'$ is a refined mesh of a mesh $M$. More formally\\
+{\it Refined}: {\tt MeshT} $\times$ {\tt MeshT} $\times$ {\tt RCinstructionT} $\rightarrow \mathbb{B}$\\
+{\it Refined}({\it m', m}: {\tt MeshT}, {\it rc}: {\tt RCinstructionT}) $\equiv$ \\
+{\it rc.rORc} = {\tt REFINE} $\wedge$ {\it ValidMesh(m)} $\wedge$ {\it ValidMesh(m')} $\wedge$ \\
+{\it CoveringUp(m', m)} $\wedge \# m' \geq \#m$
+
+\item [Coarsened (\refstepcounter{ddnum} \dtheddnum \label{dCoarsened}):] True if a mesh $M'$ is a coarsened mesh of a mesh $M$. More formally \\
+{\it Coarsened}: {\tt MeshT} $\times$ {\tt MeshT} $\times$ {\tt RCinstructionT} $\rightarrow \mathbb{B}$\\
+{\it Coarsened}({\it m', m}: {\tt MeshT}, {\it rc}: {\tt RCinstructionT}) $\equiv$ \\
+{\it rc.rORc} = {\tt COARSEN} $\wedge$ {\it ValidMesh(m)} $\wedge$ {\it ValidMesh(m')} $\wedge$ \\
+{\it CoveringUp(m', m)} $\wedge \# m' \leq \# m$
+
+\end{description}
+
+\subsubsection{System Behaviour}
+System Behaviour, shown through functional requirements, defines what the software should do. The functional requirements, as well as nonfunctional requirements in Section \ref{nonFunReq}, partially come from \citet{Smith2004}. \citet{Smith2004} listed all requirements that are common for mesh generation systems. They also considered the difference between meshes in term of variabilities. However, the mesh generations analyzed by \citet{Smith2004} are targeted at full FEA applications. PMGT only manages the geometric information about the mesh, not other FEA related information, such as boundary condition and material property. Hence, only commonalities that is meaningful for PMGT are selected. Variabilities with parameters of variation that are suitable for PMGT are also considered. Other part of the requirements are obtained from Dr. Smith.
+
+New functional requirements, \emph{RCInstruction} (\fref{RCInstruction}) and \emph{Help} (\fref{Help}) are added. \fref{RCInstruction} is unique to PMGT and \fref{Help} facilities the non-functional requirements \emph{Usability} (\nref{Usability}).
+
+We specify both functional requirements and non-functional requirements in the tables. In each table, the field \emph{Description} gives a brief description of this requirement. It tells what PMGT should do to fulfill this requirement. There are two potential sources, shown in the \emph{Source} field, for each requirement. One source is from \citet{Smith2004}, and the other comes from Dr.~Smith. If the requirement is from \citet{Smith2004}, then this field will show the commonality number, with a prefix $C$ and the associated variability, shown by a prefix $V$. Where applicable, \emph{Related Data Definitions} and \emph{Related Theoretical Models} gives the numbers of related data definitions and the numbers of related theoretical models, respectively. These two field only appear for functional requirements. The \emph{Binding Time} field either shows scope time or run time. \emph{Scope time} means that this requirement is determined when the SRS is written. \emph{Run time} means that this requirement is determined when the system is running. \emph{History} records the time of creating and changing of the requirements.
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{RefiningMesh} \\
+{\bf Requirements Name} & \mi{RefiningMesh}\\ \hline
+Description & PMGT should have capabilities for refining an existing mesh.\\
+& {\it I.rORc} = {\tt REFINE} $\wedge$\\
+& {\it Refined}($M^{\mbox{OUT}},\ M^{\mbox{IN}})$\\
+Source & C1, V3\\
+Related Data Definitions & \dref{dInstructionT}, \dref{dRCInstructionT}, \dref{dRefined}\\
+Related Theoretical Models & \tmref{tmRefining}\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+ & Modified -- October, 2005. Change the name from ``ImprovingMesh'' to ``RefiningMesh''.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{CoarseningMesh} \\
+{\bf Requirements Name} & \mi{CoarseningMesh}\\ \hline
+Description & PMGT should have capabilities for coarsening an existing mesh.\\
+& {\it I.rORc} = {\tt COARSEN} $\wedge $\\
+& {\it Coarsened}$(M^{\mbox{OUT}}, M^{\mbox{IN}})$\\
+Source & C1, V3\\
+Related Data Definitions & \dref{dInstructionT}, \dref{dRCInstructionT}, \dref{dCoarsened}\\
+Related Theoretical Models & \tmref{tmCoarsening}\\
+Binding Time & Scope time\\
+History & Created -- October, 2006.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{RefiningOrCoarsening} \\
+{\bf Requirements Name} & \mi{RefiningOrCoarsening}\\ \hline
+Description & PMGT can either refine a given mesh to a refined mesh, or coarsen a mesh to a coarsened mesh. However, PMGT cannot do both refining and coarsening at the same time.\\
+Source & C1, V3\\
+Related Data Definitions & \dref{dInstructionT}, \dref{dRCInstructionT}, \dref{dRefined}, \dref{dCoarsened}\\
+Related Theoretical Models & \tmref{tmRefining}, \tmref{tmCoarsening}\\
+Binding Time & Run time\\
+History & Created -- October, 2006.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{MeshType} \\
+{\bf Requirements Name} & \mi{MeshType}\\ \hline
+Description & The mesh generated by PMGT is unstructured.\\
+Source & C1, V6\\
+Related Data Definitions & N/A \\
+Related Theoretical Models & N/A \\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{ElmShape} \\
+{\bf Requirements Name} & \mi{ElmShape}\\ \hline
+Description & The shape of the elements in both input and output meshes are triangles.\\
+& $\forall c1, c2$: {\tt CellT} $|$\\
+& $c1\in M^{\mbox{IN}} \wedge c2\in M^{\mbox{OUT}}:$\\
+& $\# c1=3\wedge$ {\it Area}$(c1)>0 \wedge $\\
+& $\# c2 = 3 \wedge$ {\it Area}$(c2)>0$\\
+Source & C1, V9\\
+Related Data Definitions & \dref{dCellT}, \dref{dArea}\\
+Related Theoretical Models & \tmref{tmRefining}, \tmref{tmCoarsening} \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+& Modified -- October, 2006. Take out the requirement for generating quadrilateral meshes.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{DomainDimension} \\
+{\bf Requirements Name} & \mi{DomainDimension}\\ \hline
+Description & The computational domain is in 2D space.\\
+Source & C1, V13\\
+Related Data Definitions & N/A \\
+Related Theoretical Models &\tmref{tmRefining}, \tmref{tmCoarsening} \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{Conformal} \\
+{\bf Requirements Name} & \mi{Conformal}\\ \hline
+Description & Both input and output meshes are conformal.\\
+& {\it Conformal}$(M^{\mbox{IN}}) \ \wedge$ \\
+& {\it Conformal}$(M^{\mbox{OUT}})$\\
+Source & C1, V18\\
+Related Data Definitions & \dref{dConformal} \\
+Related Theoretical Models & N/A \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+& Modified -- October, 2006. Take out the requirement for generating non-conformal meshes.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{InputDefinition} \\
+{\bf Requirements Name} & \mi{InputDefinition}\\ \hline
+Description & The input of PMGT should be provided by the embedding application.\\
+Source & C8\\
+Related Data Definitions & \dref{dMeshT}, \dref{dInstructionT}, \dref{dRCInstructionT} \\
+Related Theoretical Models & \tmref{tmRefining}, \tmref{tmCoarsening} \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+ & Modified--October 2005. Change the name from ``Input'' to ``InputDefinition'' to clarify that this requirements is about the source of the input. \\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{RCInstruction} \\
+{\bf Requirements Name} & \mi{RCInstruction}\\ \hline
+Description & The Instruction on how to refine/coarsen a mesh includes the instruction of whether to refine or coarsen the mesh and an individual instruction for each element of the the mesh to indicate refining, coarsening, or no change.\\
+Source & Dr. Smith\\
+Related Data Definitions & \dref{dInstructionT}, \dref{dCellInstructionT}, \dref{dRCInstructionT} \\
+Related Theoretical Models & \tmref{tmRefining}, \tmref{tmCoarsening} \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{OutputStorage} \\
+{\bf Requirements Name} & \mi{OutputStorage}\\ \hline
+Description & The output of PMGT is stored in memory or in files or in both memory and files.\\
+Source & C12, Dr. Smith\\
+Related Data Definitions & N/A \\
+Related Theoretical Models & N/A \\
+%Depending on & None\\
+Binding Time & Run time\\
+History & Created -- June, 2005.\\
+ & Modified -- October 2005. Change the name from ``Output'' to ``OutputStorage'' to clarify that this requirements is about the storage of the output.\\
+ & Modified -- October 2006. Add the requirement of storing the output mesh in files or both memory and files.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{VertexUniqueID} \\
+{\bf Requirements Name} & \mi{VertexUniqueID}\\ \hline
+Description & Each vertex in the output file has a unique identifier.\\
+Source & C2\\
+Related Data Definitions & N/A \\
+Related Theoretical Models & N/A \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{ElmUniqueID} \\
+{\bf Requirements Name} & \mi{ElmUniqueID}\\ \hline
+Description & Each element in the output file has a unique identifier.\\
+Source & C3\\
+Related Data Definitions & N/A \\
+Related Theoretical Models & N/A \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{ElmTopology} \\
+{\bf Requirements Name} & \mi{ElmTopology}\\ \hline
+Description & The topology of an element in the output file is given by the connectivity of its set of vertices.\\
+Source & C4\\
+Related Data Definitions & N/A \\
+Related Theoretical Models & N/A \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+
+
+\vspace{1cm}
+
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{OutElmOrder} \\
+{\bf Requirements Name} & \mi{OutElmOrder}\\ \hline
+Description & The element information in output files is listed in ascending order.\\
+Source & C13, V34\\
+Related Data Definitions & N/A \\
+Related Theoretical Models & N/A \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{OutVertexOrder} \\
+{\bf Requirements Name} & \mi{OutVertexOrder}\\ \hline
+Description & The vertex information, such as the coordinates, in output files is listed in ascending order.\\
+Source & C14, V35\\
+Related Data Definitions & N/A \\
+Related Theoretical Models & N/A \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+
+\vspace{1cm}
+
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{funnum} \fthefunnum \label{Help} \\
+{\bf Requirements Name} & \mi{Help}\\ \hline
+Description & Helps on documenting the interface and the functionality of each function should be provided.\\
+Source & Dr. Smith\\
+Related Data Definitions & N/A \\
+Related Theoretical Models & N/A \\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+ & Modified -- October 2005. Add the requirement of documenting functionality of each function.\\
+ & Modified -- October, 2006. Field for ``Related Data Definitions'' and ``Related Theoretical Models'' are added.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\subsection{Non-functional Requirements \label{nonFunReq}}
+All non-functional requirements listed in \citet{Smith2004} are selected except for C16, which is solution tolerance, since a mesh refined/coarsened by different algorithms may have different solutions, but all of these solutions can still be valid. All potential output meshes are valid as long as the output meshes are covering/covered up meshes of the original mesh, and they are refined/coarsened according to the RCInstruction. The resulting mesh is difficult to measure in terms of \emph{solution tolerance}. Three new non-functional requirements, which are \emph{LookAndFeel} (\nref{LookAndFeel}), \emph{Usability} (\nref{Usability}), and \emph{Maintainability} (\nref{Maintainability}), are added. These requirements are mentioned in \citet{Lai2004}.
+
+PMGT is difficult to validate. One reason is that the solution for refining/coarsening a mesh is unknown, as mentioned above. The other reason is that it is difficult to write validatable requirements, especially for nonfunctional requirements. For example, what is the proper way for specifying the requirement of \emph{Usability} (\nref{Usability}) of PMGT? On the one hand, that \emph{the software should easy to use} is not validatable. On the other hand, that \emph{a person should be able to use the software in two days} is validatable. However, the measurement, \emph{two days}, often lacks a justifiable rationale.
+
+The approach to validate this kind of requirements are to compare it with other software with similar functionality. Phrases that are in italics and capitalized, such as \emph{MANPROP}, represent constant defined in Section \ref{SecAC}. Usually, these constants come from other applications with similar functionalities. For example, the \emph{Usability} requirement of PMGT is presented as follows:
+\begin{quotation}
+This system should be easy to use. Users with the background specified in Section~\ref{AreqUserchar} should take \emph{LEARNTIME} to reproduce an example mesh, which is specified by the test case \cref{ATCrm} in the Appendix \ref{Atest}.
+\end{quotation}
+First, more general requirement is given. Then, a suggestion to reproduce an example mesh is specified. The constant \emph{LEARNTIME} is defined as the time to produce the same mesh for users with the same background using AOMD.
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{nfnum} \nthenfnum \label{Performance} \\
+{\bf Requirements Name} & \mi{Performance}\\ \hline
+Description & Refining/coarsening a mesh using multiple processors should be faster than when using a single processor. In addition, the performance of PMGT should be comparable with that of similar applications. The execution time to refine an example mesh, which is specified by the test case \cref{ATCrm} in the Appendix \ref{Atest}.\\
+Source & C15, V39\\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{nfnum} \nthenfnum \label{Precision} \\
+{\bf Requirements Name} & \mi{Precision}\\ \hline
+Description & The number of decimal digits should agree with the IEEE standard for floating-point numbers.\\
+Source & C17, V41\\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005.\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{nfnum} \nthenfnum \label{Exception} \\
+{\bf Requirements Name} & \mi{Exception}\\ \hline
+Description & Run-time exception handling should check at least the following exceptions: division by zero, redundant vertices, redundant edges, redundant cells.\\
+Source & C18, V42\\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{nfnum} \nthenfnum \label{Portability} \\
+{\bf Requirements Name} & \mi{Portability}\\ \hline
+Description & PMGT should build on a platform with access to SHARCNET or on a the system that has similar architecture to SHARCNET. The memory capacity should be \emph{MEMCAP}.\\
+Source & C19, V37, V38\\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{nfnum} \nthenfnum \label{LookAndFeel} \\
+{\bf Requirements Name} & \mi{LookAndFeel}\\ \hline
+Description & PMGT should follow the programming conventions of the language in which the application is coded in.\\
+Source & Dr. Smith\\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{nfnum} \nthenfnum \label{Usability} \\
+{\bf Requirements Name} & \mi{Usability}\\ \hline
+Description & This system should be easy to use. Users with the background specified in Section~\ref{AreqUserchar} should take \emph{LEARNTIME} to reproduce an example mesh, which is specified in the Appendex \ref{Atest}. \\
+Source & Dr. Smith\\
+%Depending on & None\\
+Binding Time & Scope time\\
+History & Created -- June, 2005\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Requirements Number} & \refstepcounter{nfnum} \nthenfnum \label{Maintainability} \\
+{\bf Requirements Name} & \mi{Maintainability}\\ \hline
+Description & The system should be developed in the way that the effort spent to maintain the system or to add in features would be minimum. The redevelopment time to add a new algorithm to coarsen meshes in PMGT should be \emph{MANPROP}.\\
+Source & Dr. Smith\\
+Binding Time & Scope time\\
+History & Created -- June, 2005\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\section{Other System Issues \label{AreqSecOSI}}
+This section includes some other supporting information that might contribute to the success or failure of the system development. The following factors are considered:
+\begin{itemize}
+\item Open issues are statements of factors that are uncertain and might make significant difference to the system.
+ \item Off-the-shell solutions are existing systems and/or components bought or borrowed. They could be the potential solutions.
+ \item Waiting rooms provide a blueprint of how the system will be extended.
+\end{itemize}
+
+\subsection{Open Issues}
+There are no open issues for PMGT at this stage.
+\subsection{Off-the-shelf Solutions}
+The following programs may be used in PMGT.
+\begin{itemize}
+\item AOMD: a mesh management library (or database) that is able to provide a variety of services for mesh users \citep{AOMD2006}.
+\end{itemize}
+
+\subsection{Waiting Rooms}
+Here, we list the possible changes that can affect the extension of the system. These changes are related to the assumptions specified in Section \ref{AreqSolution}.
+\begin{enumerate}
+\item PMGT may produce both structured and unstructured meshes.
+\item PMGT may produce both conformal and nonconformal meshes.
+\item The elements of input and output mesh may be of a shape other than triangles.
+\item The system may deal with invalid input mesh.
+\item The system may accommodate a mixed mesh.
+\item The system may accommodate a hybrid mesh.
+\item The system may deal with a 3D problem domain.
+\end{enumerate}
+\section{Traceability Matrix \label{AreqSecTM}}
+The traceability matrix defined in this section gives a big picture of the associations among goals, assumptions, data definitions, theoretical models, and functional requirements. Goals are ideal general models. After assumptions are applied, these goals are restricted to problems that can be solved by PMGT. Data definitions and theoretical models are used to describe the requirements. The matrix is too big to fit one page. For the sake of clarity, it is split into three parts in five tables, which are Table \ref{AreqTM11}, Table \ref{AreqTM12}, Table \ref{AreqTM21}, Table \ref{AreqTM22}, and Table \ref{AreqTM3}. In addition, only items that have a relation with items in the same part are listed. If there is a \checkmark in a cell, it means that if the goal, or the assumption, or the theoretical model, or the data definition, or the requirement in the corresponding column changes, the assumption, or the data definition, or the theoretical model, or the requirement in the corresponding row should also change.
+
+\begin{table}[ht!]
+\centering
+\begin{tabular}{|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|}
+\hline
+&\gref{gRefining} & \gref{gCoarsening} & \aref{aDimension} & \aref{aClosed} & \aref{aUnstructured} & \aref{aConformal} & \aref{aElmShape} & \aref{aValidMesh}& \tmref{tmRefining} & \tmref{tmCoarsening}\\
+\hline\hline
+\aref{aDimension}& \checkmark & \checkmark & \checkmark & & & & & & & \\\hline %a1
+\aref{aClosed}& \checkmark & \checkmark & & \checkmark & & & & & & \\\hline %a2
+\aref{aUnstructured}& \checkmark & \checkmark & & & \checkmark & & & & & \\\hline %a3
+\aref{aConformal}& \checkmark & \checkmark & & & & \checkmark & & & & \\\hline %a4
+\aref{aElmShape}& \checkmark & \checkmark & \checkmark & & & & \checkmark & & &\\\hline %a5
+\aref{aValidMesh}& \checkmark & \checkmark & & & & & & \checkmark & &\\\hline %a5
+\hline
+\dref{dVertexT}& \checkmark & \checkmark & \checkmark & & & & & & & \\\hline %d1
+\dref{dEdgeT}& \checkmark & \checkmark & & & & & & & &\\\hline%d2
+\dref{dValidEdge}& \checkmark & \checkmark & & & & & & & &\\\hline%d2
+\dref{dCellT}& \checkmark & \checkmark & \checkmark & & & & \checkmark & & & \\\hline%d3
+\dref{dArea}& \checkmark & \checkmark & \checkmark & & & & \checkmark & & & \\\hline%d3
+\dref{dValidCell}& \checkmark & \checkmark & \checkmark & & & & \checkmark & & & \\\hline%d3
+\dref{dMeshT}& \checkmark & \checkmark & & & & & & & & \\\hline%d4
+\dref{dOnEdge}& \checkmark & \checkmark & \checkmark & & & & & & & \\\hline%d4
+\dref{dBelongToCell}& \checkmark & \checkmark & \checkmark& & & & & & & \\\hline%d4
+\dref{dInside}& \checkmark & \checkmark & \checkmark & & & & \checkmark & & & \\\hline%d4
+\dref{dVertices}& \checkmark & \checkmark & & & & & & & & \\\hline%d4
+\dref{dEdges}& \checkmark & \checkmark & \checkmark & & & & & \checkmark & & \\\hline%d4
+\dref{dBoundaryEdges}& \checkmark & \checkmark & \checkmark & & & & & & &\\\hline%d5
+\dref{dBoundaryVertices}& \checkmark & \checkmark & \checkmark & & & & & & &\\\hline%d5
+\dref{dBounded}& \checkmark & \checkmark & \checkmark & \checkmark & & & & & &\\\hline%d6
+\dref{dConformal}& \checkmark & \checkmark & \checkmark & & & \checkmark & & & &\\\hline%d7
+\dref{dNoInteriorIntersect}& \checkmark & \checkmark & \checkmark &\checkmark & & & & & &\\\hline%d3
+\dref{dValidMesh}& \checkmark & \checkmark & & & & & & & &\\\hline%d3
+\dref{dInstructionT}& \checkmark & \checkmark & & & & & & & &\\\hline%d3
+\dref{dCellInstructionT}& \checkmark & \checkmark & & & & & & & &\\\hline%d11
+\dref{dRCInstructionT}& \checkmark & \checkmark & & & & & & & &\\\hline%d11
+\dref{dCoveringUp}& \checkmark & \checkmark & \checkmark & \checkmark & & & & & &\\\hline%d8
+\dref{dRefined}& \checkmark & & & & & & & & &\\\hline%d9
+\dref{dCoarsened}& & \checkmark & & & & & & & &\\\hline%d10
+\hline
+\tmref{tmRefining} & \checkmark & & \checkmark & & & & & & \checkmark& \\\hline
+\tmref{tmCoarsening}& & \checkmark & \checkmark & & & & & & &\checkmark\\\hline
+\end{tabular}
+\caption{Traceability Matrix (PART I): Goals, Assumptions, Theoretical Models, Data Definitions, and Requirements (I)}
+\label{AreqTM11}
+\end{table}
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|}
+\hline
+&\gref{gRefining} & \gref{gCoarsening} & \aref{aDimension} & \aref{aClosed} & \aref{aUnstructured} & \aref{aConformal} & \aref{aElmShape} & \aref{aValidMesh}& \tmref{tmRefining} & \tmref{tmCoarsening}\\
+\hline\hline
+\fref{RefiningMesh}& \checkmark & & & & & & & & \checkmark & \\\hline%f2
+\fref{CoarseningMesh}& & \checkmark & & & & & & & &\checkmark \\\hline%f3
+\fref{RefiningOrCoarsening}& \checkmark & \checkmark & & & & & & & \checkmark & \checkmark\\\hline%f1
+\fref{MeshType}& & & & & \checkmark & & & & & \\\hline%f4
+\fref{ElmShape}& \checkmark & \checkmark & \checkmark & & & & \checkmark & & \checkmark & \checkmark \\\hline%f5
+\fref{DomainDimension}& \checkmark & \checkmark & \checkmark & & & & & & \checkmark & \checkmark \\\hline%f6
+\fref{Conformal}& \checkmark & \checkmark & & & & \checkmark & & & & \\\hline%f7
+\fref{InputDefinition}& \checkmark & \checkmark & & & & & & & \checkmark & \checkmark\\\hline%f11
+\fref{RCInstruction}& \checkmark & \checkmark & & & & & && \checkmark & \checkmark \\\hline%f12
+\fref{OutputStorage}& \checkmark & \checkmark & & & & & & & & \\\hline%f13
+\fref{Help} & \checkmark & \checkmark & & & & & & & & \\\hline%f16
+\end{tabular}
+\caption{Traceability Matrix (PART I): Goals, Assumptions, Theoretical Models, Data Definitions, and Requirements (II)}
+\label{AreqTM12}
+\end{table}
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{|p{0.05\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|}
+\hline
+&\dref{dVertexT} & \dref{dEdgeT} & \dref{dValidEdge} & \dref{dCellT} & \dref{dArea} & \dref{dValidCell} & \dref{dMeshT} & \dref{dOnEdge}& \dref{dBelongToCell}& \dref{dInside} & \dref{dVertices} & \dref{dEdges} \\
+\hline\hline
+\dref{dVertexT}& \checkmark & & & & & & & & & & & \\\hline %d1
+\dref{dEdgeT}& \checkmark & \checkmark & & & & & & & & & & \\\hline%d2
+\dref{dValidEdge}& & \checkmark & \checkmark & & & & & & & & & \\\hline%d2
+\dref{dCellT}& \checkmark & & & \checkmark & & & & & & & & \\\hline%d3
+\dref{dArea}& \checkmark & & & & \checkmark & & & & & & & \\\hline%d3
+\dref{dValidCell}& & & & \checkmark & \checkmark & \checkmark & & & & & & \\\hline%d3
+\dref{dMeshT}& & & & \checkmark & & & \checkmark & & & & & \\\hline%d4
+\dref{dOnEdge}& \checkmark & \checkmark & & & & & & \checkmark & & & & \\\hline%d4
+\dref{dBelongToCell}& \checkmark & \checkmark & & \checkmark & & & & & \checkmark& & & \\\hline%d4
+\dref{dInside}& \checkmark & & & \checkmark & & & & & & \checkmark & & \\\hline%d4
+\dref{dVertices}& \checkmark & & & \checkmark & & & \checkmark & & & & \checkmark & \\\hline%d4
+\dref{dEdges}& \checkmark & \checkmark & & \checkmark & & & \checkmark & & & & & \checkmark \\\hline%d4
+\dref{dBoundaryEdges}& & \checkmark & & \checkmark & & & & & \checkmark & & & \checkmark \\\hline%d5
+\dref{dBoundaryVertices}& \checkmark & & & & & & \checkmark & & & & & \\\hline%d5
+\dref{dBounded}& \checkmark & \checkmark & & & & & \checkmark & & & & & \\\hline%d6
+\dref{dConformal}& \checkmark & \checkmark& & \checkmark & & & \checkmark & & & & \checkmark & \checkmark\\\hline%d7
+\dref{dNoInteriorIntersect}& \checkmark & & & \checkmark & & & \checkmark & & & \checkmark & & \\\hline%d6
+\dref{dValidMesh}& & & \checkmark & & & \checkmark & \checkmark & & & & & \\\hline%d6
+\dref{dCoveringUp}& \checkmark & \checkmark & & & & & \checkmark & \checkmark & & & & \\\hline%d8
+\dref{dInstructionT}& & & & & & & & & & & & \\\hline%d10
+\dref{dCellInstructionT}& & & & \checkmark & & & & & & & & \\\hline%d11
+\dref{dRCInstructionT}& & & & & & & & & & & & \\\hline%d11
+\dref{dRefined}& & & & & & & & & & & & \\\hline%d9
+\dref{dCoarsened}& & & & & & & & & & & & \\\hline%d10
+\hline
+\tmref{tmRefining}& & & & & & & \checkmark & & & & & \\\hline%f2
+\tmref{tmCoarsening}& & & & & & & \checkmark & & & & & \\\hline%f3
+\hline
+\fref{RefiningMesh}& & & & & & & & & & & & \\\hline%f2
+\fref{CoarseningMesh}& & & & & & & & & & & & \\\hline%f3
+\fref{RefiningOrCoarsening}& & & & & & & & & & & & \checkmark \\\hline%f1
+\fref{ElmShape}& & & & \checkmark & & \checkmark & & & & & & \\\hline%f5
+\fref{Conformal}& & & & & & & & & & & & \\\hline%f7
+\fref{InputDefinition}& & & & & & & \checkmark & & & & & \\\hline%f11
+\fref{RCInstruction}& & & & & & & & & & & & \\\hline%f12
+\end{tabular}
+\caption{Traceability Matrix (PART II): Data Definitions and Requirements (I)}
+\label{AreqTM21}
+\end{table}
+
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{|p{0.05\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|p{0.04\textwidth}|}
+\hline
+&\dref{dBoundaryEdges} & \dref{dBoundaryVertices} & \dref{dBounded} & \dref{dConformal} & \dref{dNoInteriorIntersect} & \dref{dValidMesh} & \dref{dCoveringUp} & \dref{dInstructionT}& \dref{dCellInstructionT}& \dref{dRCInstructionT} & \dref{dRefined} & \dref{dCoarsened} \\
+\hline\hline
+\dref{dBoundaryEdges}& \checkmark & & & & & & & & & & & \\\hline%d5
+\dref{dBoundaryVertices}& \checkmark & \checkmark & & & & & & & & & & \\\hline%d5
+\dref{dBounded}& \checkmark & \checkmark & \checkmark & & & & & & & & & \\\hline%d6
+\dref{dConformal}& & & & \checkmark & & & & & & & & \\\hline%d7
+\dref{dNoInteriorIntersect}& & & & & \checkmark & & & & & & & \\\hline%d6
+\dref{dValidMesh}& & & \checkmark & \checkmark & \checkmark & \checkmark & & & & & & \\\hline%d6
+\dref{dCoveringUp}& \checkmark & \checkmark & & & & & \checkmark & & & & & \\\hline%d8
+\dref{dInstructionT}& & & & & & & & \checkmark & & & & \\\hline%d10
+\dref{dCellInstructionT}& & & & & & & & \checkmark & \checkmark & & & \\\hline%d11
+\dref{dRCInstructionT}& & & & & & & & \checkmark & \checkmark & \checkmark & & \\\hline%d11
+\dref{dRefined}& & & & & & \checkmark & \checkmark & \checkmark & & \checkmark& \checkmark & \\\hline%d9
+\dref{dCoarsened}& & & & & & \checkmark & \checkmark & \checkmark & & \checkmark & & \checkmark\\\hline%d10
+\hline
+\tmref{tmRefining}& & & & & & & & & & \checkmark & \checkmark& \\\hline%f2
+\tmref{tmCoarsening}& & & & & & & & & & \checkmark & & \checkmark \\\hline%f3
+\hline
+\fref{RefiningMesh}& & & & & & & & \checkmark & & \checkmark & \checkmark & \\\hline%f2
+\fref{CoarseningMesh}& & & & & & & & \checkmark & & \checkmark & & \checkmark \\\hline%f3
+\fref{RefiningOrCoarsening}& & & & & & & & \checkmark & & \checkmark & \checkmark & \checkmark \\\hline%f1
+\fref{ElmShape}& & & & & & & & & & & & \\\hline%f5
+\fref{Conformal}& & & & \checkmark & & & & & & & & \\\hline%f7
+\fref{InputDefinition}& & & & & & & & \checkmark & & \checkmark & & \\\hline%f11
+\fref{RCInstruction}& & & & & & & & \checkmark & \checkmark & \checkmark & & \\\hline%f12
+\end{tabular}
+\caption{Traceability Matrix (PART II): Data Definitions and Requirements (II)}
+\label{AreqTM22}
+\end{table}
+
+
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|p{0.05\textwidth}|}
+\hline
+& \fref{RefiningMesh}& \fref{CoarseningMesh}& \fref{DomainDimension}&\fref{InputDefinition}&\fref{OutputStorage}& \nref{Usability}\\
+\hline\hline
+\fref{RefiningOrCoarsening}& \checkmark & \checkmark & & & & \\\hline%f1
+\fref{ElmShape}& & & \checkmark & & & \\\hline%f5
+\fref{RCInstruction}& & & & \checkmark & & \\\hline%f12
+\fref{VertexUniqueID}& & & & & \checkmark & \\\hline%f8
+\fref{ElmUniqueID}& & & & & \checkmark & \\\hline%f9
+\fref{ElmTopology}& & & & & \checkmark & \\\hline%f10
+\fref{OutElmOrder}& & & & & \checkmark & \\\hline%f14
+\fref{OutVertexOrder}& & & & & \checkmark & \\\hline%f15
+\fref{Help} & & & & & & \checkmark \\\hline%f16
+\end{tabular}
+\caption{Traceability Matrix (PART III): Requirements }
+\label{AreqTM3}
+\end{table}
+
+
+\section{List of Possible Changes in the Requirements \label{AreqSecPC}}
+The system might evolve to accommodate the following changes in the future. These changes will add additional goals to the software library.
+\begin{enumerate}
+\item The input of PMGT may include material properties.
+\item The input of PMGT may include boundary conditions.
+\end{enumerate}
+
+\section{Values of Auxiliary Constants \label{SecAC}}
+The constants given in this section are used to validate some nonfunctional requirements. The compatible software chosen is AOMD. However, other software can also be used as long as the other software has the required functionalities to validate the given requirement.
+
+\begin{tabular}{p{\firstCol}p{\secondCol}}
+\emph{LEARNTIME} & The time that reproduce the same example as that specified in nonfunctional requirement \nref{Usability} using AOMD.\\
+\emph{MANPROP} & The redevelopment time to add the same algorithm as that specified in the nonfunctional requirement \nref{Maintainability}, using AOMD. If the algorithm is already in AOMD, the the time that AOMD took to add it.\\
+\emph{RSPTIME} & The execution time to refine the same mesh as that specified in nonfunctional requirement \nref{Performance} using AOMD. \\
+\emph{MEMCAP} & The typical memory capacity of a machine on SHARCNET.\\
+\end{tabular}
+
+\newpage
+
+\bibliography{WenRef}
+\bibliographystyle{plainnat}
+
+\end{document}
+
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+ exit
+ }
+ if
+ /StartData /typecheck ct_raise
+ }
+ loop
+ cid_BYTE_COUNT ct_CID_STR_SIZE le
+ {
+ 2 copy cid_BYTE_COUNT string exch exec
+ pop
+ 1 array dup
+ 3 -1 roll
+ 0 exch put
+ }
+ {
+ cid_BYTE_COUNT ct_CID_STR_SIZE div ceiling cvi
+ dup array exch 2 sub 0 exch 1 exch
+ {
+ 2 copy
+ 5 index
+ ct_CID_STR_SIZE
+ string
+ 6 index exec
+ pop
+ put
+ pop
+ }
+ for
+ 2 index
+ cid_BYTE_COUNT ct_CID_STR_SIZE mod string
+ 3 index exec
+ pop
+ 1 index exch
+ 1 index length 1 sub
+ exch put
+ }
+ ifelse
+ cid_CIDFONT exch /GlyphData exch put
+ 2 index null eq
+ {
+ pop pop pop
+ }
+ {
+ pop /readstring load
+ 1 string exch
+ {
+ 3 copy exec
+ pop
+ dup length 0 eq
+ {
+ pop pop pop pop pop
+ true exit
+ }
+ if
+ 4 index
+ eq
+ {
+ pop pop pop pop
+ false exit
+ }
+ if
+ }
+ loop
+ pop
+ }
+ ifelse
+ } bind def
+ /StartData
+ {
+ mark
+ {
+ currentdict
+ dup /FDArray get 0 get /FontMatrix get
+ 0 get 0.001 eq
+ {
+ dup /CDevProc known not
+ {
+ /CDevProc 1183615869 internaldict /stdCDevProc 2 copy known
+ { get }
+ {
+ pop pop
+ { pop pop pop pop pop 0 -1000 7 index 2 div 880 }
+ }
+ ifelse
+ def
+ }
+ if
+ }
+ {
+ /CDevProc
+ {
+ pop pop pop pop pop
+ 0
+ 1 cid_temp /cid_CIDFONT get
+ /FDArray get 0 get
+ /FontMatrix get 0 get div
+ 7 index 2 div
+ 1 index 0.88 mul
+ } def
+ }
+ ifelse
+ /cid_temp 15 dict def
+ cid_temp
+ begin
+ /cid_CIDFONT exch def
+ 3 copy pop
+ dup /cid_BYTE_COUNT exch def 0 gt
+ {
+ ct_cidfont_stream_init
+ FDArray
+ {
+ /Private get
+ dup /SubrMapOffset known
+ {
+ begin
+ /Subrs SubrCount array def
+ Subrs
+ SubrMapOffset
+ SubrCount
+ SDBytes
+ ct_Level2?
+ {
+ currentdict dup /SubrMapOffset undef
+ dup /SubrCount undef
+ /SDBytes undef
+ }
+ if
+ end
+ /cid_SD_BYTES exch def
+ /cid_SUBR_COUNT exch def
+ /cid_SUBR_MAP_OFFSET exch def
+ /cid_SUBRS exch def
+ cid_SUBR_COUNT 0 gt
+ {
+ GlyphData cid_SUBR_MAP_OFFSET cid_SD_BYTES ct_GetInterval
+ 0 cid_SD_BYTES ct_cvnsi
+ 0 1 cid_SUBR_COUNT 1 sub
+ {
+ exch 1 index
+ 1 add
+ cid_SD_BYTES mul cid_SUBR_MAP_OFFSET add
+ GlyphData exch cid_SD_BYTES ct_GetInterval
+ 0 cid_SD_BYTES ct_cvnsi
+ cid_SUBRS 4 2 roll
+ GlyphData exch
+ 4 index
+ 1 index
+ sub
+ ct_GetInterval
+ dup length string copy put
+ }
+ for
+ pop
+ }
+ if
+ }
+ { pop }
+ ifelse
+ }
+ forall
+ }
+ if
+ cleartomark pop pop
+ end
+ CIDFontName currentdict /CIDFont defineresource pop
+ end end
+ }
+ stopped
+ { cleartomark /StartData ct_reraise }
+ if
+ } bind def
+ currentdict
+ end def
+ /ct_saveCIDInit
+ {
+ /CIDInit /ProcSet ct_resourcestatus
+ { true }
+ { /CIDInitC /ProcSet ct_resourcestatus }
+ ifelse
+ {
+ pop pop
+ /CIDInit /ProcSet findresource
+ ct_UseNativeCapability?
+ { pop null }
+ { /CIDInit ct_CIDInit /ProcSet defineresource pop }
+ ifelse
+ }
+ { /CIDInit ct_CIDInit /ProcSet defineresource pop null }
+ ifelse
+ ct_Vars exch /ct_oldCIDInit exch put
+ } bind def
+ /ct_restoreCIDInit
+ {
+ ct_Vars /ct_oldCIDInit get dup null ne
+ { /CIDInit exch /ProcSet defineresource pop }
+ { pop }
+ ifelse
+ } bind def
+ /ct_BuildCharSetUp
+ {
+ 1 index
+ begin
+ CIDFont
+ begin
+ Adobe_CoolType_Utility /ct_BuildCharDict get
+ begin
+ /ct_dfCharCode exch def
+ /ct_dfDict exch def
+ CIDFirstByte ct_dfCharCode add
+ dup CIDCount ge
+ { pop 0 }
+ if
+ /cid exch def
+ {
+ GlyphDirectory cid 2 copy known
+ { get }
+ { pop pop nullstring }
+ ifelse
+ dup length FDBytes sub 0 gt
+ {
+ dup
+ FDBytes 0 ne
+ { 0 FDBytes ct_cvnsi }
+ { pop 0 }
+ ifelse
+ /fdIndex exch def
+ dup length FDBytes sub FDBytes exch getinterval
+ /charstring exch def
+ exit
+ }
+ {
+ pop
+ cid 0 eq
+ { /charstring nullstring def exit }
+ if
+ /cid 0 def
+ }
+ ifelse
+ }
+ loop
+ } def
+ /ct_SetCacheDevice
+ {
+ 0 0 moveto
+ dup stringwidth
+ 3 -1 roll
+ true charpath
+ pathbbox
+ 0 -1000
+ 7 index 2 div 880
+ setcachedevice2
+ 0 0 moveto
+ } def
+ /ct_CloneSetCacheProc
+ {
+ 1 eq
+ {
+ stringwidth
+ pop -2 div -880
+ 0 -1000 setcharwidth
+ moveto
+ }
+ {
+ usewidths?
+ {
+ currentfont /Widths get cid
+ 2 copy known
+ { get exch pop aload pop }
+ { pop pop stringwidth }
+ ifelse
+ }
+ { stringwidth }
+ ifelse
+ setcharwidth
+ 0 0 moveto
+ }
+ ifelse
+ } def
+ /ct_Type3ShowCharString
+ {
+ ct_FDDict fdIndex 2 copy known
+ { get }
+ {
+ currentglobal 3 1 roll
+ 1 index gcheck setglobal
+ ct_Type1FontTemplate dup maxlength dict copy
+ begin
+ FDArray fdIndex get
+ dup /FontMatrix 2 copy known
+ { get }
+ { pop pop ct_defaultFontMtx }
+ ifelse
+ /FontMatrix exch dup length array copy def
+ /Private get
+ /Private exch def
+ /Widths rootfont /Widths get def
+ /CharStrings 1 dict dup /.notdef
+ <d841272cf18f54fc13> dup length string copy put def
+ currentdict
+ end
+ /ct_Type1Font exch definefont
+ dup 5 1 roll put
+ setglobal
+ }
+ ifelse
+ dup /CharStrings get 1 index /Encoding get
+ ct_dfCharCode get charstring put
+ rootfont /WMode 2 copy known
+ { get }
+ { pop pop 0 }
+ ifelse
+ exch
+ 1000 scalefont setfont
+ ct_str1 0 ct_dfCharCode put
+ ct_str1 exch ct_dfSetCacheProc
+ ct_SyntheticBold
+ {
+ currentpoint
+ ct_str1 show
+ newpath
+ moveto
+ ct_str1 true charpath
+ ct_StrokeWidth setlinewidth
+ stroke
+ }
+ { ct_str1 show }
+ ifelse
+ } def
+ /ct_Type4ShowCharString
+ {
+ ct_dfDict ct_dfCharCode charstring
+ FDArray fdIndex get
+ dup /FontMatrix get dup ct_defaultFontMtx ct_matrixeq not
+ { ct_1000Mtx matrix concatmatrix concat }
+ { pop }
+ ifelse
+ /Private get
+ Adobe_CoolType_Utility /ct_Level2? get not
+ {
+ ct_dfDict /Private
+ 3 -1 roll
+ { put }
+ 1183615869 internaldict /superexec get exec
+ }
+ if
+ 1183615869 internaldict
+ Adobe_CoolType_Utility /ct_Level2? get
+ { 1 index }
+ { 3 index /Private get mark 6 1 roll }
+ ifelse
+ dup /RunInt known
+ { /RunInt get }
+ { pop /CCRun }
+ ifelse
+ get exec
+ Adobe_CoolType_Utility /ct_Level2? get not
+ { cleartomark }
+ if
+ } bind def
+ /ct_BuildCharIncremental
+ {
+ {
+ Adobe_CoolType_Utility /ct_MakeOCF get begin
+ ct_BuildCharSetUp
+ ct_ShowCharString
+ }
+ stopped
+ { stop }
+ if
+ end
+ end
+ end
+ end
+ } bind def
+ /BaseFontNameStr (BF00) def
+ /ct_Type1FontTemplate 14 dict
+ begin
+ /FontType 1 def
+ /FontMatrix [0.001 0 0 0.001 0 0] def
+ /FontBBox [-250 -250 1250 1250] def
+ /Encoding ct_cHexEncoding def
+ /PaintType 0 def
+ currentdict
+ end def
+ /BaseFontTemplate 11 dict
+ begin
+ /FontMatrix [0.001 0 0 0.001 0 0] def
+ /FontBBox [-250 -250 1250 1250] def
+ /Encoding ct_cHexEncoding def
+ /BuildChar /ct_BuildCharIncremental load def
+ ct_Clone?
+ {
+ /FontType 3 def
+ /ct_ShowCharString /ct_Type3ShowCharString load def
+ /ct_dfSetCacheProc /ct_CloneSetCacheProc load def
+ /ct_SyntheticBold false def
+ /ct_StrokeWidth 1 def
+ }
+ {
+ /FontType 4 def
+ /Private 1 dict dup /lenIV 4 put def
+ /CharStrings 1 dict dup /.notdef <d841272cf18f54fc13> put def
+ /PaintType 0 def
+ /ct_ShowCharString /ct_Type4ShowCharString load def
+ }
+ ifelse
+ /ct_str1 1 string def
+ currentdict
+ end def
+ /BaseFontDictSize BaseFontTemplate length 5 add def
+ /ct_matrixeq
+ {
+ true 0 1 5
+ {
+ dup 4 index exch get exch 3 index exch get eq and
+ dup not
+ { exit }
+ if
+ }
+ for
+ exch pop exch pop
+ } bind def
+ /ct_makeocf
+ {
+ 15 dict
+ begin
+ exch /WMode exch def
+ exch /FontName exch def
+ /FontType 0 def
+ /FMapType 2 def
+ /FontMatrix matrix def
+ /bfCount 1 index /CIDCount get 256 idiv 1 add
+ dup 256 gt { pop 256} if def
+ /Encoding
+ 256 array 0 1 bfCount 1 sub { 2 copy dup put pop } for
+ bfCount 1 255 { 2 copy bfCount put pop } for
+ def
+ /FDepVector bfCount dup 256 lt { 1 add } if array def
+ BaseFontTemplate BaseFontDictSize dict copy
+ begin
+ /CIDFont exch def
+ CIDFont /FontBBox known
+ { CIDFont /FontBBox get /FontBBox exch def }
+ if
+ CIDFont /CDevProc known
+ { CIDFont /CDevProc get /CDevProc exch def }
+ if
+ currentdict
+ end
+ BaseFontNameStr 3 (0) putinterval
+ 0 1 bfCount dup 256 eq { 1 sub } if
+ {
+ FDepVector exch
+ 2 index BaseFontDictSize dict copy
+ begin
+ dup /CIDFirstByte exch 256 mul def
+ FontType 3 eq
+ { /ct_FDDict 2 dict def }
+ if
+ currentdict
+ end
+ 1 index 16
+ BaseFontNameStr 2 2 getinterval cvrs pop
+ BaseFontNameStr exch definefont
+ put
+ }
+ for
+ ct_Clone?
+ { /Widths 1 index /CIDFont get /GlyphDirectory get length dict def }
+ if
+ FontName
+ currentdict
+ end
+ definefont
+ ct_Clone?
+ {
+ gsave
+ dup 1000 scalefont setfont
+ ct_BuildCharDict
+ begin
+ /usewidths? false def
+ currentfont /Widths get
+ begin
+ exch /CIDFont get /GlyphDirectory get
+ {
+ pop
+ dup charcode exch 1 index 0 2 index 256 idiv put
+ 1 index exch 1 exch 256 mod put
+ stringwidth 2 array astore def
+ }
+ forall
+ end
+ /usewidths? true def
+ end
+ grestore
+ }
+ { exch pop }
+ ifelse
+ } bind def
+ /ct_ComposeFont
+ {
+ ct_UseNativeCapability?
+ {
+ 2 index /CMap ct_resourcestatus
+ { pop pop exch pop }
+ {
+ /CIDInit /ProcSet findresource
+ begin
+ 12 dict
+ begin
+ begincmap
+ /CMapName 3 index def
+ /CMapVersion 1.000 def
+ /CMapType 1 def
+ exch /WMode exch def
+ /CIDSystemInfo 3 dict dup
+ begin
+ /Registry (Adobe) def
+ /Ordering
+ CMapName ct_mkocfStr100 cvs
+ (Adobe-) search
+ {
+ pop pop
+ (-) search
+ {
+ dup length string copy
+ exch pop exch pop
+ }
+ { pop (Identity)}
+ ifelse
+ }
+ { pop (Identity) }
+ ifelse
+ def
+ /Supplement 0 def
+ end def
+ 1 begincodespacerange
+ <0000> <FFFF>
+ endcodespacerange
+ 1 begincidrange
+ <0000> <FFFF> 0
+ endcidrange
+ endcmap
+ CMapName currentdict /CMap defineresource pop
+ end
+ end
+ }
+ ifelse
+ composefont
+ }
+ {
+ 3 2 roll pop
+ 0 get /CIDFont findresource
+ ct_makeocf
+ }
+ ifelse
+ } bind def
+ /ct_MakeIdentity
+ {
+ ct_UseNativeCapability?
+ {
+ 1 index /CMap ct_resourcestatus
+ { pop pop }
+ {
+ /CIDInit /ProcSet findresource begin
+ 12 dict begin
+ begincmap
+ /CMapName 2 index def
+ /CMapVersion 1.000 def
+ /CMapType 1 def
+ /CIDSystemInfo 3 dict dup
+ begin
+ /Registry (Adobe) def
+ /Ordering
+ CMapName ct_mkocfStr100 cvs
+ (Adobe-) search
+ {
+ pop pop
+ (-) search
+ { dup length string copy exch pop exch pop }
+ { pop (Identity) }
+ ifelse
+ }
+ { pop (Identity) }
+ ifelse
+ def
+ /Supplement 0 def
+ end def
+ 1 begincodespacerange
+ <0000> <FFFF>
+ endcodespacerange
+ 1 begincidrange
+ <0000> <FFFF> 0
+ endcidrange
+ endcmap
+ CMapName currentdict /CMap defineresource pop
+ end
+ end
+ }
+ ifelse
+ composefont
+ }
+ {
+ exch pop
+ 0 get /CIDFont findresource
+ ct_makeocf
+ }
+ ifelse
+ } bind def
+ currentdict readonly pop
+ end
+ end
+%%EndResource
+/currentpacking where{pop currentpacking true setpacking}if
+%%BeginResource: procset pdfvars 6.0 1
+%%Copyright: Copyright 1987-2002 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: definition of dictionary of variables used by PDF & PDFText procsets
+userdict /PDF 162 dict put
+userdict /PDFVars 89 dict dup begin put
+/docSetupDone false def
+/InitAll 0 def
+/TermAll 0 def
+/DocInitAll 0 def
+/DocTermAll 0 def
+/_pdfEncodings 2 array def
+/_pdf_str1 1 string def
+/_pdf_i 0 def
+/_pdf_na 0 def
+/_pdf_showproc 0 def
+/_italMtx [1 0 .212557 1 0 0] def
+/_italMtx_WMode1 [1 -.212557 0 1 0 0] def
+/_italMtxType0 [1 0 .1062785 1 0 0] def
+/_italMtx_WMode1Type0 [1 -.1062785 0 1 0 0] def
+/_basefont 0 def
+/_basefonto 0 def
+/_pdf_oldCIDInit null def
+/_pdf_FontDirectory 30 dict def
+/_categories 10 dict def
+/_sa? true def
+/_ColorSep5044? false def
+/nulldict 0 dict def
+/_processColors 0 def
+/overprintstack null def
+/_defaulttransfer currenttransfer def
+/_defaultflatness currentflat def
+/_defaulthalftone null def
+/_defaultcolortransfer null def
+/_defaultblackgeneration null def
+/_defaultundercolorremoval null def
+/_defaultcolortransfer null def
+PDF begin
+[/c/cs/cm/d/d0/f/h/i/j/J/l/m/M/n/q/Q/re/ri/S/sc/sh/Tf/w/W
+/applyInterpFunc/applystitchFunc/domainClip/encodeInput
+/initgs/int/limit/rangeClip
+/defineRes/undefineRes/findRes/setSA/pl
+/? /! /| /: /+ /GetGlyphDirectory
+/pdf_flushFilters /pdf_readstring /pdf_dictOp /pdf_image /pdf_maskedImage
+/pdf_shfill /pdf_sethalftone
+] {null def} bind forall
+end
+end
+%%EndResource
+PDFVars begin PDF begin
+%%BeginResource: procset pdfutil 6.0 1
+%%Copyright: Copyright 1993-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Basic utilities used by other PDF procsets
+/bd {bind def} bind def
+/ld {load def} bd
+/bld {
+dup length dict begin
+{ null def } forall
+bind
+end
+def
+} bd
+/dd { PDFVars 3 1 roll put } bd
+/xdd { exch dd } bd
+/Level2?
+systemdict /languagelevel known
+{ systemdict /languagelevel get 2 ge } { false } ifelse
+def
+/Level1? Level2? not def
+/Level3?
+systemdict /languagelevel known
+{systemdict /languagelevel get 3 eq } { false } ifelse
+def
+/getifknown {
+2 copy known { get true } { pop pop false } ifelse
+} bd
+/here {
+currentdict exch getifknown
+} bd
+/isdefined? { where { pop true } { false } ifelse } bd
+%%EndResource
+%%BeginResource: procset l2compat 6.0 1
+%%Copyright: Copyright 1987-2003 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Level 1 emulation of level 2 operators
+/setcmykcolor isdefined? not
+{
+/setcmykcolor {
+1 sub 4 1 roll
+3 {
+3 index add neg dup 0 lt { pop 0 } if
+3 1 roll
+} repeat
+setrgbcolor
+pop
+} bd
+} if
+/rectclip isdefined? not
+{
+/rectclip { newpath re clip newpath } bd
+} if
+/rectfill isdefined? not
+{
+/rectfill { gsave newpath re fill grestore } bd
+} if
+/sethalftone isdefined? not
+{
+/sethalftone {
+begin
+HalftoneType 1 eq
+{ Frequency Angle /SpotFunction load setscreen }
+if
+end
+} bd
+} if
+Level1?
+{
+/pdf_show {show} bd
+/xshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_xshow
+} bd
+/yshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_yshow
+} bd
+/xyshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_xyshow
+} bd
+} if
+/getrampcolor {
+cvi
+/indx exch def
+[
+0 1 NumComp 1 sub {
+dup
+Samples exch get
+dup type /stringtype eq { indx get } if
+exch
+Scaling exch get aload pop
+3 1 roll
+mul add
+} for
+]
+L1setcolor
+} bd
+/sssetbackground { L1setcolor } bd
+%%EndResource
+%%BeginResource: procset pdf 6.0 1
+%%Copyright: Copyright 1998-2003 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: General operators for PDF, common to all Language Levels.
+/cm { matrix astore concat } bd
+/d /setdash ld
+/f /fill ld
+/h /closepath ld
+/i {dup 0 eq {pop _defaultflatness} if setflat} bd
+/j /setlinejoin ld
+/J /setlinecap ld
+/M /setmiterlimit ld
+/n /newpath ld
+/S /stroke ld
+/w /setlinewidth ld
+/W /clip ld
+/sg /setgray ld
+/initgs {
+0 setgray
+[] 0 d
+0 j
+0 J
+10 M
+1 w
+false setSA
+/_defaulttransfer load settransfer
+0 i
+/RelativeColorimetric ri
+newpath
+} bd
+/int {
+dup 2 index sub 3 index 5 index sub div 6 -2 roll sub mul
+exch pop add exch pop
+} bd
+/limit {
+dup 2 index le { exch } if pop
+dup 2 index ge { exch } if pop
+} bd
+/domainClip {
+Domain aload pop 3 2 roll
+limit
+} [/Domain] bld
+/applyInterpFunc {
+0 1 DimOut 1 sub
+{
+dup C0 exch get exch
+dup C1 exch get exch
+3 1 roll
+1 index sub
+3 index
+N exp mul add
+exch
+currentdict /Range_lo known
+{
+dup Range_lo exch get exch
+Range_hi exch get
+3 2 roll limit
+}
+{
+pop
+}
+ifelse
+exch
+} for
+pop
+} [/DimOut /C0 /C1 /N /Range_lo /Range_hi] bld
+/encodeInput {
+NumParts 1 sub
+0 1 2 index
+{
+dup Bounds exch get
+2 index gt
+{ exit }
+{ dup
+3 index eq
+{ exit }
+{ pop } ifelse
+} ifelse
+} for
+3 2 roll pop
+dup Bounds exch get exch
+dup 1 add Bounds exch get exch
+2 mul
+dup Encode exch get exch
+1 add Encode exch get
+int
+} [/NumParts /Bounds /Encode] bld
+/rangeClip {
+exch dup Range_lo exch get
+exch Range_hi exch get
+3 2 roll
+limit
+} [/Range_lo /Range_hi] bld
+/applyStitchFunc {
+Functions exch get exec
+currentdict /Range_lo known {
+0 1 DimOut 1 sub {
+DimOut 1 add -1 roll
+rangeClip
+} for
+} if
+} [/Functions /Range_lo /DimOut] bld
+/pdf_flushfilters
+{
+aload length
+{ dup status
+1 index currentfile ne and
+{ dup flushfile closefile }
+{ pop }
+ifelse
+} repeat
+} bd
+/pdf_readstring
+{
+1 index dup length 1 sub get
+exch readstring pop
+exch pdf_flushfilters
+} bind def
+/pdf_dictOp
+{
+3 2 roll
+10 dict copy
+begin
+_Filters dup length 1 sub get def
+currentdict exch exec
+_Filters pdf_flushfilters
+end
+} [/_Filters] bld
+/pdf_image {{image} /DataSource pdf_dictOp} bd
+/pdf_imagemask {{imagemask} /DataSource pdf_dictOp} bd
+/pdf_shfill {{sh} /DataSource pdf_dictOp} bd
+/pdf_sethalftone {{sethalftone} /Thresholds pdf_dictOp} bd
+/pdf_maskedImage
+{
+10 dict copy begin
+/miDict currentdict def
+/DataDict DataDict 10 dict copy def
+DataDict begin
+/DataSource
+_Filters dup length 1 sub get
+def
+miDict image
+_Filters pdf_flushfilters
+end
+end
+} [/miDict /DataDict /_Filters] bld
+/RadialShade {
+40 dict begin
+/background exch def
+/ext1 exch def
+/ext0 exch def
+/BBox exch def
+/r2 exch def
+/c2y exch def
+/c2x exch def
+/r1 exch def
+/c1y exch def
+/c1x exch def
+/rampdict exch def
+gsave
+BBox length 0 gt {
+newpath
+BBox 0 get BBox 1 get moveto
+BBox 2 get BBox 0 get sub 0 rlineto
+0 BBox 3 get BBox 1 get sub rlineto
+BBox 2 get BBox 0 get sub neg 0 rlineto
+closepath
+clip
+newpath
+} if
+c1x c2x eq
+{
+c1y c2y lt {/theta 90 def}{/theta 270 def} ifelse
+}
+{
+/slope c2y c1y sub c2x c1x sub div def
+/theta slope 1 atan def
+c2x c1x lt c2y c1y ge and { /theta theta 180 sub def} if
+c2x c1x lt c2y c1y lt and { /theta theta 180 add def} if
+}
+ifelse
+gsave
+clippath
+c1x c1y translate
+theta rotate
+-90 rotate
+{ pathbbox } stopped
+{ 0 0 0 0 } if
+/yMax exch def
+/xMax exch def
+/yMin exch def
+/xMin exch def
+grestore
+xMax xMin eq yMax yMin eq or
+{
+grestore
+end
+}
+{
+/max { 2 copy gt { pop } {exch pop} ifelse } bind def
+/min { 2 copy lt { pop } {exch pop} ifelse } bind def
+rampdict begin
+40 dict begin
+background length 0 gt { background sssetbackground gsave clippath fill grestore } if
+gsave
+c1x c1y translate
+theta rotate
+-90 rotate
+/c2y c1x c2x sub dup mul c1y c2y sub dup mul add sqrt def
+/c1y 0 def
+/c1x 0 def
+/c2x 0 def
+ext0 {
+0 getrampcolor
+c2y r2 add r1 sub 0.0001 lt
+{
+c1x c1y r1 360 0 arcn
+pathbbox
+/aymax exch def
+/axmax exch def
+/aymin exch def
+/axmin exch def
+/bxMin xMin axmin min def
+/byMin yMin aymin min def
+/bxMax xMax axmax max def
+/byMax yMax aymax max def
+bxMin byMin moveto
+bxMax byMin lineto
+bxMax byMax lineto
+bxMin byMax lineto
+bxMin byMin lineto
+eofill
+}
+{
+c2y r1 add r2 le
+{
+c1x c1y r1 0 360 arc
+fill
+}
+{
+c2x c2y r2 0 360 arc fill
+r1 r2 eq
+{
+/p1x r1 neg def
+/p1y c1y def
+/p2x r1 def
+/p2y c1y def
+p1x p1y moveto p2x p2y lineto p2x yMin lineto p1x yMin lineto
+fill
+}
+{
+/AA r2 r1 sub c2y div def
+AA -1 eq
+{ /theta 89.99 def}
+{ /theta AA 1 AA dup mul sub sqrt div 1 atan def}
+ifelse
+/SS1 90 theta add dup sin exch cos div def
+/p1x r1 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def
+/p1y p1x SS1 div neg def
+/SS2 90 theta sub dup sin exch cos div def
+/p2x r1 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def
+/p2y p2x SS2 div neg def
+r1 r2 gt
+{
+/L1maxX p1x yMin p1y sub SS1 div add def
+/L2maxX p2x yMin p2y sub SS2 div add def
+}
+{
+/L1maxX 0 def
+/L2maxX 0 def
+}ifelse
+p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto
+L1maxX L1maxX p1x sub SS1 mul p1y add lineto
+fill
+}
+ifelse
+}
+ifelse
+} ifelse
+} if
+c1x c2x sub dup mul
+c1y c2y sub dup mul
+add 0.5 exp
+0 dtransform
+dup mul exch dup mul add 0.5 exp 72 div
+0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+1 index 1 index lt { exch } if pop
+/hires exch def
+hires mul
+/numpix exch def
+/numsteps NumSamples def
+/rampIndxInc 1 def
+/subsampling false def
+numpix 0 ne
+{
+NumSamples numpix div 0.5 gt
+{
+/numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def
+/rampIndxInc NumSamples 1 sub numsteps div def
+/subsampling true def
+} if
+} if
+/xInc c2x c1x sub numsteps div def
+/yInc c2y c1y sub numsteps div def
+/rInc r2 r1 sub numsteps div def
+/cx c1x def
+/cy c1y def
+/radius r1 def
+newpath
+xInc 0 eq yInc 0 eq rInc 0 eq and and
+{
+0 getrampcolor
+cx cy radius 0 360 arc
+stroke
+NumSamples 1 sub getrampcolor
+cx cy radius 72 hires div add 0 360 arc
+0 setlinewidth
+stroke
+}
+{
+0
+numsteps
+{
+dup
+subsampling { round } if
+getrampcolor
+cx cy radius 0 360 arc
+/cx cx xInc add def
+/cy cy yInc add def
+/radius radius rInc add def
+cx cy radius 360 0 arcn
+eofill
+rampIndxInc add
+}
+repeat
+pop
+} ifelse
+ext1 {
+c2y r2 add r1 lt
+{
+c2x c2y r2 0 360 arc
+fill
+}
+{
+c2y r1 add r2 sub 0.0001 le
+{
+c2x c2y r2 360 0 arcn
+pathbbox
+/aymax exch def
+/axmax exch def
+/aymin exch def
+/axmin exch def
+/bxMin xMin axmin min def
+/byMin yMin aymin min def
+/bxMax xMax axmax max def
+/byMax yMax aymax max def
+bxMin byMin moveto
+bxMax byMin lineto
+bxMax byMax lineto
+bxMin byMax lineto
+bxMin byMin lineto
+eofill
+}
+{
+c2x c2y r2 0 360 arc fill
+r1 r2 eq
+{
+/p1x r2 neg def
+/p1y c2y def
+/p2x r2 def
+/p2y c2y def
+p1x p1y moveto p2x p2y lineto p2x yMax lineto p1x yMax lineto
+fill
+}
+{
+/AA r2 r1 sub c2y div def
+AA -1 eq
+{ /theta 89.99 def}
+{ /theta AA 1 AA dup mul sub sqrt div 1 atan def}
+ifelse
+/SS1 90 theta add dup sin exch cos div def
+/p1x r2 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def
+/p1y c2y p1x SS1 div sub def
+/SS2 90 theta sub dup sin exch cos div def
+/p2x r2 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def
+/p2y c2y p2x SS2 div sub def
+r1 r2 lt
+{
+/L1maxX p1x yMax p1y sub SS1 div add def
+/L2maxX p2x yMax p2y sub SS2 div add def
+}
+{
+/L1maxX 0 def
+/L2maxX 0 def
+}ifelse
+p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto
+L1maxX L1maxX p1x sub SS1 mul p1y add lineto
+fill
+}
+ifelse
+}
+ifelse
+} ifelse
+} if
+grestore
+grestore
+end
+end
+end
+} ifelse
+} bd
+/GenStrips {
+40 dict begin
+/background exch def
+/ext1 exch def
+/ext0 exch def
+/BBox exch def
+/y2 exch def
+/x2 exch def
+/y1 exch def
+/x1 exch def
+/rampdict exch def
+gsave
+BBox length 0 gt {
+newpath
+BBox 0 get BBox 1 get moveto
+BBox 2 get BBox 0 get sub 0 rlineto
+0 BBox 3 get BBox 1 get sub rlineto
+BBox 2 get BBox 0 get sub neg 0 rlineto
+closepath
+clip
+newpath
+} if
+x1 x2 eq
+{
+y1 y2 lt {/theta 90 def}{/theta 270 def} ifelse
+}
+{
+/slope y2 y1 sub x2 x1 sub div def
+/theta slope 1 atan def
+x2 x1 lt y2 y1 ge and { /theta theta 180 sub def} if
+x2 x1 lt y2 y1 lt and { /theta theta 180 add def} if
+}
+ifelse
+gsave
+clippath
+x1 y1 translate
+theta rotate
+{ pathbbox } stopped
+{ 0 0 0 0 } if
+/yMax exch def
+/xMax exch def
+/yMin exch def
+/xMin exch def
+grestore
+xMax xMin eq yMax yMin eq or
+{
+grestore
+end
+}
+{
+rampdict begin
+20 dict begin
+background length 0 gt { background sssetbackground gsave clippath fill grestore } if
+gsave
+x1 y1 translate
+theta rotate
+/xStart 0 def
+/xEnd x2 x1 sub dup mul y2 y1 sub dup mul add 0.5 exp def
+/ySpan yMax yMin sub def
+/numsteps NumSamples def
+/rampIndxInc 1 def
+/subsampling false def
+xStart 0 transform
+xEnd 0 transform
+3 -1 roll
+sub dup mul
+3 1 roll
+sub dup mul
+add 0.5 exp 72 div
+0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+1 index 1 index lt { exch } if pop
+mul
+/numpix exch def
+numpix 0 ne
+{
+NumSamples numpix div 0.5 gt
+{
+/numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def
+/rampIndxInc NumSamples 1 sub numsteps div def
+/subsampling true def
+} if
+} if
+ext0 {
+0 getrampcolor
+xMin xStart lt
+{ xMin yMin xMin neg ySpan rectfill } if
+} if
+/xInc xEnd xStart sub numsteps div def
+/x xStart def
+0
+numsteps
+{
+dup
+subsampling { round } if
+getrampcolor
+x yMin xInc ySpan rectfill
+/x x xInc add def
+rampIndxInc add
+}
+repeat
+pop
+ext1 {
+xMax xEnd gt
+{ xEnd yMin xMax xEnd sub ySpan rectfill } if
+} if
+grestore
+grestore
+end
+end
+end
+} ifelse
+} bd
+/currentdistillerparams where { pop currentdistillerparams /CoreDistVersion get 5000 lt}{true}ifelse
+{
+/PDFMark5 {cleartomark} bd
+}
+{
+/PDFMark5 {pdfmark} bd
+}ifelse
+/ReadByPDFMark5
+{
+2 dict begin
+/makerString exch def string /tmpString exch def
+{
+currentfile tmpString readline pop
+makerString anchorsearch
+{
+pop pop cleartomark exit
+}
+{
+3 copy /PUT PDFMark5 pop 2 copy (\n) /PUT PDFMark5
+} ifelse
+}loop
+end
+}bd
+%%EndResource
+%%BeginResource: procset sep_ops 6.0 1
+%%Copyright: Copyright 1987-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Support for Separations in Level 1, following the conventions of Tech Note 5044
+userdict /sep_ops 50 dict dup begin put
+/bdef {bind def} bind def
+/xdef {exch def} bdef
+/colorimagebuffer {
+0 1 2 index length 1 sub {
+dup 2 index exch get 255 exch sub 2 index 3 1 roll put
+} for
+} bdef
+/addprocs {
+[ 3 1 roll
+/exec load
+dup 3 1 roll
+] cvx
+} bdef
+/L1? {
+systemdict /languagelevel known {
+systemdict /languagelevel get 2 lt
+}{
+true
+} ifelse
+} bdef
+/colorexists {
+statusdict /processcolors known {
+statusdict /processcolors get exec
+}{
+/deviceinfo where {
+pop deviceinfo /Colors known {
+deviceinfo /Colors get
+statusdict /processcolors {
+deviceinfo /Colors known {
+deviceinfo /Colors get
+}{
+1
+} ifelse
+} put
+}{
+1
+} ifelse
+}{
+1
+} ifelse
+} ifelse
+1 gt
+} bdef
+/colorplate colorexists { 0 } { 5 } ifelse def
+/negativecolorplate false def
+/setcmykcolor where {
+pop
+gsave
+1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub
+4 {4 copy} repeat
+grestore
+1 dict begin
+/foureq {
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+pop pop pop pop and and and
+} def
+1 0 0 0 foureq {/colorplate 1 store} if
+0 1 0 0 foureq {/colorplate 2 store} if
+0 0 1 0 foureq {/colorplate 3 store} if
+0 0 0 1 foureq {/colorplate 4 store} if
+0 0 0 0 foureq {/colorplate 6 store} if
+end
+} if
+0 systemdict /currenttransfer get exec exec
+1 systemdict /currenttransfer get exec exec
+2 copy
+eq
+{
+/colorplate 6 store
+pop
+/negativecolorplate exch 0.5 lt store
+}
+{
+gt /negativecolorplate exch store
+}
+ifelse
+/findcmykcustomcolor where { pop }
+{
+/findcmykcustomcolor {
+[ 6 1 roll ] readonly
+} bdef
+} ifelse
+/setoverprint where {
+pop
+}{
+/setoverprint {
+pop
+} bdef
+} ifelse
+/currentoverprint where {
+pop
+}{
+/currentoverprint {
+false
+} bdef
+} ifelse
+/setcustomcolor where {
+pop
+}{
+L1? {
+/setcustomcolor {
+exch
+aload pop pop
+4 { 4 index mul 4 1 roll } repeat
+5 -1 roll pop
+setcmykcolor
+} bdef
+}{
+/setcustomcolor {
+exch
+[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
+0 4 getinterval
+[ exch /dup load exch cvx {mul exch dup}
+/forall load /pop load dup] cvx
+] setcolorspace setcolor
+} bdef
+} ifelse
+} ifelse
+/ik 0 def
+/iy 0 def
+/im 0 def
+/ic 0 def
+/imagetint {
+ic .3 mul
+im .59 mul
+iy .11 mul
+ik add add add dup
+1 gt {pop 1} if
+} bdef
+/setcmykcolor where {
+pop
+}{
+/setcmykcolor {
+/ik xdef /iy xdef /im xdef /ic xdef
+imagetint
+1 exch sub setgray
+} bdef
+} ifelse
+/customcolorimage where {
+pop
+}{
+L1? {
+/customcolorimage{
+gsave
+colorexists {
+aload pop pop
+/ik xdef /iy xdef /im xdef /ic xdef
+currentcolortransfer
+{ik mul ik sub 1 add} addprocs
+4 1 roll {iy mul iy sub 1 add} addprocs
+4 1 roll {im mul im sub 1 add} addprocs
+4 1 roll {ic mul ic sub 1 add} addprocs
+4 1 roll setcolortransfer
+/magentabuf 0 string def
+/yellowbuf 0 string def
+/blackbuf 0 string def
+{
+colorimagebuffer dup length magentabuf length ne
+{
+dup length dup dup
+/magentabuf exch string def
+/yellowbuf exch string def
+/blackbuf exch string def
+} if
+dup magentabuf copy yellowbuf copy
+blackbuf copy pop
+} addprocs
+{magentabuf}{yellowbuf}{blackbuf} true 4 colorimage
+}{
+aload pop pop /ik xdef /iy xdef /im xdef /ic xdef /tint
+imagetint def
+currenttransfer
+{tint mul 1 tint sub add} addprocs settransfer image
+} ifelse
+grestore
+} bdef
+}{
+/customcolorimage {
+gsave
+[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
+0 4 getinterval
+[ exch /dup load exch cvx {mul exch dup}
+/forall load /pop load dup] cvx
+] setcolorspace
+10 dict begin
+/ImageType 1 def
+/DataSource exch def
+/ImageMatrix exch def
+/BitsPerComponent exch def
+/Height exch def
+/Width exch def
+/Decode [1 0] def
+currentdict end
+image
+grestore
+} bdef
+} ifelse
+} ifelse
+/setseparationgray where {
+pop
+}{
+L1? {
+/setseparationgray { 1 exch sub dup dup dup setcmykcolor } bdef
+}{
+/setseparationgray {
+[/Separation /All /DeviceCMYK {dup dup dup}] setcolorspace
+1 exch sub setcolor
+} bdef
+} ifelse
+} ifelse
+/separationimage where { pop }
+{
+/separationimage {
+gsave
+1 1 1 1 (All)
+findcmykcustomcolor customcolorimage
+grestore
+} bdef
+} ifelse
+currentdict readonly pop end
+%%EndResource
+%%BeginResource: procset pdflev15044 6.0 1
+%%Copyright: Copyright 1987-2002 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: PDF operators, Level 1, with emulated separations (TN 5044)
+/_ColorSep5044? true dd
+/docinitialize {
+PDF begin
+/_defaulthalftone
+/currenthalftone where
+{ pop currenthalftone }
+{ 4 dict dup begin
+currentscreen
+/SpotFunction exch def
+/Angle exch def
+/Frequency exch def
+/HalftoneType 1 def
+end }
+ifelse
+dd
+/currentcolortransfer where
+{ pop /_defaultcolortransfer [ currentcolortransfer ] dd }
+{ /_defaultcolortransfer [currenttransfer dup dup dup] dd }
+ifelse
+end
+} bd
+/initialize {
+/overprintstack null dd
+sep_ops begin
+50 dict begin
+_defaulthalftone sethalftone
+} bd
+/terminate {
+end end
+} bd
+/currentcolortransfer where
+{ pop }
+{
+/setcolortransfer
+{
+settransfer pop pop pop
+} bd
+} ifelse
+/pl {
+transform
+0.25 sub round 0.25 add exch
+0.25 sub round 0.25 add exch
+itransform
+} bd
+/m { _sa? { pl } if moveto } bd
+/l { _sa? { pl } if lineto } bd
+/c
+{
+_sa? {3 {pl 6 2 roll} repeat} if
+curveto
+} bd
+/ri/pop ld
+/setSA { /_sa? xdd } bd
+/re
+{
+_sa?
+{
+8 dict begin
+/:h exch def
+/:w exch def
+/:y exch def
+/:x exch def
+:x :y pl
+/:ymin exch def /:xmin exch def
+:x :w add :y :h add pl
+/:ymax exch def /:xmax exch def
+:xmin :ymin moveto
+:xmax :ymin lineto
+:xmax :ymax lineto
+:xmin :ymax lineto
+closepath
+end
+}
+{
+4 2 roll moveto
+1 index 0 rlineto
+0 exch rlineto
+neg 0 rlineto
+closepath
+} ifelse
+} bd
+/q
+{
+gsave
+[currentoverprint overprintstack] /overprintstack xdd
+}
+[/overprintstack] bld
+/Q
+{
+overprintstack aload pop /overprintstack xdd setoverprint
+grestore
+}
+[/overprintstack] bld
+/AlmostFull?
+{ dup maxlength exch length sub 2 le
+} bd
+/Expand
+{ 1 index maxlength mul cvi dict
+dup begin exch { def } forall end
+} bd
+/xput
+{ 3 2 roll
+dup 3 index known not
+{ dup AlmostFull? { 1.5 Expand } if
+} if
+dup 4 2 roll put
+} bd
+/defineRes
+{ _categories 1 index known not
+{ /_categories _categories 2 index 10 dict xput store
+} if
+_categories exch 2 copy get 5 -1 roll 4 index xput put
+} bd
+/undefineRes {
+null exch
+defineRes
+} bd
+/findRes {
+_categories exch get exch get
+} bd
+/L1setcolor {
+aload length
+dup 0 eq
+{ pop .5 setgray }
+{ dup 1 eq
+{ pop setgray }
+{ 3 eq
+{ setrgbcolor }
+{ setcmykcolor }
+ifelse }
+ifelse }
+ifelse
+} bind dd
+/concattransferfuncs {
+[ 3 1 roll /exec load exch /exec load ] cvx
+} bd
+/concatandsettransfer {
+/_defaulttransfer load concattransferfuncs settransfer
+} bd
+/concatandsetcolortransfer {
+colorplate 0 eq
+{
+_defaultcolortransfer aload pop
+8 -1 roll 5 -1 roll concattransferfuncs 7 1 roll
+6 -1 roll 4 -1 roll concattransferfuncs 5 1 roll
+4 -1 roll 3 -1 roll concattransferfuncs 3 1 roll
+concattransferfuncs
+setcolortransfer
+} if
+colorplate 1 ge colorplate 4 le and
+{
+4 colorplate sub index 4 { exch pop } repeat
+concatandsettransfer
+} if
+colorplate 5 ge
+{
+0 index 4 { exch pop } repeat
+concatandsettransfer
+} if
+} bd
+/tn5044sethalftone
+{
+begin
+HalftoneType 5 eq
+{ [/Default /Cyan /Magenta /Yellow /Black /Default /Default /Default]
+colorplate get
+here not {
+/Default here not { currentdict } if
+} if
+}
+{ currentdict }
+ifelse
+end
+begin
+/TransferFunction here
+{
+concatandsettransfer
+currentdict dup length dict
+begin
+{
+1 index /TransferFunction ne { def } { pop pop } ifelse
+} forall
+currentdict
+end
+}
+{
+currentdict
+} ifelse
+end
+sethalftone
+} bd
+/paintimage
+{
+colorplate 0 eq
+{
+{ {currentfile cyanstr readstring pop}
+{currentfile magentastr readstring pop}
+{currentfile yellowstr readstring pop}
+{currentfile blackstr readstring pop
+currentfile graystr readstring pop pop}
+}
+{ {currentfile cyanstr readhexstring pop}
+{currentfile magentastr readhexstring pop}
+{currentfile yellowstr readhexstring pop}
+{currentfile blackstr readhexstring pop
+currentfile graystr readhexstring pop pop}
+} ifelse
+true 4 colorimage
+}
+{
+3 dict begin
+/binaryOK exch def
+[
+1 1 5 {
+dup
+/currentfile cvx
+[ /cyanstr /magentastr /yellowstr /blackstr /graystr ]
+3 -1 roll 1 sub get cvx
+binaryOK { /readstring } { /readhexstring } ifelse cvx
+/pop cvx
+5 -1 roll
+colorplate dup 5 gt { pop 5 } if
+eq not { /pop cvx } if
+} for
+] cvx bind
+end
+[
+colorplate 6 eq {
+/pop cvx
+negativecolorplate { 0 } { 1 } ifelse
+} if
+colorplate 4 le
+{
+1 /exch cvx /sub cvx
+} if
+colorplate 6 ne
+{
+systemdict /currenttransfer get exec
+aload pop
+} if
+] cvx
+gsave
+systemdict /settransfer get exec
+systemdict /image get exec
+grestore
+} ifelse
+} bd
+%%EndResource
+%%BeginResource: procset pdftext 6.0 1
+%%Copyright: Copyright 1987-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Text operators for PDF
+PDF /PDFText 78 dict dup begin put
+/docinitialize
+{
+/resourcestatus where {
+pop
+/CIDParams /ProcSet resourcestatus {
+pop pop
+false /CIDParams /ProcSet findresource /SetBuildCompatible get exec
+} if
+} if
+PDF begin
+PDFText /_pdfDefineIdentity-H known
+{ PDFText /_pdfDefineIdentity-H get exec}
+if
+end
+} bd
+/initialize {
+PDFText begin
+} bd
+/terminate { end } bd
+Level2?
+{
+/_safeput
+{
+3 -1 roll load 3 1 roll put
+}
+bd
+}
+{
+/_safeput
+{
+2 index load dup dup length exch maxlength ge
+{ dup length 5 add dict copy
+3 index xdd
+}
+{ pop }
+ifelse
+3 -1 roll load 3 1 roll put
+}
+bd
+}
+ifelse
+/pdf_has_composefont? systemdict /composefont known def
+/CopyFont {
+{
+1 index /FID ne 2 index /UniqueID ne and
+{ def } { pop pop } ifelse
+} forall
+} bd
+/Type0CopyFont
+{
+exch
+dup length dict
+begin
+CopyFont
+[
+exch
+FDepVector
+{
+dup /FontType get 0 eq
+{
+1 index Type0CopyFont
+/_pdfType0 exch definefont
+}
+{
+/_pdfBaseFont exch
+2 index exec
+}
+ifelse
+exch
+}
+forall
+pop
+]
+/FDepVector exch def
+currentdict
+end
+} bd
+Level2? {currentglobal true setglobal} if
+/cHexEncoding
+[/c00/c01/c02/c03/c04/c05/c06/c07/c08/c09/c0A/c0B/c0C/c0D/c0E/c0F/c10/c11/c12
+/c13/c14/c15/c16/c17/c18/c19/c1A/c1B/c1C/c1D/c1E/c1F/c20/c21/c22/c23/c24/c25
+/c26/c27/c28/c29/c2A/c2B/c2C/c2D/c2E/c2F/c30/c31/c32/c33/c34/c35/c36/c37/c38
+/c39/c3A/c3B/c3C/c3D/c3E/c3F/c40/c41/c42/c43/c44/c45/c46/c47/c48/c49/c4A/c4B
+/c4C/c4D/c4E/c4F/c50/c51/c52/c53/c54/c55/c56/c57/c58/c59/c5A/c5B/c5C/c5D/c5E
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+/c85/c86/c87/c88/c89/c8A/c8B/c8C/c8D/c8E/c8F/c90/c91/c92/c93/c94/c95/c96/c97
+/c98/c99/c9A/c9B/c9C/c9D/c9E/c9F/cA0/cA1/cA2/cA3/cA4/cA5/cA6/cA7/cA8/cA9/cAA
+/cAB/cAC/cAD/cAE/cAF/cB0/cB1/cB2/cB3/cB4/cB5/cB6/cB7/cB8/cB9/cBA/cBB/cBC/cBD
+/cBE/cBF/cC0/cC1/cC2/cC3/cC4/cC5/cC6/cC7/cC8/cC9/cCA/cCB/cCC/cCD/cCE/cCF/cD0
+/cD1/cD2/cD3/cD4/cD5/cD6/cD7/cD8/cD9/cDA/cDB/cDC/cDD/cDE/cDF/cE0/cE1/cE2/cE3
+/cE4/cE5/cE6/cE7/cE8/cE9/cEA/cEB/cEC/cED/cEE/cEF/cF0/cF1/cF2/cF3/cF4/cF5/cF6
+/cF7/cF8/cF9/cFA/cFB/cFC/cFD/cFE/cFF] def
+Level2? {setglobal} if
+/modEnc {
+/_enc xdd
+/_icode 0 dd
+counttomark 1 sub -1 0
+{
+index
+dup type /nametype eq
+{
+_enc _icode 3 -1 roll put
+_icode 1 add
+}
+if
+/_icode xdd
+} for
+cleartomark
+_enc
+} bd
+/trEnc {
+/_enc xdd
+255 -1 0 {
+exch dup -1 eq
+{ pop /.notdef }
+{ Encoding exch get }
+ifelse
+_enc 3 1 roll put
+} for
+pop
+_enc
+} bd
+/TE {
+/_i xdd
+StandardEncoding 256 array copy modEnc
+_pdfEncodings exch _i exch put
+} bd
+/TZ
+{
+/_usePDFEncoding xdd
+findfont
+dup length 6 add dict
+begin
+{
+1 index /FID ne { def } { pop pop } ifelse
+} forall
+/pdf_origFontName FontName def
+/FontName exch def
+currentdict /PaintType known
+{ PaintType 2 eq {/PaintType 0 def} if }
+if
+_usePDFEncoding 0 ge
+{
+/Encoding _pdfEncodings _usePDFEncoding get def
+pop
+}
+{
+_usePDFEncoding -1 eq
+{
+counttomark 0 eq
+{ pop }
+{
+Encoding 256 array copy
+modEnc /Encoding exch def
+}
+ifelse
+}
+{
+256 array
+trEnc /Encoding exch def
+}
+ifelse
+}
+ifelse
+pdf_EuroProcSet pdf_origFontName known
+{
+pdf_origFontName pdf_AddEuroGlyphProc
+} if
+Level2?
+{
+currentdict /pdf_origFontName undef
+} if
+FontName currentdict
+end
+definefont pop
+}
+bd
+Level2?
+{
+/TZG
+{
+currentglobal true setglobal
+2 index _pdfFontStatus
+{
+2 index findfont
+false setglobal
+3 index findfont
+true setglobal
+ne
+{
+2 index findfont dup rcheck
+{
+dup length dict begin
+{
+1 index /FID ne { def } { pop pop } ifelse
+} forall
+currentdict end
+}
+if
+3 index exch definefont pop
+}
+if
+} if
+setglobal
+TZ
+} bd
+}
+{
+/TZG {TZ} bd
+} ifelse
+Level2?
+{
+currentglobal false setglobal
+userdict /pdftext_data 5 dict put
+pdftext_data
+begin
+/saveStacks
+{
+pdftext_data
+begin
+/vmmode currentglobal def
+false setglobal
+count array astore /os exch def
+end
+countdictstack array dictstack pdftext_data exch /ds exch put
+cleardictstack pdftext_data /dscount countdictstack put
+pdftext_data /vmmode get setglobal
+} bind def
+/restoreStacks
+{
+pdftext_data /vmmode currentglobal put false setglobal
+clear cleardictstack
+pdftext_data /ds get dup
+pdftext_data /dscount get 1 2 index length 1 sub
+{ get begin dup } for
+pop pop
+pdftext_data /os get aload pop
+pdftext_data /vmmode get setglobal
+} bind def
+/testForClonePrinterBug
+{
+currentglobal true setglobal
+/undefinedCategory /Generic /Category findresource
+dup length dict copy /Category defineresource pop
+setglobal
+pdftext_data /saveStacks get exec
+pdftext_data /vmmode currentglobal put false setglobal
+/undefined /undefinedCategory { resourcestatus } stopped
+pdftext_data exch /bugFound exch put
+pdftext_data /vmmode get setglobal
+pdftext_data /restoreStacks get exec
+pdftext_data /bugFound get
+} bind def
+end
+setglobal
+/pdf_resourcestatus
+pdftext_data /testForClonePrinterBug get exec
+{
+{
+pdftext_data /saveStacks get exec
+pdftext_data /os get dup dup length 1 sub
+dup 1 sub dup 0 lt { pop 0 } if
+exch 1 exch { get exch dup } for
+pop pop
+{ resourcestatus }
+stopped
+{
+clear cleardictstack pdftext_data /restoreStacks get exec
+{ pop pop } stopped pop false
+}
+{
+count array astore pdftext_data exch /results exch put
+pdftext_data /restoreStacks get exec pop pop
+pdftext_data /results get aload pop
+}
+ifelse
+}
+}
+{ { resourcestatus } }
+ifelse
+bd
+}
+if
+Level2?
+{
+/_pdfUndefineResource
+{
+currentglobal 3 1 roll
+_pdf_FontDirectory 2 index 2 copy known
+{undef}
+{pop pop}
+ifelse
+1 index (pdf) exch _pdfConcatNames 1 index
+1 index 1 _pdfConcatNames 1 index
+5 index 1 _pdfConcatNames 1 index
+4
+{
+2 copy pdf_resourcestatus
+{
+pop 2 lt
+{2 copy findresource gcheck setglobal undefineresource}
+{pop pop}
+ifelse
+}
+{ pop pop}
+ifelse
+} repeat
+setglobal
+} bd
+}
+{
+/_pdfUndefineResource { pop pop} bd
+}
+ifelse
+Level2?
+{
+/_pdfFontStatus
+{
+currentglobal exch
+/Font pdf_resourcestatus
+{pop pop true}
+{false}
+ifelse
+exch setglobal
+} bd
+}
+{
+/_pdfFontStatusString 50 string def
+_pdfFontStatusString 0 (fonts/) putinterval
+/_pdfFontStatus
+{
+FontDirectory 1 index known
+{ pop true }
+{
+_pdfFontStatusString 6 42 getinterval
+cvs length 6 add
+_pdfFontStatusString exch 0 exch getinterval
+{ status } stopped
+{pop false}
+{
+{ pop pop pop pop true}
+{ false }
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+ifelse
+Level2?
+{
+/_pdfCIDFontStatus
+{
+/CIDFont /Category pdf_resourcestatus
+{
+pop pop
+/CIDFont pdf_resourcestatus
+{pop pop true}
+{false}
+ifelse
+}
+{ pop false }
+ifelse
+} bd
+}
+if
+/_pdfString100 100 string def
+/_pdfComposeFontName
+{
+dup length 1 eq
+{
+0 get
+1 index
+type /nametype eq
+{
+_pdfString100 cvs
+length dup dup _pdfString100 exch (-) putinterval
+_pdfString100 exch 1 add dup _pdfString100 length exch sub getinterval
+2 index exch cvs length
+add 1 add _pdfString100 exch 0 exch getinterval
+exch pop
+true
+}
+{
+pop pop
+false
+}
+ifelse
+}
+{
+false
+}
+ifelse
+dup {exch cvn exch} if
+} bd
+/_pdfConcatNames
+{
+exch
+_pdfString100 cvs
+length dup dup _pdfString100 exch (-) putinterval
+_pdfString100 exch 1 add dup _pdfString100 length exch sub getinterval
+3 -1 roll exch cvs length
+add 1 add _pdfString100 exch 0 exch getinterval
+cvn
+} bind def
+/_pdfTextTempString 50 string def
+/_pdfRegOrderingArray [(Adobe-Japan1) (Adobe-CNS1) (Adobe-Korea1) (Adobe-GB1)] def
+/_pdf_CheckCIDSystemInfo
+{
+1 index _pdfTextTempString cvs
+(Identity) anchorsearch
+{
+pop pop pop pop true
+}
+{
+false
+_pdfRegOrderingArray
+{
+2 index exch
+anchorsearch
+{ pop pop pop true exit}
+{ pop }
+ifelse
+}
+forall
+exch pop
+exch /CIDFont findresource
+/CIDSystemInfo get
+3 -1 roll /CMap findresource
+/CIDSystemInfo get
+exch
+3 -1 roll
+{
+2 copy
+/Supplement get
+exch
+dup type /dicttype eq
+{/Supplement get}
+{pop 0 }
+ifelse
+ge
+}
+{ true }
+ifelse
+{
+dup /Registry get
+2 index /Registry get eq
+{
+/Ordering get
+exch /Ordering get
+dup type /arraytype eq
+{
+1 index type /arraytype eq
+{
+true
+1 index length 1 sub -1 0
+{
+dup 2 index exch get exch 3 index exch get ne
+{ pop false exit}
+if
+} for
+exch pop exch pop
+}
+{ pop pop false }
+ifelse
+}
+{
+eq
+}
+ifelse
+}
+{ pop pop false }
+ifelse
+}
+{ pop pop false }
+ifelse
+}
+ifelse
+} bind def
+pdf_has_composefont?
+{
+/_pdfComposeFont
+{
+2 copy _pdfComposeFontName not
+{
+2 index
+}
+if
+(pdf) exch _pdfConcatNames
+dup _pdfFontStatus
+{ dup findfont 5 2 roll pop pop pop true}
+{
+4 1 roll
+1 index /CMap pdf_resourcestatus
+{
+pop pop
+true
+}
+{false}
+ifelse
+1 index true exch
+{
+_pdfCIDFontStatus not
+{pop false exit}
+if
+}
+forall
+and
+{
+1 index 1 index 0 get _pdf_CheckCIDSystemInfo
+{
+3 -1 roll pop
+2 index 3 1 roll
+composefont true
+}
+{
+pop pop exch pop false
+}
+ifelse
+}
+{
+_pdfComposeFontName
+{
+dup _pdfFontStatus
+{
+exch pop
+1 index exch
+findfont definefont true
+}
+{
+pop exch pop
+false
+}
+ifelse
+}
+{
+exch pop
+false
+}
+ifelse
+}
+ifelse
+{ true }
+{
+dup _pdfFontStatus
+{ dup findfont true }
+{ pop false }
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+{
+/_pdfComposeFont
+{
+_pdfComposeFontName not
+{
+dup
+}
+if
+dup
+_pdfFontStatus
+{exch pop dup findfont true}
+{
+1 index
+dup type /nametype eq
+{pop}
+{cvn}
+ifelse
+eq
+{pop false}
+{
+dup _pdfFontStatus
+{dup findfont true}
+{pop false}
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+ifelse
+/_pdfStyleDicts 4 dict dup begin
+/Adobe-Japan1 4 dict dup begin
+Level2?
+{
+/Serif
+/HeiseiMin-W3-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiMin-W3}
+{
+/HeiseiMin-W3 _pdfCIDFontStatus
+{/HeiseiMin-W3}
+{/Ryumin-Light}
+ifelse
+}
+ifelse
+def
+/SansSerif
+/HeiseiKakuGo-W5-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiKakuGo-W5}
+{
+/HeiseiKakuGo-W5 _pdfCIDFontStatus
+{/HeiseiKakuGo-W5}
+{/GothicBBB-Medium}
+ifelse
+}
+ifelse
+def
+/HeiseiMaruGo-W4-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiMaruGo-W4}
+{
+/HeiseiMaruGo-W4 _pdfCIDFontStatus
+{/HeiseiMaruGo-W4}
+{
+/Jun101-Light-RKSJ-H _pdfFontStatus
+{ /Jun101-Light }
+{ SansSerif }
+ifelse
+}
+ifelse
+}
+ifelse
+/RoundSansSerif exch def
+/Default Serif def
+}
+{
+/Serif /Ryumin-Light def
+/SansSerif /GothicBBB-Medium def
+{
+(fonts/Jun101-Light-83pv-RKSJ-H) status
+}stopped
+{pop}{
+{ pop pop pop pop /Jun101-Light }
+{ SansSerif }
+ifelse
+/RoundSansSerif exch def
+}ifelse
+/Default Serif def
+}
+ifelse
+end
+def
+/Adobe-Korea1 4 dict dup begin
+/Serif /HYSMyeongJo-Medium def
+/SansSerif /HYGoThic-Medium def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+/Adobe-GB1 4 dict dup begin
+/Serif /STSong-Light def
+/SansSerif /STHeiti-Regular def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+/Adobe-CNS1 4 dict dup begin
+/Serif /MKai-Medium def
+/SansSerif /MHei-Medium def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+end
+def
+/TZzero
+{
+/_wmode xdd
+/_styleArr xdd
+/_regOrdering xdd
+3 copy
+_pdfComposeFont
+{
+5 2 roll pop pop pop
+}
+{
+[
+0 1 _styleArr length 1 sub
+{
+_styleArr exch get
+_pdfStyleDicts _regOrdering 2 copy known
+{
+get
+exch 2 copy known not
+{ pop /Default }
+if
+get
+}
+{
+pop pop pop /Unknown
+}
+ifelse
+}
+for
+]
+exch pop
+2 index 3 1 roll
+_pdfComposeFont
+{3 -1 roll pop}
+{
+findfont dup /FontName get exch
+}
+ifelse
+}
+ifelse
+dup /WMode 2 copy known
+{ get _wmode ne }
+{ pop pop _wmode 1 eq}
+ifelse
+{
+exch _wmode _pdfConcatNames
+dup _pdfFontStatus
+{ exch pop dup findfont false}
+{ exch true }
+ifelse
+}
+{
+dup /FontType get 0 ne
+}
+ifelse
+{
+dup /FontType get 3 eq _wmode 1 eq and
+{
+_pdfVerticalRomanT3Font dup length 10 add dict copy
+begin
+/_basefont exch
+dup length 3 add dict
+begin
+{1 index /FID ne {def}{pop pop} ifelse }
+forall
+/Encoding Encoding dup length array copy
+dup 16#27 /quotesingle put
+dup 16#60 /grave put
+_regOrdering /Adobe-Japan1 eq
+{dup 16#5c /yen put dup 16#a5 /yen put dup 16#b4 /yen put}
+if
+def
+FontName
+currentdict
+end
+definefont
+def
+/Encoding _basefont /Encoding get def
+/_fauxfont true def
+}
+{
+dup length 3 add dict
+begin
+{1 index /FID ne {def}{pop pop} ifelse }
+forall
+FontType 0 ne
+{
+/Encoding Encoding dup length array copy
+dup 16#27 /quotesingle put
+dup 16#60 /grave put
+_regOrdering /Adobe-Japan1 eq
+{dup 16#5c /yen put}
+if
+def
+/_fauxfont true def
+} if
+} ifelse
+/WMode _wmode def
+dup dup /FontName exch def
+currentdict
+end
+definefont pop
+}
+{
+pop
+}
+ifelse
+/_pdf_FontDirectory 3 1 roll _safeput
+}
+bd
+Level2?
+{
+/Tf {
+_pdf_FontDirectory 2 index 2 copy known
+{get exch 3 -1 roll pop}
+{pop pop}
+ifelse
+selectfont
+} bd
+}
+{
+/Tf {
+_pdf_FontDirectory 2 index 2 copy known
+{get exch 3 -1 roll pop}
+{pop pop}
+ifelse
+exch findfont exch
+dup type /arraytype eq
+{makefont}
+{scalefont}
+ifelse
+setfont
+} bd
+}
+ifelse
+/cshow where
+{
+pop /pdf_cshow /cshow load dd
+/pdf_remove2 {pop pop} dd
+}
+{
+/pdf_cshow {exch forall} dd
+/pdf_remove2 {} dd
+} ifelse
+/pdf_xshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+_pdf_x _pdf_y moveto
+0
+rmoveto
+}
+ifelse
+_pdf_i 1 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdf_yshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+_pdf_x _pdf_y moveto
+0 exch
+rmoveto
+}
+ifelse
+_pdf_i 1 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdf_xyshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+{_pdf_na _pdf_i 1 add get} stopped
+{ pop pop pop}
+{
+_pdf_x _pdf_y moveto
+rmoveto
+}
+ifelse
+}
+ifelse
+_pdf_i 2 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdfl1xs {/_pdf_showproc /show load dd pdf_xshow} bd
+/pdfl1ys {/_pdf_showproc /show load dd pdf_yshow} bd
+/pdfl1xys {/_pdf_showproc /show load dd pdf_xyshow} bd
+Level2? _ColorSep5044? not and
+{
+/pdfxs {{xshow} stopped {pdfl1xs} if} bd
+/pdfys {{yshow} stopped {pdfl1ys} if} bd
+/pdfxys {{xyshow} stopped {pdfl1xys} if} bd
+}
+{
+/pdfxs /pdfl1xs load dd
+/pdfys /pdfl1ys load dd
+/pdfxys /pdfl1xys load dd
+} ifelse
+/pdf_charpath {false charpath} bd
+/pdf_xcharpath {/_pdf_showproc /pdf_charpath load dd pdf_xshow} bd
+/pdf_ycharpath {/_pdf_showproc /pdf_charpath load dd pdf_yshow} bd
+/pdf_xycharpath {/_pdf_showproc /pdf_charpath load dd pdf_xyshow} bd
+/pdf_strokepath
+{
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 false charpath
+currentpoint S moveto
+} bind
+exch pdf_cshow
+} bd
+/pdf_xstrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_xshow} bd
+/pdf_ystrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_yshow} bd
+/pdf_xystrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_xyshow} bd
+Level2? {currentglobal true setglobal} if
+/d0/setcharwidth ld
+/nND {{/.notdef} repeat} bd
+/T3Defs {
+/BuildChar
+{
+1 index /Encoding get exch get
+1 index /BuildGlyph get exec
+}
+def
+/BuildGlyph {
+exch begin
+GlyphProcs exch get exec
+end
+} def
+/_pdfT3Font true def
+} bd
+/_pdfBoldRomanWidthProc
+{
+stringwidth 1 index 0 ne { exch .03 add exch }if setcharwidth
+0 0
+} bd
+/_pdfType0WidthProc
+{
+dup stringwidth 0 0 moveto
+2 index true charpath pathbbox
+0 -1
+7 index 2 div .88
+setcachedevice2
+pop
+0 0
+} bd
+/_pdfType0WMode1WidthProc
+{
+dup stringwidth
+pop 2 div neg -0.88
+2 copy
+moveto
+0 -1
+5 -1 roll true charpath pathbbox
+setcachedevice
+} bd
+/_pdfBoldBaseFont
+11 dict begin
+/FontType 3 def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/Encoding cHexEncoding def
+/_setwidthProc /_pdfBoldRomanWidthProc load def
+/_bcstr1 1 string def
+/BuildChar
+{
+exch begin
+_basefont setfont
+_bcstr1 dup 0 4 -1 roll put
+dup
+_setwidthProc
+3 copy
+moveto
+show
+_basefonto setfont
+moveto
+show
+end
+}bd
+currentdict
+end
+def
+pdf_has_composefont?
+{
+/_pdfBoldBaseCIDFont
+11 dict begin
+/CIDFontType 1 def
+/CIDFontName /_pdfBoldBaseCIDFont def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/_setwidthProc /_pdfType0WidthProc load def
+/_bcstr2 2 string def
+/BuildGlyph
+{
+exch begin
+_basefont setfont
+_bcstr2 1 2 index 256 mod put
+_bcstr2 0 3 -1 roll 256 idiv put
+_bcstr2 dup _setwidthProc
+3 copy
+moveto
+show
+_basefonto setfont
+moveto
+show
+end
+}bd
+currentdict
+end
+def
+/_pdfDefineIdentity-H
+{
+/Identity-H /CMap PDFText /pdf_resourcestatus get exec
+{
+pop pop
+}
+{
+/CIDInit/ProcSet findresource begin 12 dict begin
+begincmap
+/CIDSystemInfo
+3 dict begin
+/Registry (Adobe) def
+/Ordering (Identity) def
+/Supplement 0 def
+currentdict
+end
+def
+/CMapName /Identity-H def
+/CMapVersion 1 def
+/CMapType 1 def
+1 begincodespacerange
+<0000> <ffff>
+endcodespacerange
+1 begincidrange
+<0000> <ffff> 0
+endcidrange
+endcmap
+CMapName currentdict/CMap defineresource pop
+end
+end
+} ifelse
+} def
+} if
+/_pdfVerticalRomanT3Font
+10 dict begin
+/FontType 3 def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/_bcstr1 1 string def
+/BuildChar
+{
+exch begin
+_basefont setfont
+_bcstr1 dup 0 4 -1 roll put
+dup
+_pdfType0WidthProc
+moveto
+show
+end
+}bd
+currentdict
+end
+def
+Level2? {setglobal} if
+/MakeBoldFont
+{
+dup /ct_SyntheticBold known
+{
+dup length 3 add dict begin
+CopyFont
+/ct_StrokeWidth .03 0 FontMatrix idtransform pop def
+/ct_SyntheticBold true def
+currentdict
+end
+definefont
+}
+{
+dup dup length 3 add dict
+begin
+CopyFont
+/PaintType 2 def
+/StrokeWidth .03 0 FontMatrix idtransform pop def
+/dummybold currentdict
+end
+definefont
+dup /FontType get dup 9 ge exch 11 le and
+{
+_pdfBoldBaseCIDFont
+dup length 3 add dict copy begin
+dup /CIDSystemInfo get /CIDSystemInfo exch def
+/_Type0Identity /Identity-H 3 -1 roll [ exch ] composefont
+/_basefont exch def
+/_Type0Identity /Identity-H 3 -1 roll [ exch ] composefont
+/_basefonto exch def
+currentdict
+end
+/CIDFont defineresource
+}
+{
+_pdfBoldBaseFont
+dup length 3 add dict copy begin
+/_basefont exch def
+/_basefonto exch def
+currentdict
+end
+definefont
+}
+ifelse
+}
+ifelse
+} bd
+/MakeBold {
+1 index
+_pdf_FontDirectory 2 index 2 copy known
+{get}
+{exch pop}
+ifelse
+findfont
+dup
+/FontType get 0 eq
+{
+dup /WMode known {dup /WMode get 1 eq }{false} ifelse
+version length 4 ge
+and
+{version 0 4 getinterval cvi 2015 ge }
+{true}
+ifelse
+{/_pdfType0WidthProc}
+{/_pdfType0WMode1WidthProc}
+ifelse
+_pdfBoldBaseFont /_setwidthProc 3 -1 roll load put
+{MakeBoldFont} Type0CopyFont definefont
+}
+{
+dup /_fauxfont known not 1 index /SubstMaster known not and
+{
+_pdfBoldBaseFont /_setwidthProc /_pdfBoldRomanWidthProc load put
+MakeBoldFont
+}
+{
+2 index 2 index eq
+{ exch pop }
+{
+dup length dict begin
+CopyFont
+currentdict
+end
+definefont
+}
+ifelse
+}
+ifelse
+}
+ifelse
+pop pop
+dup /dummybold ne
+{/_pdf_FontDirectory exch dup _safeput }
+{ pop }
+ifelse
+}bd
+/MakeItalic {
+_pdf_FontDirectory exch 2 copy known
+{get}
+{exch pop}
+ifelse
+dup findfont
+dup /FontInfo 2 copy known
+{
+get
+/ItalicAngle 2 copy known
+{get 0 eq }
+{ pop pop true}
+ifelse
+}
+{ pop pop true}
+ifelse
+{
+exch pop
+dup /FontType get 0 eq Level2? not and
+{ dup /FMapType get 6 eq }
+{ false }
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+%%CreationDate: 1991 Aug 20 16:34:54
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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+currentdict end
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+cleartomark
+%%EndFont
+%%BeginFont: CMR12
+%!PS-AdobeFont-1.1: CMR12 1.0
+%%CreationDate: 1991 Aug 20 16:38:05
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMR12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMR12 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 11 /ff put
+dup 12 /fi put
+dup 14 /ffi put
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 43 /plus put
+dup 44 /comma put
+dup 45 /hyphen put
+dup 46 /period put
+dup 47 /slash put
+dup 48 /zero put
+dup 49 /one put
+dup 50 /two put
+dup 51 /three put
+dup 52 /four put
+dup 53 /five put
+dup 54 /six put
+dup 55 /seven put
+dup 56 /eight put
+dup 57 /nine put
+dup 58 /colon put
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+%%EndFont
+%%BeginFont: CMTI12
+%!PS-AdobeFont-1.1: CMTI12 1.0
+%%CreationDate: 1991 Aug 18 21:06:53
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMTI12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMTI12 def
+/PaintType 0 def
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+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
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+dup 120 /x put
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+readonly def
+/FontBBox{-36 -251 1103 750}readonly def
+/UniqueID 5000829 def
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+%%CreationDate: 1991 Aug 20 17:33:59
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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+-33 33 0 -33 33 0 3841 2831 4 MP stroke
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+-33 0 17 -17 16 17 3841 2831 4 MP stroke
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+33 -33 0 33 -33 0 4105 3293 4 MP stroke
+-33 0 17 -17 16 17 4072 3260 4 MP stroke
+33 0 -16 16 -17 -16 4105 3293 4 MP stroke
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+34 -33 0 33 -34 0 3577 2567 4 MP stroke
+-34 0 17 -17 17 17 3543 2534 4 MP stroke
+34 0 -17 16 -17 -16 3577 2567 4 MP stroke
+gr
+
+2217 294 mt
+(Mesh for "newVertices15.dat" and "newCells15.dat") s
+
+end
+
+eplot
+%%EndObject
+
+epage
+end
+
+showpage
+
+%%Trailer
+%%EOF
+
+%%EndDocument
+ @endspecial 17970 68608 a(Figure)f(23:)579 b(Output)431
+b(3)j(of)h(TC5)25350 73598 y(24)p eop end
+%%Trailer
+
+userdict /end-hook known{end-hook}if
+%%EOF
diff --git a/Examples/MeshGenToolbox/doc/testingApp.tex b/Examples/MeshGenToolbox/doc/testingApp.tex
new file mode 100644
index 0000000000000000000000000000000000000000..4040d93134524b9c833cfe8a5435f70dbcd36596
--- /dev/null
+++ b/Examples/MeshGenToolbox/doc/testingApp.tex
@@ -0,0 +1,539 @@
+\documentclass[12pt,titlepage]{article}
+
+\include{Preamble}
+
+\author{Wen Yu}
+
+\begin{document}
+
+\begin{titlepage}
+
+% Fonts for the title page
+\newcommand{\texttl}{\textsf} %font for the title (Emil's version is \textsf)
+\newcommand{\textau}{\textsf} %font for the authors, date, etc. (Emils version is \textsc)
+
+\begin{center}
+
+\HRule \\[0.4cm]
+{ \huge \bfseries \texttl{Summary of Validation Testing for a Parallel Mesh Generation Toolbox}}\\[0.4cm]
+
+\HRule \\[2cm]
+
+\textau{\LARGE Wen Yu}\\[2cm]
+
+\textau{\LARGE {September 2008}}
+
+\vfill
+
+% Bottom of the page
+%\includegraphics[width=0.27\textwidth]{logo.pdf}
+\hfill
+\textau{\LARGE
+\raisebox{2pt}{\begin{tabular}[b]{r}
+\raisebox{8pt}{Computing and Software} \\
+McMaster University \end{tabular}}
+}
+\end{center}
+
+\end{titlepage}
+
+\tableofcontents
+
+%to get cross-references correct
+\refstepcounter{funnum} \label{RefiningMesh}
+\refstepcounter{funnum} \label{CoarseningMesh}
+\refstepcounter{funnum} \label{RefiningOrCoarsening}
+\refstepcounter{funnum} \label{MeshType}
+\refstepcounter{funnum} \label{ElmShape}
+\refstepcounter{funnum} \label{DomainDimension}
+\refstepcounter{funnum} \label{Conformal}
+\refstepcounter{funnum} \label{InputDefinition}
+\refstepcounter{funnum} \label{RCInstruction}
+\refstepcounter{funnum} \label{OutputStorage}
+\refstepcounter{funnum} \label{VertexUniqueID}
+\refstepcounter{funnum} \label{ElmUniqueID}
+\refstepcounter{funnum} \label{ElmTopology}
+\refstepcounter{funnum} \label{OutElmOrder}
+\refstepcounter{funnum} \label{OutVertexOrder}
+\refstepcounter{funnum} \label{Help}
+\refstepcounter{nfnum} \label{Performance}
+\refstepcounter{nfnum} \label{Precision}
+\refstepcounter{nfnum} \label{Exception}
+\refstepcounter{nfnum} \label{Portability}
+\refstepcounter{nfnum} \label{LookAndFeel}
+\refstepcounter{nfnum} \label{Usability}
+\refstepcounter{nfnum} \label{Maintainability}
+
+\refstepcounter{mnum} \label{mMemory}
+\refstepcounter{mnum} \label{mFileRW}
+\refstepcounter{mnum} \label{mKeyboard}
+\refstepcounter{mnum} \label{mScreen}
+\refstepcounter{mnum} \label{mInput}
+\refstepcounter{mnum} \label{mOutput}
+\refstepcounter{mnum} \label{mService}
+\refstepcounter{mnum} \label{mVertex}
+\refstepcounter{mnum} \label{mEdge}
+\refstepcounter{mnum} \label{mCell}
+\refstepcounter{mnum} \label{mMesh}
+\refstepcounter{mnum} \label{mRefining}
+\refstepcounter{mnum} \label{mCoarsening}
+
+\newpage
+
+\section{Introduction \label{AtestSecIntro}}
+This section gives an overview of the Testing Summary for a Parallel Mesh Generation Toolbox (PMGT). First, the purpose of the document is provided. Second, the scope of the testing is identified. Third, the organization of the document is summarized.
+
+\subsection{Purpose of the Document}
+This document specifies validation tests for a PMGT. The results of the tests and analysis are also provided. The intended audience is testers who are going to test the system and developers who are going to maintain the software. Note that test document is dynamic in the sense that it should be updated when the development of the system proceeds.
+
+\subsection{Scope of the Testing }
+In general, the purpose of testing is to help produce quality software. Due to limits on the time available for testing, the scope of the testing of PMGT is restricted to test the most important test factors. Like other scientific computing software, correctness and efficiency are considered to be the two most important test factors for PMGT. For efficiency testing, the focus is on execution time rather than on storage.
+
+\subsection{Organization of the Document}
+Section \ref{AtestSecIntro} (this section) is an introduction to the report. Section \ref{AtestSecTest} shows what is going to be tested and the coverage of the testing, with respect to the software requirements and the software design. Section \ref{AtestSecResult} gives the result of the testing and the analysis.
+
+\section{Testing PMGT \label{AtestSecTest}}
+Test cases are listed in Section \ref{AtestSecTestcases}. The detailed information for these test cases can be found in Section \ref{AtestSecResult}. The traceability matrix in Section \ref{AmatrixR} shows the association between test cases and the functional and nonfunctional requirements that are specified in the Software Requirements Specification (SRS) document. Similarly, a traceability matrix for test cases and the leaf modules as introduced in the Module Guide (MG) as shown in Section \ref{AmatrixM}. Tracking these relations is useful for developing and maintaining the software.
+
+\subsection{Test Cases \label{AtestSecTestcases}}
+The correctness validation test is designed for verifying the functional requirements RefiningMesh (\fref{RefiningMesh}), CoarseningMesh (\fref{CoarseningMesh}), ElmShape (\fref{ElmShape}), and Conformal (\fref{Conformal}). Other requirements for correctness are trivial and are satisfied obviously. For example, since the vertices are stored in an array, the OutVertexOrder (\fref{OutVertexOrder}) requirement is met by outputting the vertices in the order as the order of them in the array. The tests are against above requirements are automated. The automated validation tests requirements (ACVTRs) are listed in Section \ref{ACVTRs}. Since the output mesh also can also be displayed on screen, it can be checked manually. The visual correctness validation tests requirements (VCVTRs) are listed in Section \ref{VCVTRs}. The test cases are in Section \ref{TCs}.
+\subsubsection{Automated Correctness Validation Tests Requirements \label{ACVTRs}}
+A list of ACVTRs follows. All test cases should pass these tests. Some test cases relate to data definitions defined in the SRS. In these cases the related data definition defined is shown as D$x$, where $x$ is the number of the associated data definition given in the SRS.
+\begin{itemize}
+\item The area of each element is greater than zero (referring to \textbf{D5}). %hard coded reference
+\item The boundary of the mesh is closed. (referring to \textbf{D15}). %hard coded reference
+\item The mesh is conformal (referring to \textbf{D16}). %hard coded reference
+\item The intersection of any two elements is empty (referring to \textbf{D17}). %hard coded reference
+\item The input mesh and output mesh {\em CoveringUp} each other (referring to \textbf{D19}). %hard coded reference
+\item The length of each edge is greater than zero. (This is required by the definition of a mesh, which is defined in the SRS.)
+\item The vertices of each element are listed in a counterclockwise order. (The counterclockwise order of the vertices for each element is not necessary for implementing PMGT. However, it is adopted by most meshing and FEA software. PMGT uses this convention.)
+\item The output mesh conforms to the Euler Equation. (This requirement is not documented in the SRS. However, any mesh should implicitly satisfy the equation $nc+nv-ne=1$, where $nc$ is the number of cells, $nv$ is the number of vertices, and $ne$ is the number of edges.)
+\end{itemize}
+\subsubsection{Visual Correctness Validation Tests Requirements\label{VCVTRs}}
+The output meshes should also be visually checked to ensure that the following VCVTRs are met.
+\begin{itemize}
+\item No vertex is outside of the input domain.
+\item No vertex is inside of a cell.
+\item No dangling points or edges are present.
+\item All cells are connected.
+\item The mesh is conformal.
+\end{itemize}
+Some of the VCVTRs overlap with the ACVTRs. This redundancy provides increased confidence in case one testing method fails to catch an error.
+\subsubsection{Test Cases\label{TCs}}
+The test cases developed involve testing meshes against the above requirements. In each test case, except the last one, the input mesh is refined and then coarsened. Two algorithms for refining are used. One algorithm is called {\em Split}. It splits one cell into three by adding a point in the centroid of the triangle and connecting the added point to the three original vertices. The other algorithm is simply call {\em Refine}. It refines the original mesh by longest edge bisection.
+
+The name of each test case includes three parts. For example, test case $AxxCBN$ means that the test uses $Axx$ algorithm for refining, where $Axx$ equals $Split$ or $Refine$. The letter $C$ indicates that coarsening is performed. If the $C$ is missing, the input mesh is not coarsened. $B$ is the number of refinements before coarsening. If $B$ is S, the mesh is refined once and then coarsen once. If the $B$ is M, the mesh is refined multiple time before coarsening. $N$ is a number. If the $N$ is omitted, it means only one of this kind of test performed. Otherwise the same test procedures is used several times on different input meshes. The reason for using the same procedure is that the topology of the output meshes may differ for different input meshes.
+\begin{itemize}
+\item Test Case {\em SplitCS} (\refstepcounter{casenum}\cthecasenum \label{ATCscs}): This test case tests the correctness of PMGT. The input mesh is shown in Figure \ref{input1}. The refining and coarsening criterion is that the cells intersected with the vertical line, $x=0.6$, are Split once, then the cells of the new mesh that intersect with the vertical line are coarsened once. When the splitting and coarsening is done, the vertical line is moved to the right one unit ($x=x+1.0$), and another Splitting and coarsening is performed. This procedure is repeated until no cells intersect with the vertical line.
+
+\item Test Case {\em RefineCS1} (\refstepcounter{casenum}\cthecasenum \label{ATCrcs1}): This test case tests the correctness of PMGT. The input mesh is the same as \cref{ATCscs}, which is shown in Figure \ref{input1}. There is a vertical line at $x = 0.6$. The refining and coarsening criterion is that the cells that intersect with the vertical line are refined once, then the cells of the new mesh that intersect with the vertical line are coarsened once. When the refining and coarsening are done, the vertical line is moved to the right one unit, and another refining and coarsening is performed. This procedure is repeated until no cells intersect with the vertical line.
+
+\item Test Case {\em RefineCS2} (\refstepcounter{casenum}\cthecasenum \label{ATCrcs2}): This test case tests the correctness of PMGT. The refining and coarsening criterion, vertical line function, and the test procedure are the same as test case \cref{ATCrcs1}. However, the input mesh is different. The input mesh is showed in Figure \ref{input2}.
+
+\item Test Case {\em RefineCM} (\refstepcounter{casenum}\cthecasenum \label{ATCrcm}): This test case tests the correctness of PMGT. The input mesh is shown in Figure \ref{input3}. There is a vertical line at $x = 0.5$. The refining and coarsening criterion is the size of the cells. The size of the cell is measured by the length of the longest edge of the cell. The cells that intersect with the vertical line are refined until the criterion is met. When the refining is done, the vertical line is moved to the right $0.6$ unit ($x=x+0.6$), and another refinement is performed. After five refinements are done, the cells to be left of the vertical line by up to 2 units are coarsened, until the coarsening criterion is met. The refining and coarsening are stopped when the vertical line moves to a position outside of the domain.
+
+\item Test Case {\em RefineM} (\refstepcounter{casenum}\cthecasenum \label{ATCrm}): This test case tests the correctness of PMGT. The input mesh is shown in Figure \ref{input4}. There is an arc with radius of 0.7 unit going through the mesh. Cells that intersect with the arc are refined until the required number of refinements has been reached.
+
+\item Test Case {\em Split} (\refstepcounter{casenum}\cthecasenum \label{ATCss}): This test case tests both the correctness and speed of PMGT. The input mesh is shown in Figure \ref{input5}. This test simply splits all cells of the mesh 4 times. It is done in both the serial version and the parallel version with different number of processors. The execution time of setting the cells to be refined and splitting the cells is measured.
+\end{itemize}
+
+\subsection{Traceability Matrix for SRS \label{AmatrixR}}
+In the traceability matrix for software requirements, if a test case tests the functionality of a software requirement, there will be a check mark on the cell for the corresponding test case. In each row of the traceability matrix for software requirements (Table \ref{AtestTMr}), if the requirement in that row defines the correctness or the speed of the software, one or more cells in this row are checked. Otherwise, all cells in the row are empty. Table \ref{AtestTMr} shows that the test cases developed in Section \ref{AtestSecTestcases} assist with validating the correctness and speed of the software. The detailed information for each functional and nonfunctional requirements can be found in the SRS document.
+The names of the requirements and their corresponding numbers are listed below for convenience.
+\begin{description}
+\item[\fref{RefiningMesh}:] RefiningMesh
+\item[\fref{CoarseningMesh}:] CoarseningMesh
+\item[\fref{RefiningOrCoarsening}:] RefiningOrCoarsening
+\item[\fref{MeshType}:] MeshType
+\item[\fref{ElmShape}:] ElmShape
+\item[\fref{DomainDimension}:] DomainDimension
+\item[\fref{Conformal}:] Conformal
+\item[\fref{InputDefinition}:] InputDefinition
+\item[\fref{RCInstruction}:] RCInstruction
+\item[\fref{OutputStorage}:] OutputStorage
+\item[\fref{VertexUniqueID}:] VertexUniqueID
+\item[\fref{ElmUniqueID}:] ElmUniqueID
+\item[\fref{ElmTopology}:] ElmTopology
+\item[\fref{OutElmOrder}:] OutElmOrder
+\item[\fref{OutVertexOrder}:] OutVertexOrder
+\item[\fref{Help}:] Help
+\item[\nref{Performance}:] Performance
+\item[\nref{Precision}:] Precision
+\item[\nref{Exception}:] Exception
+\item[\nref{Portability}:] Portability
+\item[\nref{LookAndFeel}:] LookAndFeel
+\item[\nref{Usability}:] Usability
+\item[\nref{Maintainability}:] Maintainability
+\end{description}
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{|p{0.06\textwidth}|p{0.06\textwidth}|p{0.06\textwidth}|p{0.06\textwidth}|p{0.06\textwidth}|p{0.06\textwidth}|p{0.06\textwidth}|}
+\hline
+ &\cref{ATCscs} & \cref{ATCrcs1} & \cref{ATCrcs2} & \cref{ATCrcm} & \cref{ATCrm}&\cref{ATCss}\\
+\hline\hline
+\fref{RefiningMesh}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark\\\hline%f2
+\fref{CoarseningMesh}& \checkmark & \checkmark & \checkmark & \checkmark & & \\\hline%f3
+\fref{RefiningOrCoarsening}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline%f1
+\fref{MeshType}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark& \\\hline%f4
+\fref{ElmShape}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark& \\\hline%f5
+\fref{DomainDimension}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark& \\\hline%f6
+\fref{Conformal}& \checkmark &\checkmark & \checkmark & \checkmark & \checkmark& \\\hline%f7
+\fref{InputDefinition}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\fref{RCInstruction}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\fref{OutputStorage}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \\\hline
+\fref{VertexUniqueID}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \\\hline
+\fref{ElmUniqueID}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \\\hline
+\fref{ElmTopology}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \\\hline
+\fref{OutElmOrder}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \\\hline
+\fref{OutVertexOrder}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \\\hline
+\fref{Help} & & & & & & \\\hline
+\nref{Performance} & & & & & & \checkmark \\\hline
+\nref{Precision} & & & & & & \\\hline
+\nref{Exception} & & & & & & \\\hline
+\nref{Portability} & & & & & & \\\hline
+\nref{LookAndFeel} & & & & & & \\\hline
+\nref{Usability} & & & & & & \\\hline
+\nref{Maintainability} & & & & & & \\\hline
+\end{tabular}
+\caption{Traceability Matrix: Test Cases and Requirements}
+\label{AtestTMr}
+\end{table}
+
+\subsection{Traceability Matrix for MG \label{AmatrixM}}
+Similar to Section \ref{AmatrixR}, the traceability matrix for modules (Table \ref{AtestTMm}) shows that the test cases validate the modules that are associated with correctness and speed. The names of modules appear in Table \ref{AtestTMm} are listed below. The detailed information for each module can be found in the MG document.
+\begin{description}
+\item[\mref{mMemory}:] Virtual Memory Module
+\item[\mref{mFileRW}:] File Read/Write Module
+\item[\mref{mKeyboard}:] Keyboard Input Module
+\item[\mref{mScreen}:] Screen Output Module
+\item[\mref{mInput}:] Input Format Module
+\item[\mref{mOutput}:] Output Format Module
+\item[\mref{mService}:] Service Module
+\item[\mref{mVertex}:] Vertex Module
+\item[\mref{mEdge}:] Edge Module
+\item[\mref{mCell}:] Cell Module
+\item[\mref{mMesh}:] Mesh Module
+\item[\mref{mRefining}:] Refining Module
+\item[\mref{mCoarsening}:] Coarsening Module
+\end{description}
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{|p{0.06\textwidth}|p{0.06\textwidth}|p{0.06\textwidth}|p{0.06\textwidth}|p{0.06\textwidth}|p{0.06\textwidth}|p{0.06\textwidth}|}
+\hline
+ &\cref{ATCscs} & \cref{ATCrcs1} & \cref{ATCrcs2} & \cref{ATCrcm} & \cref{ATCrm}&\cref{ATCss}\\
+\hline\hline
+\mref{mMemory}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mFileRW}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mKeyboard}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mScreen}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mInput}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mOutput}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mService}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \\\hline
+\mref{mVertex}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mEdge}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mCell}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mMesh}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mRefining}& \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\\hline
+\mref{mCoarsening}& \checkmark & \checkmark & \checkmark & \checkmark & & \\\hline
+\end{tabular}
+\caption{Traceability Matrix: Test Cases and Modules}
+\label{AtestTMm}
+\end{table}
+
+\section{Results and Analysis\label{AtestSecResult}}
+The results of the test cases defined in Section \ref{TCs} are listed in Section \ref{AtestSectestresult}. The analysis, including charts that compare the execution time of the parallel version to the serial version are provided in Section \ref{AtestSecAnalysis}.
+\subsection {Testing Results \label{AtestSectestresult}}
+The following tables list the testing results of each test case. The field {\em Test Case Number} and {\em Test Case Name} list the number and the name of each test case. The {\em Input field} gives the number of the figure that is the input for that test case, or a description of the input mesh. The {\em Expected Output} describes the requirements of the output mesh. The {\em Actual Output} gives the result of the test. The {\em Selected Output Mesh} field should give the output meshes. However, there are too many intermediate mesh to display, and displaying only the final mesh is too simple to illustrate the feature of the test case. Selected intermediate meshes and final mesh are included in the {\em Actual Output} field. The {\em Result} field indicates whether the test is passed or failed.
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Test Case Number} & \cref{ATCscs} \\
+{\bf Test Case Name} & SplitCS\\
+\hline
+Input & Figure \ref{input1}\\
+Expected Output & ACVTRs and VCVTRs listed in Section \ref{AtestSecTest} are met\\
+Actual Output & Summary of the correctness test:\\
+& 15 tests are performed.\\
+& 15 tests succeed.\\
+& 0 tests fail.\\
+Selected Output Mesh &Figure \ref{output11}, \ref{output12}, \ref{output13}\\
+Result & Passed\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Test Case Number} & \cref{ATCrcs1} \\
+{\bf Test Case Name} & RefineCS1\\
+\hline
+Input & Figure \ref{input1}\\
+Expected Output & ACVTRs and VCVTRs listed in Section \ref{AtestSecTest} are met\\
+Actual Output & Summary of the correctness test:\\
+& 15 tests are performed.\\
+& 15 tests succeed.\\
+& 0 tests fail.\\
+Selected Output Mesh & Figure \ref{output21}, \ref{output22}, \ref{output23}\\
+Result & Passed\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Test Case Number} & \cref{ATCrcs2} \\
+{\bf Test Case Name} & RefineCS2\\
+\hline
+Input & Figure \ref{input2}\\
+Expected Output & ACVTRs and VCVTRs listed in Section \ref{AtestSecTest} are met\\
+Actual Output & Summary of the correctness test:\\
+& 15 tests are performed.\\
+& 15 tests succeed.\\
+& 0 tests fail.\\
+Selected Output Mesh & Figure \ref{output31}, \ref{output32}, \ref{output33}\\
+Result & Passed\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Test Case Number} & \cref{ATCrcm} \\
+{\bf Test Case Name} & RefineCM\\
+\hline
+Input & Figure \ref{input3}\\
+Expected Output & ACVTRs and VCVTRs listed in Section \ref{AtestSecTest} are met\\
+Actual Output & Summary of the correctness test:\\
+& 15 tests are performed.\\
+& 15 tests succeed.\\
+& 0 tests fail.\\
+Selected Output Mesh & Figure \ref{output41}, \ref{output42}, \ref{output43}, \ref{output44}\\
+Result & Passed\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Test Case Number} & \cref{ATCrm} \\
+{\bf Test Case Name} & RefineM\\
+\hline
+Input & Figure \ref{input4}\\
+Expected Output & ACVTRs and VCVTRs listed in Section \ref{AtestSecTest} are met\\
+Actual Output & Summary of the correctness test:\\
+& 15 tests are performed.\\
+& 15 tests succeed.\\
+& 0 tests fail.\\
+Selected Output Mesh & Figure \ref{output51}, \ref{output52}, \ref{output53}\\
+Result & Passed\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\vspace{1cm}
+\begin{minipage}{\textwidth}
+\begin{tabular}{p{\colAwidth}|p{\colBwidth}}
+\hline \hline
+{\bf Test Case Number} & \cref{ATCss} \\
+{\bf Test Case Name} & SplitM\\
+\hline
+Input & Figure \ref{input4}\\
+Expected Output & ACVTRs and VCVTRs listed in Section \ref{AtestSecTest} are met\\
+& Execution time increases as the number of cells increases. Execution time decreases as the number of processors increases.\\
+Actual Output & Execution time as indicated in Figure \ref{output61}\\
+Selected Output Mesh & The mesh is too dense to be shown.\\
+Result & Passed\\
+\hline \hline
+\end{tabular}
+\end{minipage}
+
+\begin{figure}[ht]
+\centering
+\epsfig{file=output61.eps, width= \textwidth}
+\caption{Output of \cref{ATCss}}
+\label{output61}
+\end{figure}
+
+\subsection {Analysis \label{AtestSecAnalysis}}
+All of the test cases conform to the ACVTRs and VCVTRs listed in Section \ref{AtestSecTest}. The test result of \cref{ATCss} show that when the number of cells increased, the execution time increased, and when the number of processors increased, the execution time decreased. That is, this test is passed. Figure \ref{speedup} show the speedup when using different numbers of processors. The speedup is defined as
+\[ Speedup(n) = \frac{T_{1}}{T_{n}}
+\]
+Where $T_{1}$ is the execution time of the serial version, and $T_{n}$ is the execution time of the parallel version with $n$ processors. In general, $Speedup(n) < n$. However, for PMGT, when the number of cells is greater than 2700, $Speedup(n) > n$, which is a super linear speedup. Since the algorithms used for the serial version and the parallel version are the same, the super linear speedup is probably due to the cache effect. That is, when the numbers of processors increases, the size of the accumulated caches from different processors also increases. With the larger accumulated cache size, more, or even all, core data set can fit into the caches and the memory access time reduces dramatically. This may explain the extra speedup in additional to the speedup due to parallel computation.
+
+\begin{figure}
+\centering
+\epsfig{file=speedup.eps, width= \textwidth}
+\caption{Speedup for Different Numbers of Processors}
+\label{speedup}
+\end{figure}
+
+
+\begin{figure}
+\centering
+\epsfig{file=input1.eps, width= 0.7\textwidth}
+\caption{Input 1}
+\label{input1}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=input2.eps, width= 0.7\textwidth}
+\caption{Input 2}
+\label{input2}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=input3.eps, width= 0.7\textwidth}
+\caption{Input 3}
+\label{input3}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=input4.eps, width= 0.7\textwidth}
+\caption{Input 4}
+\label{input4}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=input5.eps, width= 0.7\textwidth}
+\caption{Input 5}
+\label{input5}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output11.eps, width=0.7\textwidth}
+\caption{Output 1 of \cref{ATCscs}}
+\label{output11}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output12.eps, width=0.7\textwidth}
+\caption{Output 2 of \cref{ATCscs}}
+\label{output12}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output13.eps, width=0.7\textwidth}
+\caption{Output 3 of \cref{ATCscs}}
+\label{output13}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output21.eps, width=0.7\textwidth}
+\caption{Output 1 of \cref{ATCrcs1}}
+\label{output21}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output22.eps, width=0.7\textwidth}
+\caption{Output 2 of \cref{ATCrcs1}}
+\label{output22}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output23.eps, width=0.7\textwidth}
+\caption{Output 3 of \cref{ATCrcs1}}
+\label{output23}
+\end{figure}
+
+\clearpage
+
+\begin{figure}
+\centering
+\epsfig{file=output31.eps, width=0.7\textwidth}
+\caption{Output 1 of \cref{ATCrcs2}}
+\label{output31}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output32.eps, width=0.7\textwidth}
+\caption{Output 2 of \cref{ATCrcs2}}
+\label{output32}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output33.eps, width=0.7\textwidth}
+\caption{Output 3 of \cref{ATCrcs2}}
+\label{output33}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output41.eps, width=0.7\textwidth}
+\caption{Output 1 of \cref{ATCrcm}}
+\label{output41}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output42.eps, width=0.7\textwidth}
+\caption{Output 2 of \cref{ATCrcm}}
+\label{output42}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output43.eps, width=0.7\textwidth}
+\caption{Output 3 of \cref{ATCrcm}}
+\label{output43}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output44.eps, width=0.7\textwidth}
+\caption{Output 4 of \cref{ATCrcm}}
+\label{output44}
+\end{figure}
+
+
+\begin{figure}
+\centering
+\epsfig{file=output51.eps, width=0.7\textwidth}
+\caption{Output 1 of \cref{ATCrm}}
+\label{output51}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output52.eps, width=0.7\textwidth}
+\caption{Output 2 of \cref{ATCrm}}
+\label{output52}
+\end{figure}
+
+\begin{figure}
+\centering
+\epsfig{file=output53.eps, width=0.7\textwidth}
+\caption{Output 3 of \cref{ATCrm}}
+\label{output53}
+\end{figure}
+
+%\newpage
+
+%\bibliography{WenRef}
+%\bibliographystyle{plainnat}
+
+\end{document}
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+ ct_Vars /vm currentglobal put
+ ({ResourceStatus} stopped) 0 () /SubFileDecode filter cvx exec
+ { cleartomark false }
+ { { 3 2 roll pop true } { cleartomark false } ifelse }
+ ifelse
+ ct_Vars /vm get setglobal
+ end
+ }
+ }
+ { { resourcestatus } }
+ ifelse bind def
+ /CIDFont /Category ct_resourcestatus
+ { pop pop }
+ {
+ currentglobal true setglobal
+ /Generic /Category findresource
+ dup length dict copy
+ dup /InstanceType /dicttype put
+ /CIDFont exch /Category defineresource pop
+ setglobal
+ }
+ ifelse
+ ct_UseNativeCapability?
+ {
+ /CIDInit /ProcSet findresource begin
+ 12 dict begin
+ begincmap
+ /CIDSystemInfo 3 dict dup begin
+ /Registry (Adobe) def
+ /Ordering (Identity) def
+ /Supplement 0 def
+ end def
+ /CMapName /Identity-H def
+ /CMapVersion 1.000 def
+ /CMapType 1 def
+ 1 begincodespacerange
+ <0000> <FFFF>
+ endcodespacerange
+ 1 begincidrange
+ <0000> <FFFF> 0
+ endcidrange
+ endcmap
+ CMapName currentdict /CMap defineresource pop
+ end
+ end
+ }
+ if
+ }
+ {
+ /ct_Category 2 dict begin
+ /CIDFont 10 dict def
+ /ProcSet 2 dict def
+ currentdict
+ end
+ def
+ /defineresource
+ {
+ ct_Category 1 index 2 copy known
+ {
+ get
+ dup dup maxlength exch length eq
+ {
+ dup length 10 add dict copy
+ ct_Category 2 index 2 index put
+ }
+ if
+ 3 index 3 index put
+ pop exch pop
+ }
+ { pop pop /defineresource /undefined ct_raise }
+ ifelse
+ } bind def
+ /findresource
+ {
+ ct_Category 1 index 2 copy known
+ {
+ get
+ 2 index 2 copy known
+ { get 3 1 roll pop pop}
+ { pop pop /findresource /undefinedresource ct_raise }
+ ifelse
+ }
+ { pop pop /findresource /undefined ct_raise }
+ ifelse
+ } bind def
+ /resourcestatus
+ {
+ ct_Category 1 index 2 copy known
+ {
+ get
+ 2 index known
+ exch pop exch pop
+ {
+ 0 -1 true
+ }
+ {
+ false
+ }
+ ifelse
+ }
+ { pop pop /findresource /undefined ct_raise }
+ ifelse
+ } bind def
+ /ct_resourcestatus /resourcestatus load def
+ }
+ ifelse
+ /ct_CIDInit 2 dict
+ begin
+ /ct_cidfont_stream_init
+ {
+ {
+ dup (Binary) eq
+ {
+ pop
+ null
+ currentfile
+ ct_Level2?
+ {
+ { cid_BYTE_COUNT () /SubFileDecode filter }
+ stopped
+ { pop pop pop }
+ if
+ }
+ if
+ /readstring load
+ exit
+ }
+ if
+ dup (Hex) eq
+ {
+ pop
+ currentfile
+ ct_Level2?
+ {
+ { null exch /ASCIIHexDecode filter /readstring }
+ stopped
+ { pop exch pop (>) exch /readhexstring }
+ if
+ }
+ { (>) exch /readhexstring }
+ ifelse
+ load
+ exit
+ }
+ if
+ /StartData /typecheck ct_raise
+ }
+ loop
+ cid_BYTE_COUNT ct_CID_STR_SIZE le
+ {
+ 2 copy cid_BYTE_COUNT string exch exec
+ pop
+ 1 array dup
+ 3 -1 roll
+ 0 exch put
+ }
+ {
+ cid_BYTE_COUNT ct_CID_STR_SIZE div ceiling cvi
+ dup array exch 2 sub 0 exch 1 exch
+ {
+ 2 copy
+ 5 index
+ ct_CID_STR_SIZE
+ string
+ 6 index exec
+ pop
+ put
+ pop
+ }
+ for
+ 2 index
+ cid_BYTE_COUNT ct_CID_STR_SIZE mod string
+ 3 index exec
+ pop
+ 1 index exch
+ 1 index length 1 sub
+ exch put
+ }
+ ifelse
+ cid_CIDFONT exch /GlyphData exch put
+ 2 index null eq
+ {
+ pop pop pop
+ }
+ {
+ pop /readstring load
+ 1 string exch
+ {
+ 3 copy exec
+ pop
+ dup length 0 eq
+ {
+ pop pop pop pop pop
+ true exit
+ }
+ if
+ 4 index
+ eq
+ {
+ pop pop pop pop
+ false exit
+ }
+ if
+ }
+ loop
+ pop
+ }
+ ifelse
+ } bind def
+ /StartData
+ {
+ mark
+ {
+ currentdict
+ dup /FDArray get 0 get /FontMatrix get
+ 0 get 0.001 eq
+ {
+ dup /CDevProc known not
+ {
+ /CDevProc 1183615869 internaldict /stdCDevProc 2 copy known
+ { get }
+ {
+ pop pop
+ { pop pop pop pop pop 0 -1000 7 index 2 div 880 }
+ }
+ ifelse
+ def
+ }
+ if
+ }
+ {
+ /CDevProc
+ {
+ pop pop pop pop pop
+ 0
+ 1 cid_temp /cid_CIDFONT get
+ /FDArray get 0 get
+ /FontMatrix get 0 get div
+ 7 index 2 div
+ 1 index 0.88 mul
+ } def
+ }
+ ifelse
+ /cid_temp 15 dict def
+ cid_temp
+ begin
+ /cid_CIDFONT exch def
+ 3 copy pop
+ dup /cid_BYTE_COUNT exch def 0 gt
+ {
+ ct_cidfont_stream_init
+ FDArray
+ {
+ /Private get
+ dup /SubrMapOffset known
+ {
+ begin
+ /Subrs SubrCount array def
+ Subrs
+ SubrMapOffset
+ SubrCount
+ SDBytes
+ ct_Level2?
+ {
+ currentdict dup /SubrMapOffset undef
+ dup /SubrCount undef
+ /SDBytes undef
+ }
+ if
+ end
+ /cid_SD_BYTES exch def
+ /cid_SUBR_COUNT exch def
+ /cid_SUBR_MAP_OFFSET exch def
+ /cid_SUBRS exch def
+ cid_SUBR_COUNT 0 gt
+ {
+ GlyphData cid_SUBR_MAP_OFFSET cid_SD_BYTES ct_GetInterval
+ 0 cid_SD_BYTES ct_cvnsi
+ 0 1 cid_SUBR_COUNT 1 sub
+ {
+ exch 1 index
+ 1 add
+ cid_SD_BYTES mul cid_SUBR_MAP_OFFSET add
+ GlyphData exch cid_SD_BYTES ct_GetInterval
+ 0 cid_SD_BYTES ct_cvnsi
+ cid_SUBRS 4 2 roll
+ GlyphData exch
+ 4 index
+ 1 index
+ sub
+ ct_GetInterval
+ dup length string copy put
+ }
+ for
+ pop
+ }
+ if
+ }
+ { pop }
+ ifelse
+ }
+ forall
+ }
+ if
+ cleartomark pop pop
+ end
+ CIDFontName currentdict /CIDFont defineresource pop
+ end end
+ }
+ stopped
+ { cleartomark /StartData ct_reraise }
+ if
+ } bind def
+ currentdict
+ end def
+ /ct_saveCIDInit
+ {
+ /CIDInit /ProcSet ct_resourcestatus
+ { true }
+ { /CIDInitC /ProcSet ct_resourcestatus }
+ ifelse
+ {
+ pop pop
+ /CIDInit /ProcSet findresource
+ ct_UseNativeCapability?
+ { pop null }
+ { /CIDInit ct_CIDInit /ProcSet defineresource pop }
+ ifelse
+ }
+ { /CIDInit ct_CIDInit /ProcSet defineresource pop null }
+ ifelse
+ ct_Vars exch /ct_oldCIDInit exch put
+ } bind def
+ /ct_restoreCIDInit
+ {
+ ct_Vars /ct_oldCIDInit get dup null ne
+ { /CIDInit exch /ProcSet defineresource pop }
+ { pop }
+ ifelse
+ } bind def
+ /ct_BuildCharSetUp
+ {
+ 1 index
+ begin
+ CIDFont
+ begin
+ Adobe_CoolType_Utility /ct_BuildCharDict get
+ begin
+ /ct_dfCharCode exch def
+ /ct_dfDict exch def
+ CIDFirstByte ct_dfCharCode add
+ dup CIDCount ge
+ { pop 0 }
+ if
+ /cid exch def
+ {
+ GlyphDirectory cid 2 copy known
+ { get }
+ { pop pop nullstring }
+ ifelse
+ dup length FDBytes sub 0 gt
+ {
+ dup
+ FDBytes 0 ne
+ { 0 FDBytes ct_cvnsi }
+ { pop 0 }
+ ifelse
+ /fdIndex exch def
+ dup length FDBytes sub FDBytes exch getinterval
+ /charstring exch def
+ exit
+ }
+ {
+ pop
+ cid 0 eq
+ { /charstring nullstring def exit }
+ if
+ /cid 0 def
+ }
+ ifelse
+ }
+ loop
+ } def
+ /ct_SetCacheDevice
+ {
+ 0 0 moveto
+ dup stringwidth
+ 3 -1 roll
+ true charpath
+ pathbbox
+ 0 -1000
+ 7 index 2 div 880
+ setcachedevice2
+ 0 0 moveto
+ } def
+ /ct_CloneSetCacheProc
+ {
+ 1 eq
+ {
+ stringwidth
+ pop -2 div -880
+ 0 -1000 setcharwidth
+ moveto
+ }
+ {
+ usewidths?
+ {
+ currentfont /Widths get cid
+ 2 copy known
+ { get exch pop aload pop }
+ { pop pop stringwidth }
+ ifelse
+ }
+ { stringwidth }
+ ifelse
+ setcharwidth
+ 0 0 moveto
+ }
+ ifelse
+ } def
+ /ct_Type3ShowCharString
+ {
+ ct_FDDict fdIndex 2 copy known
+ { get }
+ {
+ currentglobal 3 1 roll
+ 1 index gcheck setglobal
+ ct_Type1FontTemplate dup maxlength dict copy
+ begin
+ FDArray fdIndex get
+ dup /FontMatrix 2 copy known
+ { get }
+ { pop pop ct_defaultFontMtx }
+ ifelse
+ /FontMatrix exch dup length array copy def
+ /Private get
+ /Private exch def
+ /Widths rootfont /Widths get def
+ /CharStrings 1 dict dup /.notdef
+ <d841272cf18f54fc13> dup length string copy put def
+ currentdict
+ end
+ /ct_Type1Font exch definefont
+ dup 5 1 roll put
+ setglobal
+ }
+ ifelse
+ dup /CharStrings get 1 index /Encoding get
+ ct_dfCharCode get charstring put
+ rootfont /WMode 2 copy known
+ { get }
+ { pop pop 0 }
+ ifelse
+ exch
+ 1000 scalefont setfont
+ ct_str1 0 ct_dfCharCode put
+ ct_str1 exch ct_dfSetCacheProc
+ ct_SyntheticBold
+ {
+ currentpoint
+ ct_str1 show
+ newpath
+ moveto
+ ct_str1 true charpath
+ ct_StrokeWidth setlinewidth
+ stroke
+ }
+ { ct_str1 show }
+ ifelse
+ } def
+ /ct_Type4ShowCharString
+ {
+ ct_dfDict ct_dfCharCode charstring
+ FDArray fdIndex get
+ dup /FontMatrix get dup ct_defaultFontMtx ct_matrixeq not
+ { ct_1000Mtx matrix concatmatrix concat }
+ { pop }
+ ifelse
+ /Private get
+ Adobe_CoolType_Utility /ct_Level2? get not
+ {
+ ct_dfDict /Private
+ 3 -1 roll
+ { put }
+ 1183615869 internaldict /superexec get exec
+ }
+ if
+ 1183615869 internaldict
+ Adobe_CoolType_Utility /ct_Level2? get
+ { 1 index }
+ { 3 index /Private get mark 6 1 roll }
+ ifelse
+ dup /RunInt known
+ { /RunInt get }
+ { pop /CCRun }
+ ifelse
+ get exec
+ Adobe_CoolType_Utility /ct_Level2? get not
+ { cleartomark }
+ if
+ } bind def
+ /ct_BuildCharIncremental
+ {
+ {
+ Adobe_CoolType_Utility /ct_MakeOCF get begin
+ ct_BuildCharSetUp
+ ct_ShowCharString
+ }
+ stopped
+ { stop }
+ if
+ end
+ end
+ end
+ end
+ } bind def
+ /BaseFontNameStr (BF00) def
+ /ct_Type1FontTemplate 14 dict
+ begin
+ /FontType 1 def
+ /FontMatrix [0.001 0 0 0.001 0 0] def
+ /FontBBox [-250 -250 1250 1250] def
+ /Encoding ct_cHexEncoding def
+ /PaintType 0 def
+ currentdict
+ end def
+ /BaseFontTemplate 11 dict
+ begin
+ /FontMatrix [0.001 0 0 0.001 0 0] def
+ /FontBBox [-250 -250 1250 1250] def
+ /Encoding ct_cHexEncoding def
+ /BuildChar /ct_BuildCharIncremental load def
+ ct_Clone?
+ {
+ /FontType 3 def
+ /ct_ShowCharString /ct_Type3ShowCharString load def
+ /ct_dfSetCacheProc /ct_CloneSetCacheProc load def
+ /ct_SyntheticBold false def
+ /ct_StrokeWidth 1 def
+ }
+ {
+ /FontType 4 def
+ /Private 1 dict dup /lenIV 4 put def
+ /CharStrings 1 dict dup /.notdef <d841272cf18f54fc13> put def
+ /PaintType 0 def
+ /ct_ShowCharString /ct_Type4ShowCharString load def
+ }
+ ifelse
+ /ct_str1 1 string def
+ currentdict
+ end def
+ /BaseFontDictSize BaseFontTemplate length 5 add def
+ /ct_matrixeq
+ {
+ true 0 1 5
+ {
+ dup 4 index exch get exch 3 index exch get eq and
+ dup not
+ { exit }
+ if
+ }
+ for
+ exch pop exch pop
+ } bind def
+ /ct_makeocf
+ {
+ 15 dict
+ begin
+ exch /WMode exch def
+ exch /FontName exch def
+ /FontType 0 def
+ /FMapType 2 def
+ /FontMatrix matrix def
+ /bfCount 1 index /CIDCount get 256 idiv 1 add
+ dup 256 gt { pop 256} if def
+ /Encoding
+ 256 array 0 1 bfCount 1 sub { 2 copy dup put pop } for
+ bfCount 1 255 { 2 copy bfCount put pop } for
+ def
+ /FDepVector bfCount dup 256 lt { 1 add } if array def
+ BaseFontTemplate BaseFontDictSize dict copy
+ begin
+ /CIDFont exch def
+ CIDFont /FontBBox known
+ { CIDFont /FontBBox get /FontBBox exch def }
+ if
+ CIDFont /CDevProc known
+ { CIDFont /CDevProc get /CDevProc exch def }
+ if
+ currentdict
+ end
+ BaseFontNameStr 3 (0) putinterval
+ 0 1 bfCount dup 256 eq { 1 sub } if
+ {
+ FDepVector exch
+ 2 index BaseFontDictSize dict copy
+ begin
+ dup /CIDFirstByte exch 256 mul def
+ FontType 3 eq
+ { /ct_FDDict 2 dict def }
+ if
+ currentdict
+ end
+ 1 index 16
+ BaseFontNameStr 2 2 getinterval cvrs pop
+ BaseFontNameStr exch definefont
+ put
+ }
+ for
+ ct_Clone?
+ { /Widths 1 index /CIDFont get /GlyphDirectory get length dict def }
+ if
+ FontName
+ currentdict
+ end
+ definefont
+ ct_Clone?
+ {
+ gsave
+ dup 1000 scalefont setfont
+ ct_BuildCharDict
+ begin
+ /usewidths? false def
+ currentfont /Widths get
+ begin
+ exch /CIDFont get /GlyphDirectory get
+ {
+ pop
+ dup charcode exch 1 index 0 2 index 256 idiv put
+ 1 index exch 1 exch 256 mod put
+ stringwidth 2 array astore def
+ }
+ forall
+ end
+ /usewidths? true def
+ end
+ grestore
+ }
+ { exch pop }
+ ifelse
+ } bind def
+ /ct_ComposeFont
+ {
+ ct_UseNativeCapability?
+ {
+ 2 index /CMap ct_resourcestatus
+ { pop pop exch pop }
+ {
+ /CIDInit /ProcSet findresource
+ begin
+ 12 dict
+ begin
+ begincmap
+ /CMapName 3 index def
+ /CMapVersion 1.000 def
+ /CMapType 1 def
+ exch /WMode exch def
+ /CIDSystemInfo 3 dict dup
+ begin
+ /Registry (Adobe) def
+ /Ordering
+ CMapName ct_mkocfStr100 cvs
+ (Adobe-) search
+ {
+ pop pop
+ (-) search
+ {
+ dup length string copy
+ exch pop exch pop
+ }
+ { pop (Identity)}
+ ifelse
+ }
+ { pop (Identity) }
+ ifelse
+ def
+ /Supplement 0 def
+ end def
+ 1 begincodespacerange
+ <0000> <FFFF>
+ endcodespacerange
+ 1 begincidrange
+ <0000> <FFFF> 0
+ endcidrange
+ endcmap
+ CMapName currentdict /CMap defineresource pop
+ end
+ end
+ }
+ ifelse
+ composefont
+ }
+ {
+ 3 2 roll pop
+ 0 get /CIDFont findresource
+ ct_makeocf
+ }
+ ifelse
+ } bind def
+ /ct_MakeIdentity
+ {
+ ct_UseNativeCapability?
+ {
+ 1 index /CMap ct_resourcestatus
+ { pop pop }
+ {
+ /CIDInit /ProcSet findresource begin
+ 12 dict begin
+ begincmap
+ /CMapName 2 index def
+ /CMapVersion 1.000 def
+ /CMapType 1 def
+ /CIDSystemInfo 3 dict dup
+ begin
+ /Registry (Adobe) def
+ /Ordering
+ CMapName ct_mkocfStr100 cvs
+ (Adobe-) search
+ {
+ pop pop
+ (-) search
+ { dup length string copy exch pop exch pop }
+ { pop (Identity) }
+ ifelse
+ }
+ { pop (Identity) }
+ ifelse
+ def
+ /Supplement 0 def
+ end def
+ 1 begincodespacerange
+ <0000> <FFFF>
+ endcodespacerange
+ 1 begincidrange
+ <0000> <FFFF> 0
+ endcidrange
+ endcmap
+ CMapName currentdict /CMap defineresource pop
+ end
+ end
+ }
+ ifelse
+ composefont
+ }
+ {
+ exch pop
+ 0 get /CIDFont findresource
+ ct_makeocf
+ }
+ ifelse
+ } bind def
+ currentdict readonly pop
+ end
+ end
+%%EndResource
+/currentpacking where{pop currentpacking true setpacking}if
+%%BeginResource: procset pdfvars 6.0 1
+%%Copyright: Copyright 1987-2002 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: definition of dictionary of variables used by PDF & PDFText procsets
+userdict /PDF 162 dict put
+userdict /PDFVars 89 dict dup begin put
+/docSetupDone false def
+/InitAll 0 def
+/TermAll 0 def
+/DocInitAll 0 def
+/DocTermAll 0 def
+/_pdfEncodings 2 array def
+/_pdf_str1 1 string def
+/_pdf_i 0 def
+/_pdf_na 0 def
+/_pdf_showproc 0 def
+/_italMtx [1 0 .212557 1 0 0] def
+/_italMtx_WMode1 [1 -.212557 0 1 0 0] def
+/_italMtxType0 [1 0 .1062785 1 0 0] def
+/_italMtx_WMode1Type0 [1 -.1062785 0 1 0 0] def
+/_basefont 0 def
+/_basefonto 0 def
+/_pdf_oldCIDInit null def
+/_pdf_FontDirectory 30 dict def
+/_categories 10 dict def
+/_sa? true def
+/_ColorSep5044? false def
+/nulldict 0 dict def
+/_processColors 0 def
+/overprintstack null def
+/_defaulttransfer currenttransfer def
+/_defaultflatness currentflat def
+/_defaulthalftone null def
+/_defaultcolortransfer null def
+/_defaultblackgeneration null def
+/_defaultundercolorremoval null def
+/_defaultcolortransfer null def
+PDF begin
+[/c/cs/cm/d/d0/f/h/i/j/J/l/m/M/n/q/Q/re/ri/S/sc/sh/Tf/w/W
+/applyInterpFunc/applystitchFunc/domainClip/encodeInput
+/initgs/int/limit/rangeClip
+/defineRes/undefineRes/findRes/setSA/pl
+/? /! /| /: /+ /GetGlyphDirectory
+/pdf_flushFilters /pdf_readstring /pdf_dictOp /pdf_image /pdf_maskedImage
+/pdf_shfill /pdf_sethalftone
+] {null def} bind forall
+end
+end
+%%EndResource
+PDFVars begin PDF begin
+%%BeginResource: procset pdfutil 6.0 1
+%%Copyright: Copyright 1993-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Basic utilities used by other PDF procsets
+/bd {bind def} bind def
+/ld {load def} bd
+/bld {
+dup length dict begin
+{ null def } forall
+bind
+end
+def
+} bd
+/dd { PDFVars 3 1 roll put } bd
+/xdd { exch dd } bd
+/Level2?
+systemdict /languagelevel known
+{ systemdict /languagelevel get 2 ge } { false } ifelse
+def
+/Level1? Level2? not def
+/Level3?
+systemdict /languagelevel known
+{systemdict /languagelevel get 3 eq } { false } ifelse
+def
+/getifknown {
+2 copy known { get true } { pop pop false } ifelse
+} bd
+/here {
+currentdict exch getifknown
+} bd
+/isdefined? { where { pop true } { false } ifelse } bd
+%%EndResource
+%%BeginResource: procset l2compat 6.0 1
+%%Copyright: Copyright 1987-2003 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Level 1 emulation of level 2 operators
+/setcmykcolor isdefined? not
+{
+/setcmykcolor {
+1 sub 4 1 roll
+3 {
+3 index add neg dup 0 lt { pop 0 } if
+3 1 roll
+} repeat
+setrgbcolor
+pop
+} bd
+} if
+/rectclip isdefined? not
+{
+/rectclip { newpath re clip newpath } bd
+} if
+/rectfill isdefined? not
+{
+/rectfill { gsave newpath re fill grestore } bd
+} if
+/sethalftone isdefined? not
+{
+/sethalftone {
+begin
+HalftoneType 1 eq
+{ Frequency Angle /SpotFunction load setscreen }
+if
+end
+} bd
+} if
+Level1?
+{
+/pdf_show {show} bd
+/xshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_xshow
+} bd
+/yshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_yshow
+} bd
+/xyshow
+{
+PDFVars /_pdf_showproc /pdf_show load put
+pdf_xyshow
+} bd
+} if
+/getrampcolor {
+cvi
+/indx exch def
+[
+0 1 NumComp 1 sub {
+dup
+Samples exch get
+dup type /stringtype eq { indx get } if
+exch
+Scaling exch get aload pop
+3 1 roll
+mul add
+} for
+]
+L1setcolor
+} bd
+/sssetbackground { L1setcolor } bd
+%%EndResource
+%%BeginResource: procset pdf 6.0 1
+%%Copyright: Copyright 1998-2003 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: General operators for PDF, common to all Language Levels.
+/cm { matrix astore concat } bd
+/d /setdash ld
+/f /fill ld
+/h /closepath ld
+/i {dup 0 eq {pop _defaultflatness} if setflat} bd
+/j /setlinejoin ld
+/J /setlinecap ld
+/M /setmiterlimit ld
+/n /newpath ld
+/S /stroke ld
+/w /setlinewidth ld
+/W /clip ld
+/sg /setgray ld
+/initgs {
+0 setgray
+[] 0 d
+0 j
+0 J
+10 M
+1 w
+false setSA
+/_defaulttransfer load settransfer
+0 i
+/RelativeColorimetric ri
+newpath
+} bd
+/int {
+dup 2 index sub 3 index 5 index sub div 6 -2 roll sub mul
+exch pop add exch pop
+} bd
+/limit {
+dup 2 index le { exch } if pop
+dup 2 index ge { exch } if pop
+} bd
+/domainClip {
+Domain aload pop 3 2 roll
+limit
+} [/Domain] bld
+/applyInterpFunc {
+0 1 DimOut 1 sub
+{
+dup C0 exch get exch
+dup C1 exch get exch
+3 1 roll
+1 index sub
+3 index
+N exp mul add
+exch
+currentdict /Range_lo known
+{
+dup Range_lo exch get exch
+Range_hi exch get
+3 2 roll limit
+}
+{
+pop
+}
+ifelse
+exch
+} for
+pop
+} [/DimOut /C0 /C1 /N /Range_lo /Range_hi] bld
+/encodeInput {
+NumParts 1 sub
+0 1 2 index
+{
+dup Bounds exch get
+2 index gt
+{ exit }
+{ dup
+3 index eq
+{ exit }
+{ pop } ifelse
+} ifelse
+} for
+3 2 roll pop
+dup Bounds exch get exch
+dup 1 add Bounds exch get exch
+2 mul
+dup Encode exch get exch
+1 add Encode exch get
+int
+} [/NumParts /Bounds /Encode] bld
+/rangeClip {
+exch dup Range_lo exch get
+exch Range_hi exch get
+3 2 roll
+limit
+} [/Range_lo /Range_hi] bld
+/applyStitchFunc {
+Functions exch get exec
+currentdict /Range_lo known {
+0 1 DimOut 1 sub {
+DimOut 1 add -1 roll
+rangeClip
+} for
+} if
+} [/Functions /Range_lo /DimOut] bld
+/pdf_flushfilters
+{
+aload length
+{ dup status
+1 index currentfile ne and
+{ dup flushfile closefile }
+{ pop }
+ifelse
+} repeat
+} bd
+/pdf_readstring
+{
+1 index dup length 1 sub get
+exch readstring pop
+exch pdf_flushfilters
+} bind def
+/pdf_dictOp
+{
+3 2 roll
+10 dict copy
+begin
+_Filters dup length 1 sub get def
+currentdict exch exec
+_Filters pdf_flushfilters
+end
+} [/_Filters] bld
+/pdf_image {{image} /DataSource pdf_dictOp} bd
+/pdf_imagemask {{imagemask} /DataSource pdf_dictOp} bd
+/pdf_shfill {{sh} /DataSource pdf_dictOp} bd
+/pdf_sethalftone {{sethalftone} /Thresholds pdf_dictOp} bd
+/pdf_maskedImage
+{
+10 dict copy begin
+/miDict currentdict def
+/DataDict DataDict 10 dict copy def
+DataDict begin
+/DataSource
+_Filters dup length 1 sub get
+def
+miDict image
+_Filters pdf_flushfilters
+end
+end
+} [/miDict /DataDict /_Filters] bld
+/RadialShade {
+40 dict begin
+/background exch def
+/ext1 exch def
+/ext0 exch def
+/BBox exch def
+/r2 exch def
+/c2y exch def
+/c2x exch def
+/r1 exch def
+/c1y exch def
+/c1x exch def
+/rampdict exch def
+gsave
+BBox length 0 gt {
+newpath
+BBox 0 get BBox 1 get moveto
+BBox 2 get BBox 0 get sub 0 rlineto
+0 BBox 3 get BBox 1 get sub rlineto
+BBox 2 get BBox 0 get sub neg 0 rlineto
+closepath
+clip
+newpath
+} if
+c1x c2x eq
+{
+c1y c2y lt {/theta 90 def}{/theta 270 def} ifelse
+}
+{
+/slope c2y c1y sub c2x c1x sub div def
+/theta slope 1 atan def
+c2x c1x lt c2y c1y ge and { /theta theta 180 sub def} if
+c2x c1x lt c2y c1y lt and { /theta theta 180 add def} if
+}
+ifelse
+gsave
+clippath
+c1x c1y translate
+theta rotate
+-90 rotate
+{ pathbbox } stopped
+{ 0 0 0 0 } if
+/yMax exch def
+/xMax exch def
+/yMin exch def
+/xMin exch def
+grestore
+xMax xMin eq yMax yMin eq or
+{
+grestore
+end
+}
+{
+/max { 2 copy gt { pop } {exch pop} ifelse } bind def
+/min { 2 copy lt { pop } {exch pop} ifelse } bind def
+rampdict begin
+40 dict begin
+background length 0 gt { background sssetbackground gsave clippath fill grestore } if
+gsave
+c1x c1y translate
+theta rotate
+-90 rotate
+/c2y c1x c2x sub dup mul c1y c2y sub dup mul add sqrt def
+/c1y 0 def
+/c1x 0 def
+/c2x 0 def
+ext0 {
+0 getrampcolor
+c2y r2 add r1 sub 0.0001 lt
+{
+c1x c1y r1 360 0 arcn
+pathbbox
+/aymax exch def
+/axmax exch def
+/aymin exch def
+/axmin exch def
+/bxMin xMin axmin min def
+/byMin yMin aymin min def
+/bxMax xMax axmax max def
+/byMax yMax aymax max def
+bxMin byMin moveto
+bxMax byMin lineto
+bxMax byMax lineto
+bxMin byMax lineto
+bxMin byMin lineto
+eofill
+}
+{
+c2y r1 add r2 le
+{
+c1x c1y r1 0 360 arc
+fill
+}
+{
+c2x c2y r2 0 360 arc fill
+r1 r2 eq
+{
+/p1x r1 neg def
+/p1y c1y def
+/p2x r1 def
+/p2y c1y def
+p1x p1y moveto p2x p2y lineto p2x yMin lineto p1x yMin lineto
+fill
+}
+{
+/AA r2 r1 sub c2y div def
+AA -1 eq
+{ /theta 89.99 def}
+{ /theta AA 1 AA dup mul sub sqrt div 1 atan def}
+ifelse
+/SS1 90 theta add dup sin exch cos div def
+/p1x r1 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def
+/p1y p1x SS1 div neg def
+/SS2 90 theta sub dup sin exch cos div def
+/p2x r1 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def
+/p2y p2x SS2 div neg def
+r1 r2 gt
+{
+/L1maxX p1x yMin p1y sub SS1 div add def
+/L2maxX p2x yMin p2y sub SS2 div add def
+}
+{
+/L1maxX 0 def
+/L2maxX 0 def
+}ifelse
+p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto
+L1maxX L1maxX p1x sub SS1 mul p1y add lineto
+fill
+}
+ifelse
+}
+ifelse
+} ifelse
+} if
+c1x c2x sub dup mul
+c1y c2y sub dup mul
+add 0.5 exp
+0 dtransform
+dup mul exch dup mul add 0.5 exp 72 div
+0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+1 index 1 index lt { exch } if pop
+/hires exch def
+hires mul
+/numpix exch def
+/numsteps NumSamples def
+/rampIndxInc 1 def
+/subsampling false def
+numpix 0 ne
+{
+NumSamples numpix div 0.5 gt
+{
+/numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def
+/rampIndxInc NumSamples 1 sub numsteps div def
+/subsampling true def
+} if
+} if
+/xInc c2x c1x sub numsteps div def
+/yInc c2y c1y sub numsteps div def
+/rInc r2 r1 sub numsteps div def
+/cx c1x def
+/cy c1y def
+/radius r1 def
+newpath
+xInc 0 eq yInc 0 eq rInc 0 eq and and
+{
+0 getrampcolor
+cx cy radius 0 360 arc
+stroke
+NumSamples 1 sub getrampcolor
+cx cy radius 72 hires div add 0 360 arc
+0 setlinewidth
+stroke
+}
+{
+0
+numsteps
+{
+dup
+subsampling { round } if
+getrampcolor
+cx cy radius 0 360 arc
+/cx cx xInc add def
+/cy cy yInc add def
+/radius radius rInc add def
+cx cy radius 360 0 arcn
+eofill
+rampIndxInc add
+}
+repeat
+pop
+} ifelse
+ext1 {
+c2y r2 add r1 lt
+{
+c2x c2y r2 0 360 arc
+fill
+}
+{
+c2y r1 add r2 sub 0.0001 le
+{
+c2x c2y r2 360 0 arcn
+pathbbox
+/aymax exch def
+/axmax exch def
+/aymin exch def
+/axmin exch def
+/bxMin xMin axmin min def
+/byMin yMin aymin min def
+/bxMax xMax axmax max def
+/byMax yMax aymax max def
+bxMin byMin moveto
+bxMax byMin lineto
+bxMax byMax lineto
+bxMin byMax lineto
+bxMin byMin lineto
+eofill
+}
+{
+c2x c2y r2 0 360 arc fill
+r1 r2 eq
+{
+/p1x r2 neg def
+/p1y c2y def
+/p2x r2 def
+/p2y c2y def
+p1x p1y moveto p2x p2y lineto p2x yMax lineto p1x yMax lineto
+fill
+}
+{
+/AA r2 r1 sub c2y div def
+AA -1 eq
+{ /theta 89.99 def}
+{ /theta AA 1 AA dup mul sub sqrt div 1 atan def}
+ifelse
+/SS1 90 theta add dup sin exch cos div def
+/p1x r2 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def
+/p1y c2y p1x SS1 div sub def
+/SS2 90 theta sub dup sin exch cos div def
+/p2x r2 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def
+/p2y c2y p2x SS2 div sub def
+r1 r2 lt
+{
+/L1maxX p1x yMax p1y sub SS1 div add def
+/L2maxX p2x yMax p2y sub SS2 div add def
+}
+{
+/L1maxX 0 def
+/L2maxX 0 def
+}ifelse
+p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto
+L1maxX L1maxX p1x sub SS1 mul p1y add lineto
+fill
+}
+ifelse
+}
+ifelse
+} ifelse
+} if
+grestore
+grestore
+end
+end
+end
+} ifelse
+} bd
+/GenStrips {
+40 dict begin
+/background exch def
+/ext1 exch def
+/ext0 exch def
+/BBox exch def
+/y2 exch def
+/x2 exch def
+/y1 exch def
+/x1 exch def
+/rampdict exch def
+gsave
+BBox length 0 gt {
+newpath
+BBox 0 get BBox 1 get moveto
+BBox 2 get BBox 0 get sub 0 rlineto
+0 BBox 3 get BBox 1 get sub rlineto
+BBox 2 get BBox 0 get sub neg 0 rlineto
+closepath
+clip
+newpath
+} if
+x1 x2 eq
+{
+y1 y2 lt {/theta 90 def}{/theta 270 def} ifelse
+}
+{
+/slope y2 y1 sub x2 x1 sub div def
+/theta slope 1 atan def
+x2 x1 lt y2 y1 ge and { /theta theta 180 sub def} if
+x2 x1 lt y2 y1 lt and { /theta theta 180 add def} if
+}
+ifelse
+gsave
+clippath
+x1 y1 translate
+theta rotate
+{ pathbbox } stopped
+{ 0 0 0 0 } if
+/yMax exch def
+/xMax exch def
+/yMin exch def
+/xMin exch def
+grestore
+xMax xMin eq yMax yMin eq or
+{
+grestore
+end
+}
+{
+rampdict begin
+20 dict begin
+background length 0 gt { background sssetbackground gsave clippath fill grestore } if
+gsave
+x1 y1 translate
+theta rotate
+/xStart 0 def
+/xEnd x2 x1 sub dup mul y2 y1 sub dup mul add 0.5 exp def
+/ySpan yMax yMin sub def
+/numsteps NumSamples def
+/rampIndxInc 1 def
+/subsampling false def
+xStart 0 transform
+xEnd 0 transform
+3 -1 roll
+sub dup mul
+3 1 roll
+sub dup mul
+add 0.5 exp 72 div
+0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt
+1 index 1 index lt { exch } if pop
+mul
+/numpix exch def
+numpix 0 ne
+{
+NumSamples numpix div 0.5 gt
+{
+/numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def
+/rampIndxInc NumSamples 1 sub numsteps div def
+/subsampling true def
+} if
+} if
+ext0 {
+0 getrampcolor
+xMin xStart lt
+{ xMin yMin xMin neg ySpan rectfill } if
+} if
+/xInc xEnd xStart sub numsteps div def
+/x xStart def
+0
+numsteps
+{
+dup
+subsampling { round } if
+getrampcolor
+x yMin xInc ySpan rectfill
+/x x xInc add def
+rampIndxInc add
+}
+repeat
+pop
+ext1 {
+xMax xEnd gt
+{ xEnd yMin xMax xEnd sub ySpan rectfill } if
+} if
+grestore
+grestore
+end
+end
+end
+} ifelse
+} bd
+/currentdistillerparams where { pop currentdistillerparams /CoreDistVersion get 5000 lt}{true}ifelse
+{
+/PDFMark5 {cleartomark} bd
+}
+{
+/PDFMark5 {pdfmark} bd
+}ifelse
+/ReadByPDFMark5
+{
+2 dict begin
+/makerString exch def string /tmpString exch def
+{
+currentfile tmpString readline pop
+makerString anchorsearch
+{
+pop pop cleartomark exit
+}
+{
+3 copy /PUT PDFMark5 pop 2 copy (\n) /PUT PDFMark5
+} ifelse
+}loop
+end
+}bd
+%%EndResource
+%%BeginResource: procset sep_ops 6.0 1
+%%Copyright: Copyright 1987-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Support for Separations in Level 1, following the conventions of Tech Note 5044
+userdict /sep_ops 50 dict dup begin put
+/bdef {bind def} bind def
+/xdef {exch def} bdef
+/colorimagebuffer {
+0 1 2 index length 1 sub {
+dup 2 index exch get 255 exch sub 2 index 3 1 roll put
+} for
+} bdef
+/addprocs {
+[ 3 1 roll
+/exec load
+dup 3 1 roll
+] cvx
+} bdef
+/L1? {
+systemdict /languagelevel known {
+systemdict /languagelevel get 2 lt
+}{
+true
+} ifelse
+} bdef
+/colorexists {
+statusdict /processcolors known {
+statusdict /processcolors get exec
+}{
+/deviceinfo where {
+pop deviceinfo /Colors known {
+deviceinfo /Colors get
+statusdict /processcolors {
+deviceinfo /Colors known {
+deviceinfo /Colors get
+}{
+1
+} ifelse
+} put
+}{
+1
+} ifelse
+}{
+1
+} ifelse
+} ifelse
+1 gt
+} bdef
+/colorplate colorexists { 0 } { 5 } ifelse def
+/negativecolorplate false def
+/setcmykcolor where {
+pop
+gsave
+1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
+0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub
+4 {4 copy} repeat
+grestore
+1 dict begin
+/foureq {
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+4 index eq 8 1 roll
+pop pop pop pop and and and
+} def
+1 0 0 0 foureq {/colorplate 1 store} if
+0 1 0 0 foureq {/colorplate 2 store} if
+0 0 1 0 foureq {/colorplate 3 store} if
+0 0 0 1 foureq {/colorplate 4 store} if
+0 0 0 0 foureq {/colorplate 6 store} if
+end
+} if
+0 systemdict /currenttransfer get exec exec
+1 systemdict /currenttransfer get exec exec
+2 copy
+eq
+{
+/colorplate 6 store
+pop
+/negativecolorplate exch 0.5 lt store
+}
+{
+gt /negativecolorplate exch store
+}
+ifelse
+/findcmykcustomcolor where { pop }
+{
+/findcmykcustomcolor {
+[ 6 1 roll ] readonly
+} bdef
+} ifelse
+/setoverprint where {
+pop
+}{
+/setoverprint {
+pop
+} bdef
+} ifelse
+/currentoverprint where {
+pop
+}{
+/currentoverprint {
+false
+} bdef
+} ifelse
+/setcustomcolor where {
+pop
+}{
+L1? {
+/setcustomcolor {
+exch
+aload pop pop
+4 { 4 index mul 4 1 roll } repeat
+5 -1 roll pop
+setcmykcolor
+} bdef
+}{
+/setcustomcolor {
+exch
+[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
+0 4 getinterval
+[ exch /dup load exch cvx {mul exch dup}
+/forall load /pop load dup] cvx
+] setcolorspace setcolor
+} bdef
+} ifelse
+} ifelse
+/ik 0 def
+/iy 0 def
+/im 0 def
+/ic 0 def
+/imagetint {
+ic .3 mul
+im .59 mul
+iy .11 mul
+ik add add add dup
+1 gt {pop 1} if
+} bdef
+/setcmykcolor where {
+pop
+}{
+/setcmykcolor {
+/ik xdef /iy xdef /im xdef /ic xdef
+imagetint
+1 exch sub setgray
+} bdef
+} ifelse
+/customcolorimage where {
+pop
+}{
+L1? {
+/customcolorimage{
+gsave
+colorexists {
+aload pop pop
+/ik xdef /iy xdef /im xdef /ic xdef
+currentcolortransfer
+{ik mul ik sub 1 add} addprocs
+4 1 roll {iy mul iy sub 1 add} addprocs
+4 1 roll {im mul im sub 1 add} addprocs
+4 1 roll {ic mul ic sub 1 add} addprocs
+4 1 roll setcolortransfer
+/magentabuf 0 string def
+/yellowbuf 0 string def
+/blackbuf 0 string def
+{
+colorimagebuffer dup length magentabuf length ne
+{
+dup length dup dup
+/magentabuf exch string def
+/yellowbuf exch string def
+/blackbuf exch string def
+} if
+dup magentabuf copy yellowbuf copy
+blackbuf copy pop
+} addprocs
+{magentabuf}{yellowbuf}{blackbuf} true 4 colorimage
+}{
+aload pop pop /ik xdef /iy xdef /im xdef /ic xdef /tint
+imagetint def
+currenttransfer
+{tint mul 1 tint sub add} addprocs settransfer image
+} ifelse
+grestore
+} bdef
+}{
+/customcolorimage {
+gsave
+[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
+0 4 getinterval
+[ exch /dup load exch cvx {mul exch dup}
+/forall load /pop load dup] cvx
+] setcolorspace
+10 dict begin
+/ImageType 1 def
+/DataSource exch def
+/ImageMatrix exch def
+/BitsPerComponent exch def
+/Height exch def
+/Width exch def
+/Decode [1 0] def
+currentdict end
+image
+grestore
+} bdef
+} ifelse
+} ifelse
+/setseparationgray where {
+pop
+}{
+L1? {
+/setseparationgray { 1 exch sub dup dup dup setcmykcolor } bdef
+}{
+/setseparationgray {
+[/Separation /All /DeviceCMYK {dup dup dup}] setcolorspace
+1 exch sub setcolor
+} bdef
+} ifelse
+} ifelse
+/separationimage where { pop }
+{
+/separationimage {
+gsave
+1 1 1 1 (All)
+findcmykcustomcolor customcolorimage
+grestore
+} bdef
+} ifelse
+currentdict readonly pop end
+%%EndResource
+%%BeginResource: procset pdflev15044 6.0 1
+%%Copyright: Copyright 1987-2002 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: PDF operators, Level 1, with emulated separations (TN 5044)
+/_ColorSep5044? true dd
+/docinitialize {
+PDF begin
+/_defaulthalftone
+/currenthalftone where
+{ pop currenthalftone }
+{ 4 dict dup begin
+currentscreen
+/SpotFunction exch def
+/Angle exch def
+/Frequency exch def
+/HalftoneType 1 def
+end }
+ifelse
+dd
+/currentcolortransfer where
+{ pop /_defaultcolortransfer [ currentcolortransfer ] dd }
+{ /_defaultcolortransfer [currenttransfer dup dup dup] dd }
+ifelse
+end
+} bd
+/initialize {
+/overprintstack null dd
+sep_ops begin
+50 dict begin
+_defaulthalftone sethalftone
+} bd
+/terminate {
+end end
+} bd
+/currentcolortransfer where
+{ pop }
+{
+/setcolortransfer
+{
+settransfer pop pop pop
+} bd
+} ifelse
+/pl {
+transform
+0.25 sub round 0.25 add exch
+0.25 sub round 0.25 add exch
+itransform
+} bd
+/m { _sa? { pl } if moveto } bd
+/l { _sa? { pl } if lineto } bd
+/c
+{
+_sa? {3 {pl 6 2 roll} repeat} if
+curveto
+} bd
+/ri/pop ld
+/setSA { /_sa? xdd } bd
+/re
+{
+_sa?
+{
+8 dict begin
+/:h exch def
+/:w exch def
+/:y exch def
+/:x exch def
+:x :y pl
+/:ymin exch def /:xmin exch def
+:x :w add :y :h add pl
+/:ymax exch def /:xmax exch def
+:xmin :ymin moveto
+:xmax :ymin lineto
+:xmax :ymax lineto
+:xmin :ymax lineto
+closepath
+end
+}
+{
+4 2 roll moveto
+1 index 0 rlineto
+0 exch rlineto
+neg 0 rlineto
+closepath
+} ifelse
+} bd
+/q
+{
+gsave
+[currentoverprint overprintstack] /overprintstack xdd
+}
+[/overprintstack] bld
+/Q
+{
+overprintstack aload pop /overprintstack xdd setoverprint
+grestore
+}
+[/overprintstack] bld
+/AlmostFull?
+{ dup maxlength exch length sub 2 le
+} bd
+/Expand
+{ 1 index maxlength mul cvi dict
+dup begin exch { def } forall end
+} bd
+/xput
+{ 3 2 roll
+dup 3 index known not
+{ dup AlmostFull? { 1.5 Expand } if
+} if
+dup 4 2 roll put
+} bd
+/defineRes
+{ _categories 1 index known not
+{ /_categories _categories 2 index 10 dict xput store
+} if
+_categories exch 2 copy get 5 -1 roll 4 index xput put
+} bd
+/undefineRes {
+null exch
+defineRes
+} bd
+/findRes {
+_categories exch get exch get
+} bd
+/L1setcolor {
+aload length
+dup 0 eq
+{ pop .5 setgray }
+{ dup 1 eq
+{ pop setgray }
+{ 3 eq
+{ setrgbcolor }
+{ setcmykcolor }
+ifelse }
+ifelse }
+ifelse
+} bind dd
+/concattransferfuncs {
+[ 3 1 roll /exec load exch /exec load ] cvx
+} bd
+/concatandsettransfer {
+/_defaulttransfer load concattransferfuncs settransfer
+} bd
+/concatandsetcolortransfer {
+colorplate 0 eq
+{
+_defaultcolortransfer aload pop
+8 -1 roll 5 -1 roll concattransferfuncs 7 1 roll
+6 -1 roll 4 -1 roll concattransferfuncs 5 1 roll
+4 -1 roll 3 -1 roll concattransferfuncs 3 1 roll
+concattransferfuncs
+setcolortransfer
+} if
+colorplate 1 ge colorplate 4 le and
+{
+4 colorplate sub index 4 { exch pop } repeat
+concatandsettransfer
+} if
+colorplate 5 ge
+{
+0 index 4 { exch pop } repeat
+concatandsettransfer
+} if
+} bd
+/tn5044sethalftone
+{
+begin
+HalftoneType 5 eq
+{ [/Default /Cyan /Magenta /Yellow /Black /Default /Default /Default]
+colorplate get
+here not {
+/Default here not { currentdict } if
+} if
+}
+{ currentdict }
+ifelse
+end
+begin
+/TransferFunction here
+{
+concatandsettransfer
+currentdict dup length dict
+begin
+{
+1 index /TransferFunction ne { def } { pop pop } ifelse
+} forall
+currentdict
+end
+}
+{
+currentdict
+} ifelse
+end
+sethalftone
+} bd
+/paintimage
+{
+colorplate 0 eq
+{
+{ {currentfile cyanstr readstring pop}
+{currentfile magentastr readstring pop}
+{currentfile yellowstr readstring pop}
+{currentfile blackstr readstring pop
+currentfile graystr readstring pop pop}
+}
+{ {currentfile cyanstr readhexstring pop}
+{currentfile magentastr readhexstring pop}
+{currentfile yellowstr readhexstring pop}
+{currentfile blackstr readhexstring pop
+currentfile graystr readhexstring pop pop}
+} ifelse
+true 4 colorimage
+}
+{
+3 dict begin
+/binaryOK exch def
+[
+1 1 5 {
+dup
+/currentfile cvx
+[ /cyanstr /magentastr /yellowstr /blackstr /graystr ]
+3 -1 roll 1 sub get cvx
+binaryOK { /readstring } { /readhexstring } ifelse cvx
+/pop cvx
+5 -1 roll
+colorplate dup 5 gt { pop 5 } if
+eq not { /pop cvx } if
+} for
+] cvx bind
+end
+[
+colorplate 6 eq {
+/pop cvx
+negativecolorplate { 0 } { 1 } ifelse
+} if
+colorplate 4 le
+{
+1 /exch cvx /sub cvx
+} if
+colorplate 6 ne
+{
+systemdict /currenttransfer get exec
+aload pop
+} if
+] cvx
+gsave
+systemdict /settransfer get exec
+systemdict /image get exec
+grestore
+} ifelse
+} bd
+%%EndResource
+%%BeginResource: procset pdftext 6.0 1
+%%Copyright: Copyright 1987-2001 Adobe Systems Incorporated. All Rights Reserved.
+%%Title: Text operators for PDF
+PDF /PDFText 78 dict dup begin put
+/docinitialize
+{
+/resourcestatus where {
+pop
+/CIDParams /ProcSet resourcestatus {
+pop pop
+false /CIDParams /ProcSet findresource /SetBuildCompatible get exec
+} if
+} if
+PDF begin
+PDFText /_pdfDefineIdentity-H known
+{ PDFText /_pdfDefineIdentity-H get exec}
+if
+end
+} bd
+/initialize {
+PDFText begin
+} bd
+/terminate { end } bd
+Level2?
+{
+/_safeput
+{
+3 -1 roll load 3 1 roll put
+}
+bd
+}
+{
+/_safeput
+{
+2 index load dup dup length exch maxlength ge
+{ dup length 5 add dict copy
+3 index xdd
+}
+{ pop }
+ifelse
+3 -1 roll load 3 1 roll put
+}
+bd
+}
+ifelse
+/pdf_has_composefont? systemdict /composefont known def
+/CopyFont {
+{
+1 index /FID ne 2 index /UniqueID ne and
+{ def } { pop pop } ifelse
+} forall
+} bd
+/Type0CopyFont
+{
+exch
+dup length dict
+begin
+CopyFont
+[
+exch
+FDepVector
+{
+dup /FontType get 0 eq
+{
+1 index Type0CopyFont
+/_pdfType0 exch definefont
+}
+{
+/_pdfBaseFont exch
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+}
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+}
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+} bd
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+{
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+}
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+} bd
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+_enc 3 1 roll put
+} for
+pop
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+} bd
+/TE {
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+StandardEncoding 256 array copy modEnc
+_pdfEncodings exch _i exch put
+} bd
+/TZ
+{
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+findfont
+dup length 6 add dict
+begin
+{
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+} forall
+/pdf_origFontName FontName def
+/FontName exch def
+currentdict /PaintType known
+{ PaintType 2 eq {/PaintType 0 def} if }
+if
+_usePDFEncoding 0 ge
+{
+/Encoding _pdfEncodings _usePDFEncoding get def
+pop
+}
+{
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+{
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+}
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+}
+{
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+}
+ifelse
+}
+ifelse
+pdf_EuroProcSet pdf_origFontName known
+{
+pdf_origFontName pdf_AddEuroGlyphProc
+} if
+Level2?
+{
+currentdict /pdf_origFontName undef
+} if
+FontName currentdict
+end
+definefont pop
+}
+bd
+Level2?
+{
+/TZG
+{
+currentglobal true setglobal
+2 index _pdfFontStatus
+{
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+false setglobal
+3 index findfont
+true setglobal
+ne
+{
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+{
+dup length dict begin
+{
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+} forall
+currentdict end
+}
+if
+3 index exch definefont pop
+}
+if
+} if
+setglobal
+TZ
+} bd
+}
+{
+/TZG {TZ} bd
+} ifelse
+Level2?
+{
+currentglobal false setglobal
+userdict /pdftext_data 5 dict put
+pdftext_data
+begin
+/saveStacks
+{
+pdftext_data
+begin
+/vmmode currentglobal def
+false setglobal
+count array astore /os exch def
+end
+countdictstack array dictstack pdftext_data exch /ds exch put
+cleardictstack pdftext_data /dscount countdictstack put
+pdftext_data /vmmode get setglobal
+} bind def
+/restoreStacks
+{
+pdftext_data /vmmode currentglobal put false setglobal
+clear cleardictstack
+pdftext_data /ds get dup
+pdftext_data /dscount get 1 2 index length 1 sub
+{ get begin dup } for
+pop pop
+pdftext_data /os get aload pop
+pdftext_data /vmmode get setglobal
+} bind def
+/testForClonePrinterBug
+{
+currentglobal true setglobal
+/undefinedCategory /Generic /Category findresource
+dup length dict copy /Category defineresource pop
+setglobal
+pdftext_data /saveStacks get exec
+pdftext_data /vmmode currentglobal put false setglobal
+/undefined /undefinedCategory { resourcestatus } stopped
+pdftext_data exch /bugFound exch put
+pdftext_data /vmmode get setglobal
+pdftext_data /restoreStacks get exec
+pdftext_data /bugFound get
+} bind def
+end
+setglobal
+/pdf_resourcestatus
+pdftext_data /testForClonePrinterBug get exec
+{
+{
+pdftext_data /saveStacks get exec
+pdftext_data /os get dup dup length 1 sub
+dup 1 sub dup 0 lt { pop 0 } if
+exch 1 exch { get exch dup } for
+pop pop
+{ resourcestatus }
+stopped
+{
+clear cleardictstack pdftext_data /restoreStacks get exec
+{ pop pop } stopped pop false
+}
+{
+count array astore pdftext_data exch /results exch put
+pdftext_data /restoreStacks get exec pop pop
+pdftext_data /results get aload pop
+}
+ifelse
+}
+}
+{ { resourcestatus } }
+ifelse
+bd
+}
+if
+Level2?
+{
+/_pdfUndefineResource
+{
+currentglobal 3 1 roll
+_pdf_FontDirectory 2 index 2 copy known
+{undef}
+{pop pop}
+ifelse
+1 index (pdf) exch _pdfConcatNames 1 index
+1 index 1 _pdfConcatNames 1 index
+5 index 1 _pdfConcatNames 1 index
+4
+{
+2 copy pdf_resourcestatus
+{
+pop 2 lt
+{2 copy findresource gcheck setglobal undefineresource}
+{pop pop}
+ifelse
+}
+{ pop pop}
+ifelse
+} repeat
+setglobal
+} bd
+}
+{
+/_pdfUndefineResource { pop pop} bd
+}
+ifelse
+Level2?
+{
+/_pdfFontStatus
+{
+currentglobal exch
+/Font pdf_resourcestatus
+{pop pop true}
+{false}
+ifelse
+exch setglobal
+} bd
+}
+{
+/_pdfFontStatusString 50 string def
+_pdfFontStatusString 0 (fonts/) putinterval
+/_pdfFontStatus
+{
+FontDirectory 1 index known
+{ pop true }
+{
+_pdfFontStatusString 6 42 getinterval
+cvs length 6 add
+_pdfFontStatusString exch 0 exch getinterval
+{ status } stopped
+{pop false}
+{
+{ pop pop pop pop true}
+{ false }
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+ifelse
+Level2?
+{
+/_pdfCIDFontStatus
+{
+/CIDFont /Category pdf_resourcestatus
+{
+pop pop
+/CIDFont pdf_resourcestatus
+{pop pop true}
+{false}
+ifelse
+}
+{ pop false }
+ifelse
+} bd
+}
+if
+/_pdfString100 100 string def
+/_pdfComposeFontName
+{
+dup length 1 eq
+{
+0 get
+1 index
+type /nametype eq
+{
+_pdfString100 cvs
+length dup dup _pdfString100 exch (-) putinterval
+_pdfString100 exch 1 add dup _pdfString100 length exch sub getinterval
+2 index exch cvs length
+add 1 add _pdfString100 exch 0 exch getinterval
+exch pop
+true
+}
+{
+pop pop
+false
+}
+ifelse
+}
+{
+false
+}
+ifelse
+dup {exch cvn exch} if
+} bd
+/_pdfConcatNames
+{
+exch
+_pdfString100 cvs
+length dup dup _pdfString100 exch (-) putinterval
+_pdfString100 exch 1 add dup _pdfString100 length exch sub getinterval
+3 -1 roll exch cvs length
+add 1 add _pdfString100 exch 0 exch getinterval
+cvn
+} bind def
+/_pdfTextTempString 50 string def
+/_pdfRegOrderingArray [(Adobe-Japan1) (Adobe-CNS1) (Adobe-Korea1) (Adobe-GB1)] def
+/_pdf_CheckCIDSystemInfo
+{
+1 index _pdfTextTempString cvs
+(Identity) anchorsearch
+{
+pop pop pop pop true
+}
+{
+false
+_pdfRegOrderingArray
+{
+2 index exch
+anchorsearch
+{ pop pop pop true exit}
+{ pop }
+ifelse
+}
+forall
+exch pop
+exch /CIDFont findresource
+/CIDSystemInfo get
+3 -1 roll /CMap findresource
+/CIDSystemInfo get
+exch
+3 -1 roll
+{
+2 copy
+/Supplement get
+exch
+dup type /dicttype eq
+{/Supplement get}
+{pop 0 }
+ifelse
+ge
+}
+{ true }
+ifelse
+{
+dup /Registry get
+2 index /Registry get eq
+{
+/Ordering get
+exch /Ordering get
+dup type /arraytype eq
+{
+1 index type /arraytype eq
+{
+true
+1 index length 1 sub -1 0
+{
+dup 2 index exch get exch 3 index exch get ne
+{ pop false exit}
+if
+} for
+exch pop exch pop
+}
+{ pop pop false }
+ifelse
+}
+{
+eq
+}
+ifelse
+}
+{ pop pop false }
+ifelse
+}
+{ pop pop false }
+ifelse
+}
+ifelse
+} bind def
+pdf_has_composefont?
+{
+/_pdfComposeFont
+{
+2 copy _pdfComposeFontName not
+{
+2 index
+}
+if
+(pdf) exch _pdfConcatNames
+dup _pdfFontStatus
+{ dup findfont 5 2 roll pop pop pop true}
+{
+4 1 roll
+1 index /CMap pdf_resourcestatus
+{
+pop pop
+true
+}
+{false}
+ifelse
+1 index true exch
+{
+_pdfCIDFontStatus not
+{pop false exit}
+if
+}
+forall
+and
+{
+1 index 1 index 0 get _pdf_CheckCIDSystemInfo
+{
+3 -1 roll pop
+2 index 3 1 roll
+composefont true
+}
+{
+pop pop exch pop false
+}
+ifelse
+}
+{
+_pdfComposeFontName
+{
+dup _pdfFontStatus
+{
+exch pop
+1 index exch
+findfont definefont true
+}
+{
+pop exch pop
+false
+}
+ifelse
+}
+{
+exch pop
+false
+}
+ifelse
+}
+ifelse
+{ true }
+{
+dup _pdfFontStatus
+{ dup findfont true }
+{ pop false }
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+{
+/_pdfComposeFont
+{
+_pdfComposeFontName not
+{
+dup
+}
+if
+dup
+_pdfFontStatus
+{exch pop dup findfont true}
+{
+1 index
+dup type /nametype eq
+{pop}
+{cvn}
+ifelse
+eq
+{pop false}
+{
+dup _pdfFontStatus
+{dup findfont true}
+{pop false}
+ifelse
+}
+ifelse
+}
+ifelse
+} bd
+}
+ifelse
+/_pdfStyleDicts 4 dict dup begin
+/Adobe-Japan1 4 dict dup begin
+Level2?
+{
+/Serif
+/HeiseiMin-W3-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiMin-W3}
+{
+/HeiseiMin-W3 _pdfCIDFontStatus
+{/HeiseiMin-W3}
+{/Ryumin-Light}
+ifelse
+}
+ifelse
+def
+/SansSerif
+/HeiseiKakuGo-W5-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiKakuGo-W5}
+{
+/HeiseiKakuGo-W5 _pdfCIDFontStatus
+{/HeiseiKakuGo-W5}
+{/GothicBBB-Medium}
+ifelse
+}
+ifelse
+def
+/HeiseiMaruGo-W4-83pv-RKSJ-H _pdfFontStatus
+{/HeiseiMaruGo-W4}
+{
+/HeiseiMaruGo-W4 _pdfCIDFontStatus
+{/HeiseiMaruGo-W4}
+{
+/Jun101-Light-RKSJ-H _pdfFontStatus
+{ /Jun101-Light }
+{ SansSerif }
+ifelse
+}
+ifelse
+}
+ifelse
+/RoundSansSerif exch def
+/Default Serif def
+}
+{
+/Serif /Ryumin-Light def
+/SansSerif /GothicBBB-Medium def
+{
+(fonts/Jun101-Light-83pv-RKSJ-H) status
+}stopped
+{pop}{
+{ pop pop pop pop /Jun101-Light }
+{ SansSerif }
+ifelse
+/RoundSansSerif exch def
+}ifelse
+/Default Serif def
+}
+ifelse
+end
+def
+/Adobe-Korea1 4 dict dup begin
+/Serif /HYSMyeongJo-Medium def
+/SansSerif /HYGoThic-Medium def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+/Adobe-GB1 4 dict dup begin
+/Serif /STSong-Light def
+/SansSerif /STHeiti-Regular def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+/Adobe-CNS1 4 dict dup begin
+/Serif /MKai-Medium def
+/SansSerif /MHei-Medium def
+/RoundSansSerif SansSerif def
+/Default Serif def
+end
+def
+end
+def
+/TZzero
+{
+/_wmode xdd
+/_styleArr xdd
+/_regOrdering xdd
+3 copy
+_pdfComposeFont
+{
+5 2 roll pop pop pop
+}
+{
+[
+0 1 _styleArr length 1 sub
+{
+_styleArr exch get
+_pdfStyleDicts _regOrdering 2 copy known
+{
+get
+exch 2 copy known not
+{ pop /Default }
+if
+get
+}
+{
+pop pop pop /Unknown
+}
+ifelse
+}
+for
+]
+exch pop
+2 index 3 1 roll
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+{3 -1 roll pop}
+{
+findfont dup /FontName get exch
+}
+ifelse
+}
+ifelse
+dup /WMode 2 copy known
+{ get _wmode ne }
+{ pop pop _wmode 1 eq}
+ifelse
+{
+exch _wmode _pdfConcatNames
+dup _pdfFontStatus
+{ exch pop dup findfont false}
+{ exch true }
+ifelse
+}
+{
+dup /FontType get 0 ne
+}
+ifelse
+{
+dup /FontType get 3 eq _wmode 1 eq and
+{
+_pdfVerticalRomanT3Font dup length 10 add dict copy
+begin
+/_basefont exch
+dup length 3 add dict
+begin
+{1 index /FID ne {def}{pop pop} ifelse }
+forall
+/Encoding Encoding dup length array copy
+dup 16#27 /quotesingle put
+dup 16#60 /grave put
+_regOrdering /Adobe-Japan1 eq
+{dup 16#5c /yen put dup 16#a5 /yen put dup 16#b4 /yen put}
+if
+def
+FontName
+currentdict
+end
+definefont
+def
+/Encoding _basefont /Encoding get def
+/_fauxfont true def
+}
+{
+dup length 3 add dict
+begin
+{1 index /FID ne {def}{pop pop} ifelse }
+forall
+FontType 0 ne
+{
+/Encoding Encoding dup length array copy
+dup 16#27 /quotesingle put
+dup 16#60 /grave put
+_regOrdering /Adobe-Japan1 eq
+{dup 16#5c /yen put}
+if
+def
+/_fauxfont true def
+} if
+} ifelse
+/WMode _wmode def
+dup dup /FontName exch def
+currentdict
+end
+definefont pop
+}
+{
+pop
+}
+ifelse
+/_pdf_FontDirectory 3 1 roll _safeput
+}
+bd
+Level2?
+{
+/Tf {
+_pdf_FontDirectory 2 index 2 copy known
+{get exch 3 -1 roll pop}
+{pop pop}
+ifelse
+selectfont
+} bd
+}
+{
+/Tf {
+_pdf_FontDirectory 2 index 2 copy known
+{get exch 3 -1 roll pop}
+{pop pop}
+ifelse
+exch findfont exch
+dup type /arraytype eq
+{makefont}
+{scalefont}
+ifelse
+setfont
+} bd
+}
+ifelse
+/cshow where
+{
+pop /pdf_cshow /cshow load dd
+/pdf_remove2 {pop pop} dd
+}
+{
+/pdf_cshow {exch forall} dd
+/pdf_remove2 {} dd
+} ifelse
+/pdf_xshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+_pdf_x _pdf_y moveto
+0
+rmoveto
+}
+ifelse
+_pdf_i 1 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdf_yshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+_pdf_x _pdf_y moveto
+0 exch
+rmoveto
+}
+ifelse
+_pdf_i 1 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdf_xyshow
+{
+/_pdf_na xdd
+/_pdf_i 0 dd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 /_pdf_showproc load exec
+{_pdf_na _pdf_i get} stopped
+{ pop pop }
+{
+{_pdf_na _pdf_i 1 add get} stopped
+{ pop pop pop}
+{
+_pdf_x _pdf_y moveto
+rmoveto
+}
+ifelse
+}
+ifelse
+_pdf_i 2 add /_pdf_i xdd
+currentpoint
+/_pdf_y xdd
+/_pdf_x xdd
+}
+exch
+pdf_cshow
+} bd
+/pdfl1xs {/_pdf_showproc /show load dd pdf_xshow} bd
+/pdfl1ys {/_pdf_showproc /show load dd pdf_yshow} bd
+/pdfl1xys {/_pdf_showproc /show load dd pdf_xyshow} bd
+Level2? _ColorSep5044? not and
+{
+/pdfxs {{xshow} stopped {pdfl1xs} if} bd
+/pdfys {{yshow} stopped {pdfl1ys} if} bd
+/pdfxys {{xyshow} stopped {pdfl1xys} if} bd
+}
+{
+/pdfxs /pdfl1xs load dd
+/pdfys /pdfl1ys load dd
+/pdfxys /pdfl1xys load dd
+} ifelse
+/pdf_charpath {false charpath} bd
+/pdf_xcharpath {/_pdf_showproc /pdf_charpath load dd pdf_xshow} bd
+/pdf_ycharpath {/_pdf_showproc /pdf_charpath load dd pdf_yshow} bd
+/pdf_xycharpath {/_pdf_showproc /pdf_charpath load dd pdf_xyshow} bd
+/pdf_strokepath
+{
+{
+pdf_remove2
+_pdf_str1 exch 0 exch put
+_pdf_str1 false charpath
+currentpoint S moveto
+} bind
+exch pdf_cshow
+} bd
+/pdf_xstrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_xshow} bd
+/pdf_ystrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_yshow} bd
+/pdf_xystrokepath {/_pdf_showproc {pdf_charpath S} dd pdf_xyshow} bd
+Level2? {currentglobal true setglobal} if
+/d0/setcharwidth ld
+/nND {{/.notdef} repeat} bd
+/T3Defs {
+/BuildChar
+{
+1 index /Encoding get exch get
+1 index /BuildGlyph get exec
+}
+def
+/BuildGlyph {
+exch begin
+GlyphProcs exch get exec
+end
+} def
+/_pdfT3Font true def
+} bd
+/_pdfBoldRomanWidthProc
+{
+stringwidth 1 index 0 ne { exch .03 add exch }if setcharwidth
+0 0
+} bd
+/_pdfType0WidthProc
+{
+dup stringwidth 0 0 moveto
+2 index true charpath pathbbox
+0 -1
+7 index 2 div .88
+setcachedevice2
+pop
+0 0
+} bd
+/_pdfType0WMode1WidthProc
+{
+dup stringwidth
+pop 2 div neg -0.88
+2 copy
+moveto
+0 -1
+5 -1 roll true charpath pathbbox
+setcachedevice
+} bd
+/_pdfBoldBaseFont
+11 dict begin
+/FontType 3 def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/Encoding cHexEncoding def
+/_setwidthProc /_pdfBoldRomanWidthProc load def
+/_bcstr1 1 string def
+/BuildChar
+{
+exch begin
+_basefont setfont
+_bcstr1 dup 0 4 -1 roll put
+dup
+_setwidthProc
+3 copy
+moveto
+show
+_basefonto setfont
+moveto
+show
+end
+}bd
+currentdict
+end
+def
+pdf_has_composefont?
+{
+/_pdfBoldBaseCIDFont
+11 dict begin
+/CIDFontType 1 def
+/CIDFontName /_pdfBoldBaseCIDFont def
+/FontMatrix[1 0 0 1 0 0]def
+/FontBBox[0 0 1 1]def
+/_setwidthProc /_pdfType0WidthProc load def
+/_bcstr2 2 string def
+/BuildGlyph
+{
+exch begin
+_basefont setfont
+_bcstr2 1 2 index 256 mod put
+_bcstr2 0 3 -1 roll 256 idiv put
+_bcstr2 dup _setwidthProc
+3 copy
+moveto
+show
+_basefonto setfont
+moveto
+show
+end
+}bd
+currentdict
+end
+def
+/_pdfDefineIdentity-H
+{
+/Identity-H /CMap PDFText /pdf_resourcestatus get exec
+{
+pop pop
+}
+{
+/CIDInit/ProcSet findresource begin 12 dict begin
+begincmap
+/CIDSystemInfo
+3 dict begin
+/Registry (Adobe) def
+/Ordering (Identity) def
+/Supplement 0 def
+currentdict
+end
+def
+/CMapName /Identity-H def
+/CMapVersion 1 def
+/CMapType 1 def
+1 begincodespacerange
+<0000> <ffff>
+endcodespacerange
+1 begincidrange
+<0000> <ffff> 0
+endcidrange
+endcmap
+CMapName currentdict/CMap defineresource pop
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diff --git a/Examples/MeshGenToolbox/mgt/Cell.h b/Examples/MeshGenToolbox/mgt/Cell.h
new file mode 100644
index 0000000000000000000000000000000000000000..ed2a0d67e676b1b32fd9f41ae3539b8a30896786
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Cell.h
@@ -0,0 +1,79 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/* This file includes classes for the cell module. */
+/*****************************************************************************/
+
+#ifndef CELL
+#define CELL
+#endif
+
+#ifndef VERTEX
+#include "Vertex.h"
+#endif
+
+#ifndef EDGE
+#include "Edge.h"
+#endif
+
+namespace PMGT{
+//namespace Cell{
+
+//using namespace Vertex;
+//using namespace Edge;
+
+class Cell{
+public:
+ Cell(int cId=-1, int LhId = -1, MFLAG mFlag=UNCHANGE, bool del=false){
+ cId_ = cId;
+ LhId_ = LhId;
+ mFlag_ = mFlag;
+ del_ = del;
+ }
+
+ inline int cId(){ return cId_;}
+ inline MFLAG mFlag(){ return mFlag_; }
+ inline int LhId(){ return LhId_; }
+ inline bool del(){ return del_; }
+
+
+ inline void setCId(int cId){ cId_ = cId; }
+ inline void setMflag(MFLAG flag){ mFlag_ = flag; }
+ inline void setLhId(int LhId){ LhId_ = LhId; }
+ inline void setDel(bool del) { del_ = del; }
+
+ inline void ccopy(Cell& other){
+ cId_ = other.cId_;
+ LhId_ = other.LhId_;
+ mFlag_ = other.mFlag_;
+ del_ = other.del_;
+ }
+
+private:
+ int cId_; //id
+ int LhId_; //longest halfedge
+ MFLAG mFlag_; //flag for modification
+ bool del_; // a flag to indicate if the cell
+ // is marked to be deleted
+}; // end of class Cell
+
+//} // end of namespace Cell
+
+
+} // end of namespace PMGT
diff --git a/Examples/MeshGenToolbox/mgt/Coarsening.cpp b/Examples/MeshGenToolbox/mgt/Coarsening.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..09a6d7f28f153afbc2874c95f7c9db78c576e0f5
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Coarsening.cpp
@@ -0,0 +1,323 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/*****************************************************************************/
+#ifndef COARSENING
+#include "Coarsening.h"
+#endif
+
+namespace PMGT{
+
+ // coarsen the mesh by edge collapse
+ void Coarsening::edge_collapse(Mesh& mesh){
+ int i, j, k,
+ cId, // temp cell Id
+ eId, // temp edge Id
+ hId, // temp halfedge Id
+ vId, // temp vertex Id
+
+ acId, // adjacent cell
+ first_acId, // the first adjacent cell
+ rvId, // the vertex to be remained
+ dvId; // the vertex to be deleted
+
+ vector<int> del_cells, // cells to be deleted
+ mutual_halfedges, // halfedges of the mutual edge
+ del_halfedges, // halfedges to be deleted/merged
+ remain_halfedges, // halfedges to be remained
+ update_halfedges, // halfedges whose target vertices
+ // to be updated
+ update_cells; // cells whose edge length are changed
+
+ //int nc = mesh.n_of_c();
+ for (i=0; i<mesh.n_of_c(); i++){
+ bool legal = false;
+ if (mesh.cell(i).mFlag() == COARSEN && !mesh.cell(i).del()){
+ // check if it is legal to delete i
+
+ // check if one of the adjacent cells is to be coarsened
+ acId = mesh.cc_first(i);
+
+ for (int k=0; k<3; k++){ // try 3 neighbour of cell i
+//cout << "coarsen i=" << i << " acId=" << acId << " k=" << k <<endl;
+ if (acId == -1){
+ break;
+ }
+ // check if the i-th neighbour is to be coarsened
+ if (mesh.cell(acId).mFlag() != COARSEN){
+ acId = mesh.cc_next(i, acId);
+ continue;
+ }
+ /* check if the mutual edge is legal to be removed */
+
+ // find one halfedge of the mutual edge
+ hId = mesh.ch_first(i);
+
+ if (mesh.IcId_from_hId(mesh.ops_hId(hId)) != acId){
+ if (mesh.IcId_from_hId(mesh.ops_hId
+ (mesh.prev_hId(hId))) == acId){
+ hId = mesh.prev_hId(hId);
+ }
+ else if(mesh.IcId_from_hId(mesh.ops_hId
+ (mesh.next_hId(hId))) == acId){
+ hId = mesh.next_hId(hId);
+ }
+ else assert(false);
+ }
+
+ // find the vertex to be delated
+ int illegal_vId = -1; // the vertex that can not be deleted
+ bool both_illegal = false; // both vertices are illegal to be deleted
+ dvId = mesh.tvId_from_hId(hId);
+ rvId = mesh.svId_from_hId(hId);
+ int old_hId = hId;
+ for (int x=0; x<2; x++){ // try two vertices of hId
+ if (mesh.is_b_v(dvId)){
+ if (illegal_vId == -1){
+ illegal_vId = dvId;
+ dvId = mesh.svId_from_hId(old_hId);
+ rvId = mesh.tvId_from_hId(old_hId);
+ hId = mesh.ops_hId(old_hId);
+ continue;
+ }
+ else{
+ both_illegal = true;
+ break;
+ }
+ }
+//cout << "mutual_h:"<<hId<<",";
+ // reserve the entities that will be modified
+ del_cells.clear();
+ mutual_halfedges.clear();
+ del_halfedges.clear();
+ remain_halfedges.clear();
+ update_halfedges.clear();
+ update_cells.clear();
+ // set variables
+ mutual_halfedges.push_back(hId);
+ del_halfedges.push_back(mesh.next_hId(hId));
+ remain_halfedges.push_back(mesh.prev_hId(hId));
+ del_cells.push_back(mesh.IcId_from_hId(hId));
+
+ hId = mesh.ops_hId(hId);
+//cout << hId<< endl;
+
+ mutual_halfedges.push_back(hId);
+ del_halfedges.push_back(mesh.prev_hId(hId));
+ remain_halfedges.push_back(mesh.next_hId(hId));
+ del_cells.push_back(mesh.IcId_from_hId(hId));
+//cout << "del_cells "<< del_cells[0]<<","<<del_cells[1]<<endl;
+ assert(del_cells[0]==i || del_cells[0]==acId);
+ assert(del_cells[1]==i || del_cells[1]==acId);
+ assert(del_cells[0] != del_cells[1]);
+ assert(!mesh.is_b_v(dvId));
+
+ // find the halfedges whose target vertices are dvId
+ hId = mesh.vih_first(dvId);
+ do{
+ if (hId == -1){
+ break;
+ }
+ if (hId != mutual_halfedges[0] && hId != del_halfedges[1]
+ && hId != mesh.ops_hId(del_halfedges[0])){
+ update_halfedges.push_back(hId);
+ //update_cells.push_back(mesh.IcId_from_hId(hId));
+ }
+//cout << "dvId="<<dvId<<"vih id=" << hId << endl;
+
+ hId = mesh.vih_next(dvId, hId);
+ }while (hId != mesh.vih_first(dvId));
+
+ // find the cells whose whose one vertices are dvId
+ cId = mesh.vc_first(dvId);
+ do{
+ if (cId ==-1){
+ break;
+ }
+ if (cId != del_cells[0] && cId != del_cells[1]){
+ update_cells.push_back(cId);
+ //update_cells.push_back(mesh.IcId_from_hId(hId));
+ }
+
+ cId = mesh.vc_next(dvId, cId);
+
+ }while (cId != mesh.vc_first(dvId));
+
+
+ for (j=0; j<update_cells.size(); j++){
+ vector<int> vIds;
+ vIds.clear();
+ vIds = mesh.vIds_from_cId(update_cells[j]);
+ for (int jj=0; jj<3; jj++){
+ if (vIds[jj] == dvId){
+ vIds[jj] = rvId;
+ }
+ }
+ if ( !mesh.is_ccw(vIds)){
+ break;// for j
+ }
+
+ }
+ if (j==update_cells.size()){
+ break; // from (for x)
+ }
+ // dvId is not legal to be deleted
+ if (illegal_vId == -1){
+ illegal_vId = dvId;
+ dvId = mesh.svId_from_hId(old_hId);
+ rvId = mesh.tvId_from_hId(old_hId);
+ hId = mesh.ops_hId(old_hId);
+ continue;
+ }
+ else {// both vertices are illegal to be deleted
+ both_illegal = true;
+ break; // from (for x)
+ }
+ }// for x
+
+ if (both_illegal){
+ acId = mesh.cc_next(i, acId);
+ if (acId == -1){
+ break;
+ }
+ continue;
+ }
+ else {
+ legal = true;
+ break; // from (for k) since dvId is found
+ }
+ } // for k
+ if (legal){
+//cout << "legal coarsen i=" << i << " acId=" << acId << endl;
+
+ // reset Mflag
+ for (j=0; j<update_halfedges.size(); j++){
+ mesh.halfedge(update_halfedges[j]).setTvId(rvId);
+
+ }
+ for (j=0; j<2; j++){
+ hId = mesh.ops_hId(del_halfedges[j]);
+ cId = mesh.IcId_from_hId(hId);
+ if (mesh.LhId_from_cId(cId) == hId){
+ int LhId = remain_halfedges[j];
+ int next_hId = mesh.next_hId(hId);
+ int prev_hId = mesh.prev_hId(hId);
+ if (mesh.dist(LhId) < mesh.dist(next_hId)){
+ LhId = next_hId;
+ }
+ if (mesh.dist(LhId) < mesh.dist(prev_hId)){
+ LhId = prev_hId;
+ }
+ mesh.cell(cId).setLhId(LhId);
+//cout << " ____cId = " << cId << " LhId = " << LhId <<endl;
+ }
+ }
+
+
+ for (j=0; j<update_cells.size(); j++){
+ mesh.cell(update_cells[j]).setMflag(UNCHANGE);
+ }
+//cout << "---update_cells:";
+//for (int ii=0; ii<update_cells.size(); ii++){
+// cout <<" " << update_cells[ii]<< "("<<mesh.cell(update_cells[ii]).mFlag()<<")";
+//}
+
+//cout << endl;
+
+ // reset OhId
+ int svId = mesh.svId_from_hId(del_halfedges[1]);
+ if (mesh.OhId_from_vId(svId) == del_halfedges[1]){
+ //mesh.vertex(svId).setOhId(mesh.ccw_hId(del_halfedges[1]));
+ //assert(mesh.svId_from_hId(del_halfedges[1])==
+ //mesh.svId_from_hId(remain_halfedges[1]));
+ mesh.vertex(svId).setOhId(mesh.ops_hId(remain_halfedges[1]));
+//cout << "reset OhId of vertex " << svId << " to " << mesh.vertex(svId).OhId() << endl;
+ }
+
+ svId = mesh.svId_from_hId(mesh.ops_hId(del_halfedges[0]));
+ if (mesh.OhId_from_vId(svId) == mesh.ops_hId(del_halfedges[0])){
+ //mesh.vertex(svId).setOhId(mesh.ccw_hId(mutual_halfedges[0]));
+ //assert(mesh.svId_from_hId(del_halfedges[0])==
+ //mesh.svId_from_hId(remain_halfedges[0]));
+ mesh.vertex(svId).setOhId(remain_halfedges[0]);
+
+//cout << "reset OhId of vertex " << svId << " to " << mesh.vertex(svId).OhId() << endl;
+ }
+ svId = mesh.svId_from_hId(mutual_halfedges[0]);
+ if (mesh.OhId_from_vId(svId) == mutual_halfedges[0]){
+ //mesh.vertex(svId).setOhId(mesh.ccw_hId(mutual_halfedges[0]));
+ //assert(mesh.svId_from_hId(mutual_halfedges[0])==
+ //mesh.svId_from_hId(remain_halfedges[0]));
+
+ mesh.vertex(svId).setOhId(remain_halfedges[1]);
+//cout << "reset OhId of vertex " << svId << " to " << mesh.vertex(svId).OhId() << endl;
+ }
+
+
+ for (j=0; j<2; j++){
+ hId = mesh.ops_hId(del_halfedges[j]);
+
+
+ int phId = mesh.prev_hId(hId);
+ int nhId = mesh.next_hId(hId);
+ cId = mesh.IcId_from_hId(hId);
+
+ mesh.halfedge(remain_halfedges[j]).setIcId(cId);
+ mesh.halfedge(remain_halfedges[j]).setPhId(phId);
+ mesh.halfedge(remain_halfedges[j]).setNhId(nhId);
+ mesh.halfedge(nhId).setPhId(remain_halfedges[j]);
+ mesh.halfedge(phId).setNhId(remain_halfedges[j]);
+
+
+ mesh.halfedge(del_halfedges[j]).setIcId(-1);
+
+ }
+
+
+ // mark edges to be deleted
+ mesh.edge(mesh.eId_from_hId(mutual_halfedges[0])).setDel(true);
+ mesh.edge(mesh.eId_from_hId(del_halfedges[0])).setDel(true);
+ mesh.edge(mesh.eId_from_hId(del_halfedges[1])).setDel(true);
+
+//cout << "deleted edges:"<< mesh.eId_from_hId(mutual_halfedges[0])
+//<< " "<< mesh.eId_from_hId(del_halfedges[0])
+//<< " "<< mesh.eId_from_hId(del_halfedges[1])<< endl;
+
+ // mark cells to be deleted
+ mesh.cell(del_cells[0]).setDel(true);
+ mesh.cell(del_cells[1]).setDel(true);
+
+
+ // delete dvId
+ mesh.vertex(dvId).set_isolated_v();
+ mesh.vertex(dvId).setDel(true);
+ }// if (legal)
+ }// if COARSEN
+ } // for i
+
+ // delete entities
+ mesh.delete_cells();
+ mesh.delete_edges();//mesh.display_info();
+
+ mesh.delete_vertices();
+
+ // reset mFlags
+ }// edge_collapse
+
+}
diff --git a/Examples/MeshGenToolbox/mgt/Coarsening.h b/Examples/MeshGenToolbox/mgt/Coarsening.h
new file mode 100644
index 0000000000000000000000000000000000000000..0d6907b0304e980f226fd3ef704e3f691e3fa329
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Coarsening.h
@@ -0,0 +1,38 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/* This file contains the class for corsening module. */
+/*****************************************************************************/
+
+#ifndef COARSENING
+#define COARSENING
+#endif
+
+#ifndef MESH
+#include "Mesh.h"
+#endif
+
+namespace PMGT{
+class Coarsening{
+public:
+
+ // coarsen the mesh by edge collapse
+ void edge_collapse(Mesh& mesh);
+};
+}
diff --git a/Examples/MeshGenToolbox/mgt/Edge.h b/Examples/MeshGenToolbox/mgt/Edge.h
new file mode 100644
index 0000000000000000000000000000000000000000..525d9933ead4855bbbfba74c5a6d87e648e50638
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Edge.h
@@ -0,0 +1,138 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/* This file includes classes for the edge module. */
+/*****************************************************************************/
+
+#ifndef EDGE
+#define EDGE
+#endif
+
+#ifndef VERTEX
+#include "Vertex.h"
+#endif
+
+namespace PMGT{
+//namespace Edge{
+
+//using namespace Vertex;
+
+
+class Halfedge{
+public:
+ Halfedge(int hId=-1, int TvId=-1, int IcId=-1, int PhId=-1, int NhId=-1){
+ hId_ = hId;
+ TvId_ = TvId;
+ IcId_ = IcId;
+ PhId_ = PhId;
+ NhId_ = NhId;
+ }
+
+ inline int hId(){ return hId_; }
+ inline int IcId(){ return IcId_; }
+ inline int TvId(){ return TvId_; }
+ inline int NhId(){ return NhId_; }
+ inline int PhId(){ return PhId_; }
+
+ inline void setHId(int hId){ hId_ = hId; }
+ inline void setTvId(int TvId){ TvId_ = TvId; }
+ inline void setIcId(int IcId){ IcId_ = IcId; }
+ inline void setNhId(int NhId){ NhId_ = NhId; }
+ inline void setPhId(int PhId){ PhId_ = PhId; }
+
+ inline bool is_boundary(){ return IcId_ == -1; }
+ //opposite halfedge
+ inline int ops_hId(){ return ((hId_ & 1) ? hId_-1: hId_+1); }
+ inline void hcopy(Halfedge& other){
+ hId_ = other.hId_;
+ TvId_ = other.TvId_;
+ IcId_ = other.IcId_;
+ PhId_ = other.PhId_;
+ NhId_ = other.NhId_;
+ }
+
+private:
+ int hId_; //id
+ int TvId_; //target vertex
+ int IcId_; //its cel
+ int PhId_; //previous halfedge
+ int NhId_; //next halfedge
+
+}; // end of class Halfedge
+
+
+class Edge{
+public:
+ Edge(int svId=-2, int tvId=-1, int eId=-1, bool del=false){
+ assert(svId != tvId);
+ eId_ = eId;
+ pair_[0].setHId(eId << 1);
+ pair_[0].setTvId(tvId);
+ pair_[1].setHId((eId << 1)+1);
+ pair_[1].setTvId(svId);
+ del_ = del;
+ }
+
+
+ inline int eId(){ return eId_;}
+ inline Halfedge* pair(){ return pair_; }
+ inline bool del(){ return del_; }
+
+ inline void setEId(int eId){ eId_ = eId; }
+ inline void setPair(Halfedge& h1, Halfedge& h2){
+ pair_[0].hcopy(h1);
+ pair_[1].hcopy(h2);
+ }
+ inline void setDel(bool del) { del_ = del; }
+
+
+ inline bool is_isolated_e(){
+ return pair_[0].IcId() == -1
+ && pair_[1].IcId() == -1;
+ }
+ inline void set_isolated_e(){
+ pair_[0].setIcId(-1);
+ pair_[1].setIcId(-1);
+ }
+
+ inline bool same (int svId, int tvId){
+ int v1Id = pair_[0].TvId();
+ int v2Id = pair_[1].TvId();
+ return ((v1Id==svId && v2Id==tvId) || (v1Id==tvId && v2Id==svId));
+ }
+
+ inline void ecopy(Edge& other){
+ eId_ = other.eId_;
+ pair_[0].hcopy(other.pair_[0]);
+ pair_[1].hcopy(other.pair_[1]);
+ del_ = other.del_;
+ }
+
+private:
+ int eId_; // id
+ Halfedge pair_[2]; //a pair of halfedges
+ bool del_; // a flag to indicate if the edge
+ // is marked to be deleted
+}; // end of class Edge
+
+
+//} // end of namespace Edge
+
+
+} // end of namespace PMGT
diff --git a/Examples/MeshGenToolbox/mgt/Input.cpp b/Examples/MeshGenToolbox/mgt/Input.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..fcf3aaaf32a7230ca0fea3998ba0899550244a13
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Input.cpp
@@ -0,0 +1,143 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/*****************************************************************************/
+
+#include "Input.h"
+
+namespace PMGT{
+
+
+ // Read the mesh from two files
+ // One is the coordinates of points
+ // The other is the vertex list of cells
+ void Input::read_file(Mesh& mesh, char* vertexFile, char* cellFile){
+/**/
+ FILE *v;
+ FILE *c;
+ Point p;
+ Ids ids;
+ vector<Point> points;
+ vector<Ids> cells;
+
+ char *s, *t;
+ char line[100];
+ bool error = false;
+
+ // Open the file. If NULL is returned there was an error
+ if((v = fopen(vertexFile, "r")) == NULL) {
+ cout << "Error opening file " << vertexFile << "." << endl;
+ exit(1);
+ }
+
+ if((c = fopen(cellFile, "r")) == NULL) {
+ cout << "Error opening file " << cellFile << "." << endl;
+ exit(1);
+ }
+
+ //assert(vertices_.size() == 0);
+ //assert(edges_.size() == 0);
+ //assert(cells_.size() == 0);
+
+ // get vertices
+ points.clear();
+ int count = 0;
+ while( fgets(line, sizeof(line), v) != NULL ) {
+ // Get each line from the infile
+ s = line;
+ p.clear();
+
+ p.push_back(strtod(s, &t));
+ while ( *s != ' ' && *s !='\n'){
+ s++;
+ }
+ if (*s == '\n'){
+ error = true;
+ break;
+ }
+ p.push_back(strtod(s, &t));
+ points.push_back(p);
+ count++;
+ }
+ fclose(v); // Close the file
+ if (error){ // error message for input file
+ cout <<"Something wrong in your input file " << vertexFile <<
+ " line " << count+1 << endl;
+ exit(1);
+ }
+
+ // get cells
+ int n=points.size();
+ count = 0;
+ cells.clear();
+ while( fgets(line, sizeof(line), c) != NULL ) {
+ // Get each line from the infile
+ s = line;
+ ids.clear();
+
+ ids.push_back(strtol(s, &t, 10));
+
+ if (ids[ids.size()-1] <0 || ids[ids.size()-1]>=n){
+ error = true;
+ break;
+ }
+ while ( *s != ' ' && *s !='\n'){
+ s++;
+ }
+ while(*s == ' ') s++;
+ if (*s == '\n'){
+ error = true;
+ break;
+ }
+
+ ids.push_back(strtol(s, &t, 10));
+ while(*s == ' ') s++;
+ if (ids[ids.size()-1] <0 || ids[ids.size()-1]>=n){
+ error = true;
+ break;
+ }
+
+ while ( *s != ' ' && *s !='\n'){
+ s++;
+ }
+ while(*s == ' ') s++;
+ if (*s == '\n'){
+ error = true;
+ break;
+ }
+
+ ids.push_back(strtol(s, &t, 10));
+ if (ids[ids.size()-1] <0 || ids[ids.size()-1]>=n){
+ error = true;
+ break;
+ }
+ cells.push_back(ids);
+
+ count++;
+ }
+ fclose(c);
+ if (error){ // error message for input file
+ cout <<"Something wrong in your input file " << cellFile <<
+ " line " << count+1 <<endl;
+ exit(1);
+ }
+ mesh.create(points, cells);
+ }
+}
+
diff --git a/Examples/MeshGenToolbox/mgt/Input.h b/Examples/MeshGenToolbox/mgt/Input.h
new file mode 100644
index 0000000000000000000000000000000000000000..2c1e184c7a2b99c8469f59882f37addde9739830
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Input.h
@@ -0,0 +1,42 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/* This file includes classes for the input module. */
+/*****************************************************************************/
+
+#ifndef INPUT
+#define INPUT
+#endif
+
+#ifndef MESH
+#include "Mesh.h"
+#endif
+
+namespace PMGT{
+class Input{
+public:
+
+ // Read the mesh from two files
+ // One is the coordinates of points
+ // The other is the vertex list of cells
+ void read_file(Mesh& mesh, char* vertexFile, char* cellFile);
+};
+}
+
+
diff --git a/Examples/MeshGenToolbox/mgt/Mesh.cpp b/Examples/MeshGenToolbox/mgt/Mesh.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..57fcda4c18524e0d72ba49398e1c67c20d85921a
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Mesh.cpp
@@ -0,0 +1,534 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/*****************************************************************************/
+
+#include "Mesh.h"
+
+namespace PMGT{
+//namespace Mesh{
+
+ // Returns the id of the vertex that has given coordinate.
+ // Returns -1 if the vertex does not exist.
+ int Mesh::find_vertex(Point point){
+ for (int i=0; i<vertices_.size(); i++){
+ if (vertices_[i].point() == point)
+ return i;
+ }
+ return -1;
+ }
+
+ // Returns the id of the edge that has given points.
+ // Returns -1 if the edge does not exist.
+ int Mesh::find_edge(int svId, int tvId){
+ assert(is_valid_vId(svId));
+ assert(is_valid_vId(tvId));
+ for (int i=0; i<edges_.size(); i++){
+ if (edges_[i].pair()[0].TvId() == tvId){
+ if (edges_[i].pair()[1].TvId() == svId)
+ return i;
+ }
+ if (edges_[i].pair()[0].TvId() == svId){
+ if (edges_[i].pair()[1].TvId() == tvId)
+ return i;
+ }
+ }
+ return -1;
+ }
+
+ // Returns the id of the halfedge that has given start and targate points.
+ // Returns -1 if the halfedge does not exist.
+ int Mesh::find_halfedge(int svId, int tvId){
+ assert(is_valid_vId(svId));
+ assert(is_valid_vId(tvId));
+ for (int i=0; i<edges_.size(); i++){
+ if (edges_[i].pair()[0].TvId() == tvId){
+ if (edges_[i].pair()[1].TvId() == svId)
+ return (i<<1);
+ }
+ if (edges_[i].pair()[0].TvId() == svId){
+ if (edges_[i].pair()[1].TvId() == tvId)
+ return (i<<1)+1;
+ }
+ }
+ return -1;
+ }
+
+ // Returns the id of the cell that has given vertices.
+ // Returns -1 if the cell does not exist.
+ // Make sure that vIds and corresponding halfedges exist.
+ int Mesh::find_cell(vector<int> vIds){
+ assert(vIds.size() == 3);
+ for (int i=0; i<3; i++){
+ assert(is_valid_vId(vIds[i]));
+ }
+ vector<int> hId(3);
+ for (int i=0; i<3; i++){
+ hId[i] = find_halfedge(vIds[i], vIds[(i+1)%3]);
+ if(hId[i] == -1) return -1;
+ }
+
+ for (int i=0; i<cells_.size(); i++){
+ for (int j=0; j<3; j++){
+ if (cells_[i].LhId()==hId[j]){
+ int k;
+ for (k=0; k<3; k++){
+ if (vIds[k]=tvId_from_hId(hId[j])){
+
+ break;
+ }
+ }
+ if (k<3 && vIds[(k+1)%3]==tvId_from_hId(hId[(j+1)%3])
+ && vIds[(k+2)%3]==tvId_from_hId(hId[(j+2)%3])){
+ // three vertices is target vertices of three halfedges
+ return i;
+ }
+ }
+ }
+ }
+ return -1;
+ }
+
+
+ // Create a vertex and add it to the end of the vertex list.
+ // Returns false if the vertex already exists.
+ bool Mesh::add_vertex(Point point){
+ int vId = find_vertex(point);
+ if (vId != -1) return false;
+ Vertex v(point, vertices_.size());
+ vertices_.push_back(v);
+ return true;
+ }
+
+
+ // Create an edge and add it to the end of the edge list.
+ // Returns false if the edge already exists.
+ bool Mesh::add_edge(int svId, int tvId){
+ assert(is_valid_vId(svId));
+ assert(is_valid_vId(tvId));
+ int eId = find_edge(svId, tvId);
+ if (eId != -1){
+ cout << "add edge " << svId << " " << tvId << " failed" << endl;
+ return false;
+ }
+ Edge e(svId, tvId, edges_.size());
+ e.pair()[0].setIcId(-1);
+ e.pair()[1].setIcId(-1);
+ edges_.push_back(e);
+ edge(edges_.size()-1).pair()[0].setIcId(-1);
+ edge(edges_.size()-1).pair()[1].setIcId(-1);
+ return true;
+ }
+
+
+ // Create a cell and add it to the end of the vertex list.
+ // Returns false if the cell already exists.
+ bool Mesh::add_cell(vector<int> vIds){
+ assert(vIds.size() == 3);
+ for (int i=0; i<3; i++){
+ assert(is_valid_vId(vIds[i]));
+ }
+ int cId = find_cell(vIds);
+ if (cId != -1) return false;
+ assert(cId == -1);
+ vector<int> hId(3);
+ for (int i=0; i<3; i++){
+
+ hId[i] = find_halfedge(vIds[i], vIds[(i+1)%3]);
+ assert(hId[i] != -1);
+ }
+ int LhId = hId[0];
+ if (dist(hId[1]) > dist(LhId)) LhId = hId[1];
+ if (dist(hId[2]) > dist(LhId)) LhId = hId[2];
+
+ //Cell c(cells_.size(), LhId);
+ Cell c;
+ cells_.push_back(c);
+ cId = cells_.size()-1;
+ cell(cId).setCId(cId);
+ cell(cId).setLhId(LhId);
+ // resolve connectivity of edges and vertices
+ for (int i=0; i<3; i++){
+ halfedge(hId[i]).setIcId(cId);
+ halfedge(hId[i]).setNhId(hId[(i+1)%3]);
+ halfedge(hId[i]).setPhId(hId[(i+2)%3]);
+
+ }
+ for (int i=0; i<3; i++){
+ int OhId = vertex(vIds[i]).OhId();
+ if (OhId ==-1 || (!is_b_h(ops_hId(OhId)))){
+ vertex(vIds[i]).setOhId(hId[i]);
+ }
+ else if(svId_from_hId(OhId) != vIds[i]){
+ vertex(vIds[i]).setOhId(hId[i]);
+ }
+ }
+ return true;
+
+ }
+
+ // update the cell using given vertex.
+ // Returns false if the cell does not exist
+ // or the new cell is already exists.
+ bool Mesh::update_cell(vector<int> vIds, int cId){
+ if (!is_valid_cId(cId)) {
+ cout << "update cell " << cId << " failed. " <<
+ cId << " is not valid." << endl;
+ return false;
+ }
+ int newId = find_cell(vIds);
+ if (newId != -1){
+ cout << "update cell " << cId << " failed. The cell (" <<
+ vIds[0]<<","<<vIds[1]<<","<<vIds[2]<<") exists."<<endl;
+ return false;
+ }
+
+ vector<int> hId(3);
+ for (int i=0; i<3; i++){
+ hId[i] = find_halfedge(vIds[i], vIds[(i+1)%3]);
+ assert(hId[i] != -1);
+ }
+ int LhId = hId[0];
+ if (dist(hId[1]) > dist(LhId)) LhId = hId[1];
+ if (dist(hId[2]) > dist(LhId)) LhId = hId[2];
+ Cell& c = cell(cId);
+ c.setLhId(LhId);
+ c.setMflag(UNCHANGE);
+
+ // resolve connectivity of edges and vertices
+ for (int i=0; i<3; i++){
+ halfedge(hId[i]).setIcId(c.cId());
+ halfedge(hId[i]).setNhId(hId[(i+1)%3]);
+ halfedge(hId[i]).setPhId(hId[(i+5)%3]);
+
+ int OhId = vertex(vIds[i]).OhId();
+ if (OhId ==-1 || (!is_b_h(ops_hId(OhId)))){
+ vertex(vIds[i]).setOhId(hId[i]);
+ }
+ else if(svId_from_hId(OhId) != vIds[i]){
+ vertex(vIds[i]).setOhId(hId[i]);
+ }
+ }
+ return true;
+
+ }
+
+
+ // refine two cells whose longest edges are oppsite to each other
+ bool Mesh::longest_ref2(int hId, int o_hId, int n_hId){
+
+ assert(o_hId == ops_hId(hId));
+ int cId = IcId_from_hId(hId);
+ int ops_cId = IcId_from_hId(o_hId);
+ vector<int> vIds;
+ // reserve vertices
+ if (cId != -1){
+ //vIds = vIds_from_cId(cId);
+ vIds.push_back(tvId_from_hId(hId));
+ vIds.push_back(tvId_from_hId(next_hId(hId)));
+ vIds.push_back(svId_from_hId(hId));
+ }
+ vector<int> ops_vIds;// = vIds_from_cId(ops_cId);
+ ops_vIds.push_back(tvId_from_hId(o_hId));
+ ops_vIds.push_back(tvId_from_hId(next_hId(o_hId)));
+ ops_vIds.push_back(svId_from_hId(o_hId));
+
+ if (cId !=-1){
+ assert(ops_vIds[0] == vIds[2]);
+ assert(ops_vIds[2] == vIds[0]);
+ }
+
+ // reset mFlag
+ cell(ops_cId).setMflag(UNCHANGE);
+ if (cId != -1){
+ cell(cId).setMflag(UNCHANGE);
+ }
+
+ // add new vertex
+ Point p = mid_point(hId);
+ assert(add_vertex(p));
+ int new_vId = n_of_v()-1;
+
+ // add/update edges
+ assert(add_edge(ops_vIds[1], new_vId));
+ if (cId != -1){
+ assert(add_edge(vIds[1], new_vId));
+ }
+
+ halfedge(hId).setTvId(new_vId);
+ assert(add_edge(ops_vIds[2], new_vId));
+
+ // add/update cells
+ int next_svId=0;
+ if (n_hId != -1){
+ for(int k=0; k<2; k++){
+ if(ops_vIds[k]==svId_from_hId(n_hId)){
+ next_svId = k;
+ break;
+ }
+ }
+ }
+ vector<int> temp_vIds;
+ temp_vIds.clear();
+ temp_vIds.push_back(new_vId);
+ temp_vIds.push_back(ops_vIds[next_svId]);
+ temp_vIds.push_back(ops_vIds[next_svId+1]);
+ assert(update_cell(temp_vIds, ops_cId));
+
+ if (next_svId == 0){
+ temp_vIds[1] = ops_vIds[1];
+ temp_vIds[2] = ops_vIds[2];
+ }
+ else {
+ temp_vIds[1] = ops_vIds[0];
+ temp_vIds[2] = ops_vIds[1];
+ }
+
+ assert(add_cell(temp_vIds));
+ if (cId != -1){
+ temp_vIds.clear();
+ temp_vIds.push_back(new_vId);
+ temp_vIds.push_back(vIds[0]);
+ temp_vIds.push_back(vIds[1]);
+ assert(update_cell(temp_vIds, cId));
+
+ temp_vIds[1] = vIds[1];
+ temp_vIds[2] = vIds[2];
+ assert(add_cell(temp_vIds));
+ }
+ }
+
+
+
+ // ****** delete an entity *****
+
+ // Delete vertices that marked to be deleted.
+ bool Mesh::delete_vertices(){
+ for (int i=vertices_.size()-1; i>=0; i--){
+ if (vertices_[i].del() == true){
+
+ // the vertex to be deleted is not the last one
+ if (vertices_.size()-1 != i){
+ int vnId = vertices_.size()-1;
+ int hId = vih_first(vnId);
+
+ do{
+ int old_hId = hId;
+ hId = vih_next(vnId, hId);
+ halfedge(old_hId).setTvId(i);
+ if (hId == -1){
+ break;
+ }
+ }while (hId != vih_first(vnId));
+
+ vertices_[i].vcopy(vertices_[vnId]);
+ vertices_[i].setVId(i);
+
+ }
+ vertices_.pop_back();
+ }
+ }
+ return true;
+ }
+
+
+
+// Delete edges that marked to be deleted from the list.
+ bool Mesh::delete_edges(){
+ vector<int> vIds(2);
+ int j;
+ for (int i=edges_.size()-1; i>=0; i--){
+ if (edges_[i].del() == true){
+ //assert(IcId_from_hId(hId_from_eId(i,0)) == -1);
+ //assert(IcId_from_hId(hId_from_eId(i,1)) == -1);
+ if (i!=edges_.size()-1){
+
+
+ int enId = edges_.size()-1;
+ // relink last edge in the edge list
+ // this edge will be moved to to position i
+ vIds = vIds_from_eId(enId);
+ for (j=0; j<2; j++){
+ int hnj = hId_from_eId(enId,j);
+ int hij = hId_from_eId(i,j);
+ // resolve OhIds of endpoints
+ if (OhId_from_vId(vIds[j]) == hnj){
+ vertex(vIds[j]).setOhId(hij);
+ }
+
+
+ // resolve PhIds and NhIds
+ if (!is_b_h(hnj)){
+ halfedge(prev_hId(hnj)).setNhId(hij);
+ halfedge(next_hId(hnj)).setPhId(hij);
+ }
+
+ // resolve LhId of the incident cell
+ if (IcId_from_hId(hnj) != -1 &&
+ LhId_from_cId(IcId_from_hId(hnj))==hnj){
+ cell(IcId_from_hId(hnj)).setLhId(hij);
+ }
+ }// for j
+ // copy last edge
+ edges_[i].ecopy(edges_[enId]);
+ edges_[i].setEId(i);
+ edges_[i].pair()[0].setHId(i<<1);
+ edges_[i].pair()[1].setHId((i<<1)+1);
+ }// if i
+ // delete last edge
+ edges_.pop_back();
+
+
+ }
+ } // for i
+ return true;
+ }
+
+
+ // Delete cells that marked to be deleted from the list.
+ bool Mesh::delete_cells(){
+
+ //vector<int> hIds(3);
+ for (int i=cells_.size()-1; i>=0; i--){
+ if (cells_[i].del() == true){
+ // the cell to be deleted is not the last one
+ if (i!=cells_.size()-1){
+
+ int cnId = cells_.size()-1;
+ // relink last cell in the cell list
+ // this cell will be moved to cId
+ vector<int> hIds;
+ hIds.push_back(LhId_from_cId(cnId));
+ hIds.push_back(next_hId(LhId_from_cId(cnId)));
+ hIds.push_back(prev_hId(LhId_from_cId(cnId)));
+
+ for(int j=0; j<3; j++){
+ halfedge(hIds[j]).setIcId(i);
+ }
+ // copy last cell
+ cells_[i].ccopy(cells_[cnId]);
+ cells_[i].setCId(i);
+
+ }
+ // delete last cell
+ cells_.pop_back();
+ }
+ }
+ return true;
+ }
+
+
+ // create a mesh using two input variables.
+ // One is the coordinates of points
+ // The other is the vertex list of cells
+ bool Mesh::create(vector<Point> points, vector<Ids> cells){
+ int i,j;
+ int nv = points.size();
+ int nc = cells.size();
+ int eId[3];
+
+ vector<int> vIds;
+
+ for (i=0; i<nv; i++){
+ // point duplication check
+ if (!add_vertex(points[i])){
+ cout << "Duplicate point is detected " <<
+ "during mesh creatation."<< endl;
+ return false;
+ }
+ }
+
+ for (i=0; i<nc; i++){
+ vIds.clear();
+
+ for (j=0; j<3; j++){
+ // validation check
+ if (!is_valid_vId(cells[i][j])){
+
+ cout << "Invalid id is detected " <<
+ "during mesh creatation."<< endl;
+ return false;
+ }
+
+ // find vertices
+ vIds.push_back(cells[i][j]);
+
+ // boundary check
+ if (!is_b_v(vIds[j])){
+ cout << "Complex vertex is detected " <<
+ "during mesh creatation."<< endl;
+ return false;
+ }
+ }
+ // cell duplication check
+ if (find_cell(vIds) != -1){
+ cout << "Duplicate cell is detected " <<
+ "during mesh creatation."<< endl;
+ return false;
+ }
+
+ // add edges if necessary
+ for (j=0; j<3; j++){
+ eId[j] = find_edge(vIds[j], vIds[(j+1)%3]);
+ if (eId[j] == -1){
+ add_edge(vIds[j], vIds[(j+1)%3]);
+ }
+
+ }
+
+ // add the cell
+ add_cell(vIds);
+ }
+
+ }
+
+
+ // display the internal information of a mesh on the screen
+ void Mesh::display_info(){
+ vector<int> ids;
+
+ cout << endl <<"vertices:" << endl;
+ for (int i=0; i< vertices_.size(); i++){
+ cout << "id=" << vertex(i).vId() << " x=" << vertex(i).x() << " y=" << vertex(i).y() <<
+ " OhId=" << vertex(i).OhId() << endl;
+ }
+
+ cout <<endl << "edges:" << endl;
+ for (int i=0; i<edges_.size(); i++){
+ cout << "id=" << edge(i).eId() << " svId=" << vIds_from_eId(i)[0] <<
+ " tvId=" << vIds_from_eId(i)[1] << endl;
+ cout << "hid=" << edge(i).pair()[0].hId() << " prev=" << edge(i).pair()[0].PhId() <<
+ " next=" << edge(i).pair()[0].NhId() << " IcId=" << edge(i).pair()[0].IcId() << endl;
+ cout << "hid=" << edge(i).pair()[1].hId() << " prev=" << edge(i).pair()[1].PhId() <<
+ " next=" << edge(i).pair()[1].NhId() << " IcId=" << edge(i).pair()[1].IcId() << endl;
+ }
+
+ cout <<endl << "cells:" << endl;
+ for (int i=0; i< cells_.size(); i++){
+ cout << "id=" << cell(i).cId() << " LhId=" << cell(i).LhId() <<
+ " vIds=" << vIds_from_cId(i)[0] << ","
+ << vIds_from_cId(i)[1] << ","
+ << vIds_from_cId(i)[2] <<
+ " mFlag=" << cell(i).mFlag() << endl;
+ }
+ }
+
+
+//}
+}
diff --git a/Examples/MeshGenToolbox/mgt/Mesh.h b/Examples/MeshGenToolbox/mgt/Mesh.h
new file mode 100644
index 0000000000000000000000000000000000000000..731f88f61a03b6f97afef004f4b2cfb37abfe026
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Mesh.h
@@ -0,0 +1,632 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/* This file includes classes for the mesh module. */
+/*****************************************************************************/
+
+#ifndef MESH
+#define MESH
+#endif
+
+#ifndef VERTEX
+#include "Vertex.h"
+#endif
+
+#ifndef EDGE
+#include "Edge.h"
+#endif
+
+#ifndef CELL
+#include "Cell.h"
+#endif
+
+namespace PMGT{
+//namespace Mesh{
+
+//using namespace Vertex;
+//using namespace Edge;
+//using namespace Cell;
+
+
+typedef vector<int> Ids;
+class Mesh{
+public:
+ //constructor/destructor
+ Mesh(){}
+
+ // ***** size *****
+ inline int n_of_v(){ return vertices_.size(); }
+ inline int n_of_e(){ return edges_.size();}
+ inline int n_of_c(){ return cells_.size(); }
+
+ // ***** Id validation check *****
+ inline bool is_valid_vId(int vId){
+ return (vId < vertices_.size()) && (vId >= 0);
+ }
+
+ inline bool is_valid_hId(int hId){
+ return (hId < (edges_.size()<<1)) && (hId >= 0);
+ }
+
+ inline bool is_valid_eId(int eId){
+ return eId < edges_.size() && eId >= 0;
+ }
+
+ inline bool is_valid_cId(int cId){
+ return cId < cells_.size() && cId >= 0;
+ }
+
+
+ // ***** get entity from id *****
+ inline Vertex& vertex(int vId){
+ assert(is_valid_vId(vId));
+ return vertices_[vId];
+ }
+
+ inline Halfedge& halfedge(int hId){
+ assert(is_valid_hId(hId));
+ return edges_[hId>>1].pair()[hId & 1];
+ }
+
+ inline Edge& edge(int eId){
+ assert(is_valid_eId(eId));
+ return edges_[eId];
+ }
+
+ inline Cell& cell(int cId){
+ assert(is_valid_cId(cId));
+ return cells_[cId];
+ }
+
+ // ***** boundary check *****
+ inline bool is_b_h(int hId){
+ assert(is_valid_hId(hId));
+ return halfedge(hId).IcId() == -1;
+ }
+
+ inline bool is_b_v(int vId){
+ assert(is_valid_vId(vId));
+ if(vertex(vId).OhId() == -1) { return true;}
+ return is_b_h(ops_hId(vertex(vId).OhId()));
+ }
+
+ inline bool is_b_e(int eId){
+ assert(is_valid_eId(eId));
+ return is_b_h(eId << 1) || is_b_h((eId << 1) + 1);
+ }
+ inline bool is_b_c(int cId){
+ assert(is_valid_cId(cId));
+ int hId = cell(cId).LhId();
+ return is_b_h(ops_hId(hId)) ||
+ is_b_h(ops_hId(next_hId(hId))) ||
+ is_b_h(ops_hId(prev_hId(hId)));
+ }
+
+ // ***** connectivity *****
+
+ // ----- eId <==> hId -----
+
+ inline int eId_from_hId(int hId){
+ assert(is_valid_hId(hId));
+ return (hId >> 1);
+ }
+ inline int hId_from_eId(int eId, int index){
+ assert(is_valid_eId(eId));
+ assert( index < 2 && index >= 0 );
+ return (eId << 1) + index;
+ }
+
+ // ----- halfedge-halfedge -----
+
+ inline int ops_hId(int hId){
+ assert(is_valid_hId(hId));
+ return ((hId & 1) ? hId - 1: hId + 1);
+ }
+ inline int next_hId(int hId){
+ assert(is_valid_hId(hId));
+ return halfedge(hId).NhId();
+ }
+ inline int prev_hId(int hId){
+ assert(is_valid_hId(hId));
+ return halfedge(hId).PhId();
+ }
+ // ccw rotated halfedge
+ inline int ccw_hId(int hId){
+ assert(is_valid_hId(hId));
+ if (is_b_h(hId)) return -1;
+ return ops_hId(prev_hId(hId));
+ }
+ // cw rotated halfedge
+ inline int cw_hId(int hId){
+ assert(is_valid_hId(hId));
+ if (is_b_h(ops_hId(hId))) return -1;
+ return next_hId(ops_hId(hId));
+ }
+
+ // ----- vertex -----
+
+ // first outgoing halfedge
+ inline int OhId_from_vId(int vId){
+ assert(is_valid_vId(vId));
+ return vertex(vId).OhId();
+ }
+
+ // ----- halfedge -----
+
+ // targate vertex
+ inline int tvId_from_hId(int hId){
+ assert(is_valid_hId(hId));
+ return halfedge(hId).TvId();
+ }
+
+ // start vertex
+ inline int svId_from_hId(int hId){
+ assert(is_valid_hId(hId));
+ return tvId_from_hId(ops_hId(hId));
+ }
+
+ // its cell
+ inline int IcId_from_hId(int hId){
+ assert(is_valid_hId(hId));
+ return halfedge(hId).IcId();
+ }
+
+ // ----- edge -----
+ // vertices
+ inline vector<int> vIds_from_eId(int eId){
+ assert(is_valid_eId(eId));
+ vector<int> vIds;
+ vIds.push_back(svId_from_hId(hId_from_eId(eId, 0)));
+ vIds.push_back(tvId_from_hId(hId_from_eId(eId, 0)));
+ return vIds;
+ }
+
+ // cells
+ inline vector<int> cIds_from_eId(int eId){
+ assert(is_valid_eId(eId));
+ vector<int> cIds;
+ cIds.push_back(IcId_from_hId(hId_from_eId(eId, 0)));
+ cIds.push_back(IcId_from_hId(hId_from_eId(eId, 1)));
+ return cIds;
+ }
+
+ // ----- cell -----
+
+ // its longest halfedge
+ inline int LhId_from_cId(int cId){
+ assert(is_valid_cId(cId));
+ return cell(cId).LhId();
+ }
+
+ // three vertices
+ inline vector<int> vIds_from_cId(int cId){
+ assert(is_valid_cId(cId));
+ vector<int> vIds;
+ vIds.push_back(tvId_from_hId(cell(cId).LhId()));
+ vIds.push_back(tvId_from_hId(next_hId(cell(cId).LhId())));
+ vIds.push_back(svId_from_hId(cell(cId).LhId()));
+ return vIds;
+ }
+
+ // ***** isolation test *****
+
+ // is the vertex is isolated
+ inline bool is_isolated_v(int vId){
+ assert(is_valid_vId(vId));
+ return !is_valid_hId(OhId_from_vId(vId));
+ }
+
+ // ***** circulators *****
+
+ // ----- vertex - vertex (ccw) one ring circulator -----
+
+ inline int vv_first(int vId){
+ assert(is_valid_vId(vId));
+ return tvId_from_hId(OhId_from_vId(vId));
+ }
+
+ // Returns -1 if there is no next
+ inline int vv_next(int svId, int tvId){
+ assert(is_valid_vId(svId));
+ assert(is_valid_vId(tvId));
+ int hId = voh_first(svId);
+ while (tvId_from_hId(hId) != tvId && hId != -1){
+ hId = voh_next(svId, hId);
+ }
+ if (hId != -1){
+ if (is_b_h(hId)) return -1;
+ return tvId_from_hId(next_hId(hId));
+ }
+ assert(false);
+ }
+
+ // ----- vertex - outgoing-halfedge (ccw) one ring circulator -----
+ inline int voh_first(int vId){
+ assert(is_valid_vId(vId));
+ return OhId_from_vId(vId);
+ }
+
+ // Returns -1 if there is no next
+ inline int voh_next(int vId, int hId){
+ assert(is_valid_vId(vId));
+ assert(is_valid_hId(hId));
+ assert(vId == svId_from_hId(hId));
+ return ccw_hId(hId);
+ }
+
+ // ----- vertex - incoming-halfedge (ccw) one ring circulator -----
+ inline int vih_first(int vId){
+ assert(is_valid_vId(vId));
+ if ( is_isolated_v(vId)) return -1;
+ return ops_hId(voh_first(vId));
+ }
+
+ // Returns -1 if there is no next
+ inline int vih_next(int vId, int hId){
+ assert(is_valid_vId(vId));
+ assert(is_valid_hId(hId));
+ assert(vId == tvId_from_hId(hId));
+ int ops = ops_hId(hId);
+ if (is_b_h(ops)) return -1;
+ //return prev_hId(ops);
+ return ops_hId(voh_next(vId, ops));
+ }
+
+ // ----- vertex - edge (ccw) one ring circulator -----
+ inline int ve_first(int vId){
+ assert(is_valid_vId(vId));
+ if (is_isolated_v(vId)) return -1;
+ return eId_from_hId(voh_first(vId));
+ }
+
+ // Return -1 if there is no next
+ inline int ve_next(int vId, int eId){
+ assert(is_valid_vId(vId));
+ assert(is_valid_eId(eId));
+ int hId = hId_from_eId(eId,0);
+ if (vId == svId_from_hId(hId)){ // hId is an outgoing halfedge
+ int voNext = voh_next(vId, hId);
+ if (voNext == -1) return -1;
+ return eId_from_hId(voNext);
+ }
+ //hId is an incoming halfedge
+ assert(vId == tvId_from_hId(hId));
+ int viNext = vih_next(vId, hId);
+ if (viNext == -1) return -1;
+ return eId_from_hId(viNext);
+ }
+
+ // ----- vertex - cell (cww) one ring circulator -----
+
+ inline int vc_first(int vId){
+ assert(is_valid_vId(vId));
+ if (is_isolated_v(vId)) return -1;
+ return IcId_from_hId(voh_first(vId));
+ }
+
+ // Returns -1 if there is no next
+ inline int vc_next(int vId, int cId){
+ assert(is_valid_vId(vId));
+ assert(is_valid_cId(cId));
+ // find the halfedge whose targate vertex is vId
+ int hId = LhId_from_cId(cId);
+ if (tvId_from_hId(hId) != vId){
+ if (tvId_from_hId(prev_hId(hId)) == vId)
+ hId = prev_hId(hId);
+ else if (tvId_from_hId(next_hId(hId)) == vId)
+ hId = next_hId(hId);
+ else assert(false);
+ }
+ if (is_b_h(ops_hId(hId))) return -1;
+ return IcId_from_hId(ops_hId(hId));
+ }
+
+ // ----- cell - vertex (cww) one ring circulator -----
+ // The first vertex is the tartage vertex of the longest halfedge
+ inline int cv_first(int cId){
+ assert(is_valid_cId(cId));
+ return tvId_from_hId(LhId_from_cId(cId));
+ }
+
+ inline int cv_next(int cId, int vId){
+ assert(is_valid_cId(cId));
+ assert(is_valid_vId(vId));
+ // find the halfedge whose start vertex is vId
+ int hId = LhId_from_cId(cId);
+ if (svId_from_hId(hId) != vId){
+ if (svId_from_hId(prev_hId(hId)) == vId)
+ hId = prev_hId(hId);
+ else if (svId_from_hId(next_hId(hId)) == vId)
+ hId = next_hId(hId);
+ else assert(false);
+ }
+ return tvId_from_hId(hId);
+ }
+
+ // ----- cell - halfedge (cww) one ring circulator -----
+ // The first halfedge is the longest halfedge
+ inline int ch_first(int cId){
+ assert(is_valid_cId(cId));
+ return LhId_from_cId(cId);
+ }
+ inline int ch_next(int cId, int hId){
+ assert(is_valid_cId(cId));
+ assert(is_valid_hId(hId));
+ assert(IcId_from_hId(hId) == cId);
+ return next_hId(hId);
+ }
+
+ // ----- cell - edge (cww) one ring circulator -----
+ // The first edge is the longest edge
+ inline int ce_first(int cId){
+ assert(is_valid_cId(cId));
+ return eId_from_hId(ch_first(cId));
+ }
+ // next should change
+ inline int ce_next(int cId, int eId){
+ assert(is_valid_cId(cId));
+ assert(is_valid_eId(eId));
+ int hId = hId_from_eId(eId, 0);
+ if (IcId_from_hId(hId) == cId)
+ return eId_from_hId(ch_next(cId,hId));
+ else if (IcId_from_hId(ops_hId(hId)) == cId)
+ return eId_from_hId(ch_next(cId, ops_hId(hId)));
+ else assert(false);
+ }
+
+ // ----- cell - cell (cww) one ring circulator -----
+
+ // The first cell is the cell adjacent the longest edge
+ // if the given cell is not a boundary cell.
+ // If one edge is boundary edge, returns the cell adjacent to the next edge (ccw).
+ // If two edges are boundary edges, refturns the only adjacent cell.
+ // Returns -1 if there is no adjacent cell.
+ inline int cc_first(int cId){
+ assert(is_valid_cId(cId));
+ int hId = LhId_from_cId(cId);
+ if (!is_b_c(cId)) return IcId_from_hId(ops_hId(hId));
+
+ if (!is_b_h(ops_hId(hId))){
+ if ( is_b_h(ops_hId(next_hId(hId))) && !is_b_h(ops_hId(prev_hId(hId))) )
+ return IcId_from_hId(ops_hId(prev_hId(hId)));
+ else return IcId_from_hId(ops_hId(hId));
+ }
+ else {
+ if ( !is_b_h(ops_hId(next_hId(hId))) )
+ return IcId_from_hId(ops_hId(next_hId(hId)));
+ else return IcId_from_hId(ops_hId(prev_hId(hId)));
+ }
+ }
+
+ // Returns -1 if there is no next
+ inline int cc_next(int scId, int tcId){
+ assert(is_valid_cId(tcId));
+ assert(is_valid_cId(scId));
+ int hId = LhId_from_cId(scId);
+
+ if (IcId_from_hId(ops_hId(hId)) != tcId){
+ if (IcId_from_hId(ops_hId(next_hId(hId))) == tcId)
+ hId = next_hId(hId);
+ else if (IcId_from_hId(ops_hId(prev_hId(hId))) == tcId)
+ hId = prev_hId(hId);
+ else assert(false);
+ }
+ return IcId_from_hId(ops_hId(next_hId(hId)));
+ }
+
+
+
+ // ***** find an entity *****
+
+ // Returns the id of the vertex that has given coordinate.
+ // Returns -1 if the vertex does not exist.
+ int find_vertex(Point point);
+
+ // Returns the id of the edge that has given points.
+ // Returns -1 if the edge does not exist.
+ int find_edge(int svId, int tvId);
+
+ // Returns the id of the halfedge that has given start and targate points.
+ // Returns -1 if the halfedge does not exist.
+ int find_halfedge(int svId, int tvId);
+
+ // Returns the id of the cell that has given vertices.
+ // Returns -1 if the cell does not exist.
+ int find_cell(vector<int> vIds);
+
+
+ // ***** Geometric properties *****
+
+ // Returns the distance of two vertex
+ inline double dist(int svId, int tvId){
+ assert(is_valid_vId(svId) && is_valid_vId(tvId));
+ Point ps = vertex(svId).point(),
+ pt = vertex(tvId).point();
+ return sqrt((ps[0]-pt[0])*(ps[0]-pt[0]) +
+ (ps[1]-pt[1])*(ps[1]-pt[1]));
+ }
+
+ inline double dist(int hId){
+ assert(is_valid_hId(hId));
+ return dist(svId_from_hId(hId), tvId_from_hId(hId));
+ }
+
+ // ----- mid point of a halfedge
+ inline Point mid_point(int hId){
+ assert(is_valid_hId(hId));
+ double sx = vertex(svId_from_hId(hId)).x();
+ double sy = vertex(svId_from_hId(hId)).y();
+ double tx = vertex(tvId_from_hId(hId)).x();
+ double ty = vertex(tvId_from_hId(hId)).y();
+ Point mid;
+ mid.push_back((sx+tx)/2);
+ mid.push_back((sy+ty)/2);
+ return mid;
+ }
+
+ // ----- mid point of two points
+ inline Point mid_point(int svId, int tvId){
+ double sx = vertex(svId).x();
+ double sy = vertex(svId).y();
+ double tx = vertex(tvId).x();
+ double ty = vertex(tvId).y();
+ Point mid;
+ mid.push_back((sx+tx)/2);
+ mid.push_back((sy+ty)/2);
+ return mid;
+ }
+
+ // ----- mid point of the longest halfedge of a cell
+ inline Point longest_mid(int cId){
+ assert(is_valid_cId(cId));
+ return mid_point(LhId_from_cId(cId));
+ }
+
+ // ----- centroid point of a cell -----
+ inline Point centroid(int cId){
+ assert(is_valid_cId(cId));
+ Point point = longest_mid(cId);
+ // find the opposite point to the longest halfedge
+ Vertex& v = vertex(tvId_from_hId(next_hId(LhId_from_cId(cId))));
+ point[0] = point[0]*2/3 + v.x()/3;
+ point[1] = point[1]*2/3 + v.y()/3;
+
+ return point;
+ }
+
+
+ // ----- size of a cell ----- //
+ // The size of a cell if the length of longest halfedge of the cell
+ inline double size(int cId){
+ assert(is_valid_cId(cId));
+ return dist(LhId_from_cId(cId));
+ }
+
+ // ----- Test for counter clockwise ----- //
+ inline bool is_ccw(Point pa, Point pb, Point pc){
+ double detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
+ double detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
+ return detleft - detright > DBL_EPSILON*100;
+ }
+
+ inline bool is_ccw(vector<int> vIds){
+ assert(vIds.size() == 3);
+ assert(is_valid_vId(vIds[0]));
+ assert(is_valid_vId(vIds[1]));
+ assert(is_valid_vId(vIds[2]));
+ return is_ccw(vertex(vIds[0]).point(),
+ vertex(vIds[1]).point(),
+ vertex(vIds[2]).point());
+ }
+
+/* // ----- Test for collinear ------ //
+ inline bool is_collinear(Point pa, Point pb, Point pc){
+ double detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
+ double detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
+ return detleft - detright == 0;
+ }
+*/
+ // ----- Test for the same side ----- //
+
+ inline bool is_same_side(int hId, Point pa, Point pb){
+ Point ps = vertex(svId_from_hId(hId)).point();
+ Point pt = vertex(tvId_from_hId(hId)).point();
+ double deta = (pa[1]-ps[1])*(pt[0]-ps[0]) -
+ (pa[0]-ps[0])*(pt[1]-ps[1]);
+ double detb = (pb[1]-ps[1])*(pt[0]-ps[0]) -
+ (pb[0]-ps[0])*(pt[1]-ps[1]);
+ return deta*detb > 0;
+ }
+
+/* inline bool is_in_halfedge(int hId, Point p){
+ Point ps = vertex(svId_from_hId(hId)).point();
+ Point pt = vertex(tvId_from_hId(hId)).point();
+ return is_collinear(ps, pt, p);
+ }
+*/
+ /** \ Add an entity
+ */
+
+ // Create a vertex and add it to the end of the vertex list.
+ // Returns false if the vertex already exists.
+ bool add_vertex(Point point);
+
+
+ // Create an edge and add it to the end of the edge list.
+ // Returns false if the edge already exists.
+ bool add_edge(int svId, int tvId);
+
+
+ // Create a cell and add it to the end of the cell list.
+ // Returns false if the cell already exists.
+ bool add_cell(vector<int> vIds);
+
+ /** \ Update an entity
+ */
+
+ // update a cell using three vertices.
+ // Returns false if the new cell already exists.
+ bool update_cell(vector<int> vIds, int cId);
+
+
+ // split 2 cells by split their common longest edge
+
+ bool longest_ref2(int hId, int o_hId, int next_hId);
+
+ // ****** delete an entity *****
+
+ // Delete vertices that marked to be deleted from the list.
+ bool delete_vertices();
+
+ // Delete edges that marked to be deleted from the list.
+ bool delete_edges();
+
+ // Delete cells that marked to be deleted from the list.
+ bool delete_cells();
+
+ // ***** create a mesh ******
+ // create a mesh using two input variables.
+ // One is the coordinates of points
+ // The other is the vertex list of cells
+ bool create(vector<Point>, vector<Ids>);
+
+ // ***** write a mesh *****
+ // write the mesh to two variables
+ // One is the coordinates of points
+ // The other is the vertex list of cells
+ void write_var(vector<Point>&, vector<Ids>&);
+
+
+
+ // display the internal information of a mesh on the screen
+ void display_info();
+
+
+private:
+ vector<Vertex> vertices_;
+ vector<Edge> edges_;
+ vector<Cell> cells_;
+
+
+};
+
+
+//}
+
+}
diff --git a/Examples/MeshGenToolbox/mgt/Output.cpp b/Examples/MeshGenToolbox/mgt/Output.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..7252dd5080cc74731eb50f9a8fee0e03581424bf
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Output.cpp
@@ -0,0 +1,60 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/*****************************************************************************/
+
+#include "Output.h"
+
+namespace PMGT{
+ // write the mesh to two files
+ // One is the coordinates of points
+ // The other is the vertex list of cells
+ bool Output::write_file(Mesh& mesh, char* vertexFile, char* cellFile){
+ FILE *v;
+ FILE *c;
+ int i;
+ vector<int> vIds(3);
+
+ /* Open files. If NULL is returned there was an error */
+ if((v = fopen(vertexFile, "w")) == NULL) {
+ printf("Error Opening Vertex File.\n");
+ exit(1);
+ }
+ if((c = fopen(cellFile, "w")) == NULL) {
+ printf("Error Opening Cell File.\n");
+ exit(1);
+ }
+
+ // write vertex file
+ for (i=0; i<mesh.n_of_v(); i++){
+ fprintf(v, "%.6g %.6g\n",
+ mesh.vertex(i).x(), mesh.vertex(i).y());
+ }
+ // write cell file
+ for (i=0; i<mesh.n_of_c(); i++){
+ vIds[0] = mesh.tvId_from_hId(mesh.LhId_from_cId(i));
+ vIds[1] = mesh.tvId_from_hId(mesh.next_hId(mesh.LhId_from_cId(i)));
+ vIds[2] = mesh.tvId_from_hId(mesh.prev_hId(mesh.LhId_from_cId(i)));
+ fprintf(c, "%d %d %d\n", vIds[0], vIds[1], vIds[2]);
+ }
+ fclose(v);
+ fclose(c);
+ }
+
+}
diff --git a/Examples/MeshGenToolbox/mgt/Output.h b/Examples/MeshGenToolbox/mgt/Output.h
new file mode 100644
index 0000000000000000000000000000000000000000..f7026348d36a8089e38e0b770706b2b1e6dbfb89
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Output.h
@@ -0,0 +1,41 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/* This file includes classes for the output module. */
+/*****************************************************************************/
+
+#ifndef OUTPUT
+#define OUTPUT
+#endif
+
+#ifndef MESH
+#include "Mesh.h"
+#endif
+
+namespace PMGT{
+class Output{
+public:
+ // write the mesh to two files
+ // One is the coordinates of points
+ // The other is the vertex list of cells
+ bool write_file(Mesh& mesh, char* vertexFile, char* cellFile);
+};
+}
+
+
diff --git a/Examples/MeshGenToolbox/mgt/Refining.cpp b/Examples/MeshGenToolbox/mgt/Refining.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..def4fac68379ccfb03cb760785902461ef3845fd
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Refining.cpp
@@ -0,0 +1,120 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/*****************************************************************************/
+#ifndef REFINING
+#include "Refining.h"
+#endif
+
+namespace PMGT{
+ // split cells at their centroid points
+ void Refining::split(Mesh& mesh){
+ vector<int> vIds;
+ vector<int> newIds;
+ int i,j, newvId;
+ Point p;
+
+ for (i=0; i<mesh.n_of_c(); i++){
+ if (mesh.cell(i).mFlag() == REFINE){
+ // get three vertices
+ vIds.clear();
+ vIds.push_back(mesh.cv_first(i));
+ vIds.push_back(mesh.cv_next(i, vIds[0]));
+ vIds.push_back(mesh.cv_next(i, vIds[1]));
+ // add the centroid point
+ Point np = mesh.centroid(i);
+ mesh.add_vertex(np);
+ newvId = mesh.find_vertex(np);
+ assert(newvId !=-1);
+ // add three new edges
+ for (j=0; j<3; j++){
+ mesh.add_edge(newvId, vIds[j]);
+ }
+ // add/update three cells
+ for (j=0; j<3; j++){
+ newIds.clear();
+ newIds.push_back(newvId);
+ newIds.push_back(vIds[j]);
+ newIds.push_back(vIds[(j+1)%3]);
+ if (j==0){
+ mesh.update_cell(newIds, i);
+ }
+ else
+ mesh.add_cell(newIds);
+ }
+ }// if
+ }
+
+ }
+
+
+
+ void Refining::longest_edge(Mesh& mesh){
+
+ for(int i=0; i<mesh.n_of_c(); i++){
+ if (mesh.cell(i).mFlag() == REFINE){
+ int LhId = mesh.cell(i).LhId();
+ int ops_LhId = mesh.ops_hId(LhId);
+ int next_cell = mesh.IcId_from_hId(ops_LhId);
+
+ vector<int> lepp;
+ lepp.clear();
+
+ while(1){
+ lepp.push_back(LhId);
+ lepp.push_back(ops_LhId);
+ if (next_cell == -1){
+ break;
+ }
+ if (mesh.LhId_from_cId(next_cell) == ops_LhId){
+ break;
+ }
+
+ LhId = mesh.cell(next_cell).LhId();;
+ ops_LhId = mesh.ops_hId(LhId);
+ next_cell = mesh.IcId_from_hId(ops_LhId);
+ } // while(1)
+
+ assert(lepp.size()%2 == 0);
+
+ // refine LEPP
+ while (lepp.size() > 0){
+ int hId = lepp[lepp.size()-1];
+ lepp.pop_back();
+ assert(lepp.size() > 0);
+ int ops_hId = lepp[lepp.size()-1];
+ lepp.pop_back();
+
+ assert(ops_hId == mesh.ops_hId(hId));
+ int next_hId = -1;
+ if (lepp.size() > 0){
+ next_hId = lepp[lepp.size()-1];
+ }
+
+ mesh.longest_ref2(hId, ops_hId, next_hId);
+ }// while
+
+ } // if REFINE
+ }// for i
+
+ }
+
+
+
+}
diff --git a/Examples/MeshGenToolbox/mgt/Refining.h b/Examples/MeshGenToolbox/mgt/Refining.h
new file mode 100644
index 0000000000000000000000000000000000000000..33b7e200129187fd04a0d19b77f092048ff037a0
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Refining.h
@@ -0,0 +1,44 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/* This file contains the class for refine module. */
+/* There are two algorithms: */
+/* split -- the point insertion algorithm for refining */
+/* longest_edge -- the longest side bisection algorithm for refining */
+/*****************************************************************************/
+
+#ifndef REFINING
+#define REFINING
+#endif
+
+#ifndef MESH
+#include "Mesh.h"
+#endif
+
+namespace PMGT{
+class Refining{
+public:
+ // split cells at their centroid points
+ void split(Mesh& mesh);
+
+ // refine cells at their longest edges
+ void longest_edge(Mesh& mesh);
+
+};
+}
diff --git a/Examples/MeshGenToolbox/mgt/Service.cpp b/Examples/MeshGenToolbox/mgt/Service.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..dbfe6051f9bddf7142a84f3edb93e344bc9ff357
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Service.cpp
@@ -0,0 +1,272 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This program used for correctness test of PMGT. */
+/*****************************************************************************/
+
+#include "Service.h"
+
+namespace PMGT{
+
+// auxiliary functions
+vector<int> Service::boundary_list(Mesh& mesh){
+ vector<int> list;
+ vector<int> b_edges;
+ vector<int>::iterator tempIterator;
+
+ for(int i=0; i<mesh.n_of_e(); i++){
+ if (mesh.is_b_e(i)){
+ b_edges.push_back(i);
+ }
+ }
+ vector<int> vIds;
+ vIds = mesh.vIds_from_eId(b_edges[0]);
+ list.push_back(vIds[0]);
+ //list.push_back(vIds[1]);
+ int first_vId = vIds[0];
+ int current = vIds[1];
+ b_edges[0] = b_edges[b_edges.size()-1];
+ b_edges.pop_back();
+ bool error = false, found;
+
+ int next_vertex, i;
+ while(b_edges.size()!=0){
+ found = false;
+ for( i=0; i<b_edges.size(); i++){
+ vIds = mesh.vIds_from_eId(b_edges[i]);
+ for(int j=0; j<2; j++){
+ if(vIds[j] == current){ // find next boundary edge
+ list.push_back(vIds[j]);
+ b_edges[i] = b_edges[b_edges.size()-1];
+ b_edges.pop_back();
+ current = vIds[(j+1)%2];
+ found = true;
+ break;
+ }
+ }
+ if(found) break;
+ }
+ if (!found){ // the boundary is not close
+ error = true;
+ break;
+ }
+ else if(first_vId==current){// find a close boundary
+ if(b_edges.size()!=0){ // there are boundary edges left
+ error = true;
+ }
+ break; //find an unique close boundary
+ }
+ }
+
+ if (error){
+ list.clear();
+ }
+ return list;
+}
+
+
+bool Service::in_boundary(Mesh& mesh1, int vId1, Mesh& mesh2, vector<int> b_list2){
+ double x = mesh1.vertex(vId1).x();
+ double y = mesh1.vertex(vId1).x();
+ for (int i=0; i<b_list2.size()-2; i++){
+ double xa = mesh2.vertex(b_list2[i]).x();
+ double ya = mesh2.vertex(b_list2[i]).y();
+ double xb = mesh2.vertex(b_list2[i+1]).x();
+ double yb = mesh2.vertex(b_list2[i+1]).y();
+ double xc = mesh2.vertex(b_list2[i+2]).x();
+ double yc = mesh2.vertex(b_list2[i+2]).y();
+
+ double detAB = (y-ya)*(xb-xa) - (x-xa)*(yb-ya);
+ double detBC = (y-yb)*(xc-xb) - (x-xb)*(yc-yb);
+
+ if (detAB*detBC < 0) return false;
+ }
+ return true;
+}
+
+
+double Service::area(Mesh& mesh, int vId1, int vId2, int vId3){
+ double x1 = mesh.vertex(vId1).x();
+ double y1 = mesh.vertex(vId1).y();
+ double x2 = mesh.vertex(vId2).x();
+ double y2 = mesh.vertex(vId2).y();
+ double x3 = mesh.vertex(vId3).x();
+ double y3 = mesh.vertex(vId3).y();
+
+ return abs((x1*y2-x2*y1+x1*y3-x3*y1+x2*y3-x3*y2)/2.0);
+}
+
+
+bool Service::inside(Mesh& mesh, int vId, int cId){
+ double x = mesh.vertex(vId).x();
+ double y = mesh.vertex(vId).y();
+
+ vector<int> vIds = mesh.vIds_from_cId(cId);
+ double x1 = mesh.vertex(vIds[0]).x();
+ double y1 = mesh.vertex(vIds[0]).y();
+ double x2 = mesh.vertex(vIds[1]).x();
+ double y2 = mesh.vertex(vIds[1]).y();
+ double x3 = mesh.vertex(vIds[2]).x();
+ double y3 = mesh.vertex(vIds[2]).y();
+
+ double det12 = (y-y1)*(x2-x1) - (x-x1)*(y2-y1);
+ double det23 = (y-y2)*(x3-x2) - (x-x2)*(y3-y2);
+ double det31 = (y-y3)*(x1-x3) - (x-x3)*(y1-y3);
+ //(x,y) in the same side of 12, 23, 31
+ return (det12*det23>0)&&(det23*det31>0);
+
+}
+
+// http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d
+bool Service::across(Mesh& mesh, int eId1, int eId2){
+
+ vector<int> vIds1 = mesh.vIds_from_eId(eId1);
+ double x1,y1,x2,y2,x3,y3,x4,y4;
+ x1 = mesh.vertex(vIds1[0]).x();
+ y1 = mesh.vertex(vIds1[0]).y();
+ x2 = mesh.vertex(vIds1[1]).x();
+ y2 = mesh.vertex(vIds1[1]).y();
+
+ vector<int> vIds2 = mesh.vIds_from_eId(eId2);
+ x3 = mesh.vertex(vIds2[0]).x();
+ y3 = mesh.vertex(vIds2[0]).y();
+ x4 = mesh.vertex(vIds2[1]).x();
+ y4 = mesh.vertex(vIds2[1]).y();
+
+ double det312 = (y3-y1)*(x2-x1) - (x3-x1)*(y2-y1);
+ double det412 = (y4-y1)*(x2-x1) - (x4-x1)*(y2-y1);
+
+ double det134 = (y1-y3)*(x4-x3) - (x1-x3)*(y4-y3);
+ double det234 = (y2-y3)*(x4-x3) - (x2-x3)*(y4-y3);
+
+
+ // 3 and 4 in the different side of 12 and
+ // 1 and 2 in the different side of 34
+ return (det312*det412<0 && det134*det234<0);
+}
+
+
+// functions test correctness
+bool Service::length_gt0(Mesh& mesh){
+ for (int i=0; i<mesh.n_of_e(); i++){
+ if (mesh.dist(mesh.hId_from_eId(i,0)) < 0){
+ cout << "length_gt0 is false." << endl;
+ return false;
+ }
+ }
+ return true;
+}
+
+bool Service::areas_gt0(Mesh& mesh){
+ for (int i=0; i<mesh.n_of_c(); i++){
+ vector<int> vIds = mesh.vIds_from_cId(i);
+ if (area(mesh, vIds[0], vIds[1], vIds[2]) <= 0){
+ cout << "areas_gt0 is false." << endl;
+ return false;
+ }
+ }
+ return true;
+}
+
+bool Service::bounded(Mesh& mesh){
+ return (boundary_list(mesh).size()!=0);
+}
+
+
+bool Service::no_interior_intersection(Mesh& mesh){
+ for (int i=0; i<mesh.n_of_v(); i++){
+ for (int j=0; j<mesh.n_of_c(); j++){
+ if (inside(mesh, i, j)){
+ cout << "no_interior_intersection is false." << endl;
+ return false;
+ }
+ }
+ }
+
+ for (int i=0; i<mesh.n_of_e(); i++){
+ for (int j=0; j<mesh.n_of_e(); j++){
+ if (across(mesh, i, j)){
+ cout << "no_interior_intersection is false." << endl;
+ return false;
+ }
+ }
+ }
+ return true;
+}
+
+
+bool Service::conformal(Mesh& mesh){
+ for (int i=0; i<mesh.n_of_v(); i++){
+ for (int j=0; j<mesh.n_of_e(); j++){
+ vector<int> vIds = mesh.vIds_from_eId(j);
+ double x = mesh.vertex(i).x();
+ double y = mesh.vertex(i).y();
+ double x1 = mesh.vertex(vIds[0]).x();
+ double y1 = mesh.vertex(vIds[0]).y();
+ double x2 = mesh.vertex(vIds[1]).x();
+ double y2 = mesh.vertex(vIds[1]).y();
+ if((x<x1&&y<y1 && x>x2&&y>y2) || (x>x1&&y>y1 && x<x2&&y<y2)){
+ if (area(mesh,i,vIds[0],vIds[1])<10E-10){
+ cout << "conformal is false." << endl;
+ return false;
+ }
+ }
+ }
+ }
+ return true;
+
+}
+
+
+bool Service::counterclockwise(Mesh& mesh){
+ for (int i=0; i<mesh.n_of_c(); i++){
+ vector<int> vIds = mesh.vIds_from_cId(i);
+ Vertex v1 = mesh.vertex(vIds[0]);
+ Vertex v2 = mesh.vertex(vIds[1]);
+ Vertex v3 = mesh.vertex(vIds[2]);
+ double detleft = (v1.x()-v3.x())*(v2.y()-v3.y());
+ double detright = (v1.y()-v3.y())*(v2.x()-v3.x());
+ //return detleft - detright > DBL_EPSILON*100;
+ if ( detleft < detright + DBL_EPSILON*100){
+ cout << "counterclockwise is false."<< endl;
+ return false;
+ }
+ }
+ return true;
+}
+
+bool Service::covering_up(Mesh& mesh1, Mesh& mesh2){
+ vector<int> b_list = boundary_list(mesh1);
+ for (int i=0; i<mesh2.n_of_v(); i++){
+ if (!in_boundary(mesh2, i, mesh1, b_list)){
+ return false;
+ }
+ }
+ b_list = boundary_list(mesh2);
+ for (int i=0; i<mesh1.n_of_v(); i++){
+ if (!in_boundary(mesh1, i, mesh2, b_list)){
+ return false;
+ }
+ }
+
+ return true;
+}
+
+
+}
+
diff --git a/Examples/MeshGenToolbox/mgt/Service.h b/Examples/MeshGenToolbox/mgt/Service.h
new file mode 100644
index 0000000000000000000000000000000000000000..c8be60c373399a45fdc0fbba6d14294ce5631a19
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Service.h
@@ -0,0 +1,81 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This program is used for correctness test of PMGT. */
+/* This file includes classes for the service module. */
+/*****************************************************************************/
+
+#ifndef SERVICE
+#define SERVICE
+#endif
+
+#ifndef VERTEX
+#include "Vertex.h"
+#endif
+
+#ifndef EDGE
+#include "Edge.h"
+#endif
+
+#ifndef CELL
+#include "Cell.h"
+#endif
+
+#ifndef MESH
+#include "Mesh.h"
+#endif
+
+namespace PMGT{
+class Service{
+public:
+
+ // auxiliary functions
+ vector<int> boundary_list(Mesh& mesh);
+ bool in_boundary(Mesh& mesh1, int vId1, Mesh& mesh2, vector<int> b_list2);
+ double area(Mesh& mesh, int vId1, int vId2, int vId3);
+ bool inside(Mesh& mesh, int vId, int cId);
+ bool across(Mesh& mesh, int eId1, int eId2);
+
+
+ // functions test correctness
+ inline bool euler(Mesh& mesh){
+ return (mesh.n_of_v() +
+ mesh.n_of_c() -
+ mesh.n_of_e() == 1);
+ }
+ bool length_gt0(Mesh& mesh);
+ bool areas_gt0(Mesh& mesh);
+ bool no_interior_intersection(Mesh& mesh);
+ bool conformal(Mesh& mesh);
+ bool bounded(Mesh& mesh);
+ bool counterclockwise(Mesh& mesh);
+
+ // functions in the service module
+ inline bool is_valid_mesh(Mesh& mesh){
+ return areas_gt0(mesh) && bounded(mesh) &&
+ conformal(mesh) && no_interior_intersection(mesh) &&
+ length_gt0(mesh) && counterclockwise(mesh) &&
+ euler(mesh);
+
+ }
+ bool covering_up(Mesh& mesh1, Mesh& mesh2);
+
+
+};
+}
+
diff --git a/Examples/MeshGenToolbox/mgt/Vertex.h b/Examples/MeshGenToolbox/mgt/Vertex.h
new file mode 100644
index 0000000000000000000000000000000000000000..4522b0537e39d5b7aa65dab8750a89b1730588c7
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/Vertex.h
@@ -0,0 +1,114 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the serial version of PMGT */
+/* This file includes classes for the vertex module. */
+/*****************************************************************************/
+
+#ifndef VERTEX
+#define VERTEX
+#endif
+
+#include <vector>
+#include <cfloat>
+#include <cmath>
+#include <iostream>
+#include <cstdlib>
+using namespace std;
+
+namespace PMGT{
+//namespace Vertex{
+// type definition
+
+// Point defines a coordinate of a point.
+// The first is x coordinate,
+// and the second is y coordinate.
+typedef vector<double> Point;
+
+// MFLAG is a flag that indicates what should be done to a cell.
+enum MFLAG {COARSEN = -1, UNCHANGE = 0, REFINE = 1};
+
+class Vertex{
+public:
+
+ //constractor
+ Vertex(Point point, int vId=-1, int OhId=-1, bool del=false){
+ point_ = point;
+ vId_= vId;
+ OhId_= OhId;
+ del_= del;
+ }
+
+ Vertex(double x=0, double y=0, int vId=-1, int OhId=-1, int del=false){
+ point_.push_back(x);
+ point_.push_back(y);
+ vId_ = vId;
+ OhId_ = OhId;
+ del_ = del;
+ }
+
+ inline double x(){ return point_[0]; }
+ inline double y(){ return point_[1]; }
+ inline Point& point(){ return point_;}
+ inline int vId(){ return vId_;}
+ inline int OhId(){ return OhId_; }
+ inline bool del(){ return del_; }
+
+
+ inline void setPoint(double x, double y){
+ point_[0] = x;
+ point_[1] = y;
+ }
+ inline void setPoint(Point point){
+ point_ = point;
+ }
+ inline void setVId(int vId){ vId_ = vId; }
+ inline void setOhId(int OhId){ OhId_ = OhId; }
+ inline void setDel(bool del) { del_ = del; }
+
+ inline bool is_isolated_v(){ return OhId_ == -1; }
+ inline void set_isolated_v(){ OhId_ = -1; }
+
+ inline bool same(double x, double y){
+ return (x==point_[0] && y==point_[1]);
+ }
+ inline bool same(Point point){
+ return point_ == point;
+ }
+ inline void vcopy(Vertex& other){
+ point_[0] = other.point_[0];
+ point_[1] = other.point_[1];
+ vId_ = other.vId_;
+ OhId_ = other.OhId_;
+ del_ = other.del_;
+ }
+
+ inline double distance(Point& p){
+ return sqrt((p[0]-point_[0])*(p[0]-point_[0])+(p[1]-point_[1])*(p[1]-point_[1]));
+ }
+
+private:
+ Point point_; // coordinate
+ int vId_; // id
+ int OhId_; // the first (ccw) outgoing halfedge.
+ bool del_; // a flag to indicate if the vertex
+ // is marked to be deleted
+}; // end of class Vertex
+
+//} // end of namespace Vertex
+} // end of namespace PMGT
diff --git a/Examples/MeshGenToolbox/mgt/makefile b/Examples/MeshGenToolbox/mgt/makefile
new file mode 100644
index 0000000000000000000000000000000000000000..fd6bc6e5d686bc5c32c91121d05292d65b455888
--- /dev/null
+++ b/Examples/MeshGenToolbox/mgt/makefile
@@ -0,0 +1,16 @@
+OBJECTS = Service.o Coarsening.o Refining.o Output.o Input.o Mesh.o
+
+SOURCES = Service.cpp Coarsening.cpp Refining.cpp Output.cpp Input.cpp Mesh.cpp
+
+HEADERS = Service.h Coarsening.h Refining.h Input.h Input.h Mesh.h Cell.h Edge.h Vertex.h
+
+# all testing excutable
+all: $(OBJECTS)
+
+# all object files of PMGT
+$(OBJECTS): $(SOURCES) $(HEADERS)
+ g++ -c $(SOURCES)
+
+# remove generated files
+clean:
+ rm -f *.o
\ No newline at end of file
diff --git a/Examples/MeshGenToolbox/testdriver/5_test_sr_arc b/Examples/MeshGenToolbox/testdriver/5_test_sr_arc
new file mode 100644
index 0000000000000000000000000000000000000000..8cb1965e0a75256929f762bf483eacc3ad3dcbb8
Binary files /dev/null and b/Examples/MeshGenToolbox/testdriver/5_test_sr_arc differ
diff --git a/Examples/MeshGenToolbox/testdriver/5_test_sr_arc.cpp b/Examples/MeshGenToolbox/testdriver/5_test_sr_arc.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..ce16c3db03233323bf20192eef805c0dc020e732
--- /dev/null
+++ b/Examples/MeshGenToolbox/testdriver/5_test_sr_arc.cpp
@@ -0,0 +1,120 @@
+/*****************************************************************************/
+/* PMGT */
+/* */
+/* January, 2007 */
+/* */
+/* Copyright 2007 */
+/* Wen Yu */
+/* Department of Computing and Software */
+/* McMaster University */
+/* yuw4@mcmaster.ca */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices are not removed. You may distribute modified versions*/
+/* of this code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS */
+/* MADE TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL */
+/* AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT */
+/* CHARGE, AND CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. */
+/* */
+/* This is the test case TC5. */
+/* This test case is design for test correctness of PMGT. */
+/*****************************************************************************/
+#include <iostream>
+
+#ifndef SERVICE
+#include "Service.h"
+#endif
+
+#ifndef COARSENING
+#include "Coarsening.h"
+#endif
+
+#ifndef REFINING
+#include "Refining.h"
+#endif
+
+#ifndef OUTPUT
+#include "Output.h"
+#endif
+
+#ifndef INPUT
+#include "Input.h"
+#endif
+
+#ifndef MESH
+#include "Mesh.h"
+#endif
+
+using namespace PMGT;
+int main(){
+
+ Mesh mesh;
+ Input input;
+ Refining ref;
+ Output output;
+
+ input.read_file(mesh, "oldVertices.dat", "oldCells.dat");
+
+
+ double x = 0.4;
+ int count = 0;
+ char vfile[32];
+ char* vp = vfile;
+ char cfile[32];
+ char* cp = cfile;
+ char number[8];
+ while(1){
+
+ // refine
+ count++;
+ sprintf(number, "%i", count);
+
+ vp = strcpy(vp, "newVertices");
+ vp = strcat(vp, number);
+ vp = strcat(vp,".dat");
+
+ cp = strcpy(cp, "newCells");
+ cp = strcat(cp, number);
+ cp = strcat(cp,".dat");
+
+ int n = mesh.n_of_c();
+ vector<int> vIds;
+ Point zero;
+ Vertex vtx[3];
+
+ zero.clear();
+ zero.push_back(0);
+ zero.push_back(0);
+
+ for (int i=0; i<n; i++){
+ vIds.clear();
+ vIds = mesh.vIds_from_cId(i);
+ for (int j=0; j<3; j++){
+ vtx[j] = mesh.vertex(vIds[j]);
+ }
+
+ double first = vtx[0].distance(zero)-0.7;
+ double second = vtx[1].distance(zero)-0.7;
+ if (first*second<DBL_EPSILON){
+ mesh.cell(i).setMflag(REFINE);
+ }
+ else{
+ double third = vtx[2].distance(zero)-0.7;
+ if (first*third < DBL_EPSILON){
+ mesh.cell(i).setMflag(REFINE);
+ }
+ }
+ }
+
+ ref.longest_edge(mesh);
+ output.write_file(mesh,vp, cp);
+
+ if (count==15){
+ break;
+ }
+ }
+
+ cout << "There are " << count << " meshes generated." << endl;
+
+ return 0;
+}
diff --git a/Examples/MeshGenToolbox/testdriver/ReadMe.txt b/Examples/MeshGenToolbox/testdriver/ReadMe.txt
new file mode 100644
index 0000000000000000000000000000000000000000..57aff0be3fe439a4bc4fa13825cf01f1b167b5af
--- /dev/null
+++ b/Examples/MeshGenToolbox/testdriver/ReadMe.txt
@@ -0,0 +1,9 @@
+This is the serial version of PMGT.
+
+There is only one test case (TC5).
+
+To compile this test file, just type "make"
+
+To remove generated object files and the executable file, type "make cleanAll"
+
+To remove generated output files, type "make cleanOutput"
\ No newline at end of file
diff --git a/Examples/MeshGenToolbox/testdriver/makefile b/Examples/MeshGenToolbox/testdriver/makefile
new file mode 100644
index 0000000000000000000000000000000000000000..6e9f102eccc07b4d97d8d739e28fe172cd4759e6
--- /dev/null
+++ b/Examples/MeshGenToolbox/testdriver/makefile
@@ -0,0 +1,28 @@
+OBJECTS = ../mgt/Service.o ../mgt/Coarsening.o ../mgt/Refining.o ../mgt/Output.o ../mgt/Input.o ../mgt/Mesh.o
+TEST_OBJ = 5_test_sr_arc.o
+
+TEST_SRC = 5_test_sr_arc.cpp
+
+ALL_TEST = 5_test_sr_arc
+
+# all testing executable
+all: $(TEST_OBJ)
+ @cd ../mgt; $(MAKE) $@
+ g++ -o 5_test_sr_arc $(OBJECTS) 5_test_sr_arc.o
+
+$(TEST_OBJ): $(TEST_SRC)
+ g++ -c $(TEST_SRC) -I../mgt
+
+# remove generated testing and PMGT files
+clean:
+ @cd ../mgt; $(MAKE) $@
+ rm -f *.o $(ALL_TEST)
+
+# remove generated testing files.
+# keep the PMGT files
+cleanTest:
+ rm -f $(TEST_OBJ) $(ALL_TEST)
+
+# remove generated output files
+cleanOutput:
+ rm newVertices* newCells*
diff --git a/Examples/MeshGenToolbox/testdriver/makefile2.txt b/Examples/MeshGenToolbox/testdriver/makefile2.txt
new file mode 100644
index 0000000000000000000000000000000000000000..aeb5ea39a53cdaa70a5dd7b4d90531ae4c594deb
--- /dev/null
+++ b/Examples/MeshGenToolbox/testdriver/makefile2.txt
@@ -0,0 +1,34 @@
+OBJECTS = Service.o Coarsening.o Refining.o Output.o Input.o Mesh.o
+TEST_OBJ = 5_test_sr_arc.o
+
+SOURCES = Service.cpp Coarsening.cpp Refining.cpp Output.cpp Input.cpp Mesh.cpp
+TEST_SRC = 5_test_sr_arc.cpp
+
+HEADERS = Service.h Coarsening.h Refining.h Input.h Input.h Mesh.h Cell.h Edge.h Vertex.h
+
+ALL_TEST = 5_test_sr_arc
+
+# all testing executable
+all: $(TEST_OBJ)
+ @cd ../mgt; $(MAKE) $@
+ g++ -o 5_test_sr_arc $(OBJECTS) 5_test_sr_arc.o -L../mgt
+
+5_test_sr_arc:5_test_sr_arc.o
+ g++ -o 5_test_sr_arc $(OBJECTS) 5_test_sr_arc.o
+
+$(TEST_OBJ): $(TEST_SRC)
+ g++ -c $(TEST_SRC)
+
+# remove generated testing and PMGT files
+clean:
+ @cd src; $(MAKE) $@
+ rm *.o $(ALL_TEST)
+
+# remove generated testing files.
+# keep the PMGT files
+cleanTest:
+ rm $(TEST_OBJ) $(ALL_TEST)
+
+# remove generated output files
+cleanOutput:
+ rm newVertices* newCells*
\ No newline at end of file
diff --git a/Examples/MeshGenToolbox/testdriver/oldCells.dat b/Examples/MeshGenToolbox/testdriver/oldCells.dat
new file mode 100644
index 0000000000000000000000000000000000000000..cd0e3452d1c6c7b847b5ae89421a894541be700b
--- /dev/null
+++ b/Examples/MeshGenToolbox/testdriver/oldCells.dat
@@ -0,0 +1,2 @@
+0 1 3
+0 3 2
diff --git a/Examples/MeshGenToolbox/testdriver/oldVertices.dat b/Examples/MeshGenToolbox/testdriver/oldVertices.dat
new file mode 100644
index 0000000000000000000000000000000000000000..4367637ff40fe22324e97d106e3e4618e7e330c8
--- /dev/null
+++ b/Examples/MeshGenToolbox/testdriver/oldVertices.dat
@@ -0,0 +1,4 @@
+0.0 0.0
+1.0 0.0
+0.0 1.0
+1.0 1.0
diff --git a/Examples/MeshGenToolbox/testdriver/show_serial.m b/Examples/MeshGenToolbox/testdriver/show_serial.m
new file mode 100644
index 0000000000000000000000000000000000000000..6f0fedae9e8133875c5200da8834540c1bee2f18
--- /dev/null
+++ b/Examples/MeshGenToolbox/testdriver/show_serial.m
@@ -0,0 +1,66 @@
+function show_serial(n)
+
+% plot original mesh
+load oldVertices.dat; load oldCells.dat;
+oldCells(:,:) = oldCells(:,:)+1;
+triplot(oldCells, oldVertices(:,1), oldVertices(:,2))
+title('Original Mesh')
+axis equal
+
+% plot new mesh
+for (i=1:n)
+ vfile = strcat('newVertices',num2str(i),'.dat');
+ vfid = fopen(vfile, 'r');
+ v = fscanf(vfid,'%f %f');
+ fclose(vfid);
+
+ [nv,nnv] = size(v);
+ vv = zeros(nv/2, 2);
+ [mv,mmv] = size(vv);
+ for(j=1:mv)
+ vv(j,1) = v((j-1)*2+1);
+ vv(j,2) = v((j-1)*2+2);
+ end
+
+
+ cfile = strcat('newCells',num2str(i),'.dat');
+ cfid = fopen(cfile, 'r');
+ c = fscanf(cfid,'%g %g %g');
+ fclose(cfid);
+
+ [nc,nnc] = size(c);
+ cc = zeros(nc/3, 3);
+ [mc,mmc] = size(cc);
+ for(j=1:mc)
+ cc(j,1) = c((j-1)*3+1);
+ cc(j,2) = c((j-1)*3+2);
+ cc(j,3) = c((j-1)*3+3);
+ end
+ cc(:,:) = cc(:,:)+1;
+ % plot
+ figure
+ triplot(cc, vv(:,1), vv(:,2))
+ t = strcat('Mesh for "', vfile,'" and "', cfile,'"');
+ title(t)
+ axis equal
+end
+
+
+
+% cells2(:,:) = cells2(:,:)+1;
+% cells3(:,:) = cells3(:,:)+1;
+%
+% % plot
+% triplot(cells1, vertices1(:,1), vertices1(:,2))
+% title('Test Creation')
+% axis equal
+%
+% figure
+% triplot(cells2, vertices2(:,1), vertices2(:,2))
+% title('Test Refinement')
+% axis equal
+%
+% figure
+% triplot(cells3, vertices3(:,1), vertices3(:,2))
+% title('Test Coarsening')
+% axis equal
\ No newline at end of file
diff --git a/Examples/MeshGenToolbox/testdriver/testingCode.cpp b/Examples/MeshGenToolbox/testdriver/testingCode.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..326472874b951ed6c120b2ec3d3eb77ecedb2325
--- /dev/null
+++ b/Examples/MeshGenToolbox/testdriver/testingCode.cpp
@@ -0,0 +1,89 @@
+// testing code
+
+#include <iostream>
+
+
+#ifndef MESH
+#include "Mesh.h"
+#endif
+
+#ifndef INPUT
+#include "Input.h"
+#endif
+
+#ifndef OUTPUT
+#include "Output.h"
+#endif
+
+
+#ifndef REFINING
+#include "Refining.h"
+#endif
+
+#ifndef COARSENING
+#include "Coarsening.h"
+#endif
+
+#ifndef SERVICE
+#include "Service.h"
+#endif
+
+
+//using namespace PMGT::Vertex;
+//using namespace PMGT::Edge;
+//using namespace PMGT::Cell;
+//using namespace PMGT::Mesh;
+
+using namespace PMGT;
+
+int main(){
+
+ char* vertexFile = "oldVertices.dat";
+ char* cellFile = "oldCells.dat";
+
+ int i,nc;
+
+ Mesh mesh;
+ Input input;
+ Output output;
+ Refining ref;
+ Coarsening cos;
+ Service sev;
+
+ input.read_file(mesh, vertexFile, cellFile);
+ if (sev.is_valid_mesh(mesh)){
+ cout << "Mesh creatation is ok. The # of cells is " << mesh.n_of_c() << endl;
+ }
+ else{
+ cout << "Mesh creatation is wrong." << endl;
+ }
+
+ nc=mesh.n_of_c();
+ for (i=0; i<nc; i++){
+ mesh.cell(i).setMflag(REFINE);
+ }
+ //ref.split(mesh);
+ ref.longest_edge(mesh);
+ if (sev.is_valid_mesh(mesh)){
+ cout << "Mesh refinement is ok. The # of cells is " << mesh.n_of_c() << endl;
+ }
+ else{
+ cout << "Mesh refinement is wrong." << endl;
+ }
+
+
+ nc=mesh.n_of_c();
+ for (i=0; i<nc; i++){
+ mesh.cell(i).setMflag(COARSEN);
+ }
+ cos.edge_collapse(mesh);
+ if (sev.is_valid_mesh(mesh)){
+ cout << "Mesh coarsening is ok. The # of cells is " << mesh.n_of_c() << endl;
+ }
+ else{
+ cout << "Mesh coarsening is wrong." << endl;
+ }
+
+ output.write_file(mesh, "newVertices.dat", "newCells.dat");
+ return 0;
+}
diff --git a/Lectures/Figures/BinarySearch.png b/Lectures/Figures/BinarySearch.png
new file mode 100644
index 0000000000000000000000000000000000000000..9ada2128b32791d254ec6dcf249b0f6926e002b8
Binary files /dev/null and b/Lectures/Figures/BinarySearch.png differ
diff --git a/Lectures/Figures/CompleteCoveragePrinciple.png b/Lectures/Figures/CompleteCoveragePrinciple.png
new file mode 100644
index 0000000000000000000000000000000000000000..e3fcbbd3e4c1122f6f57cbeccfc6da854290f6b8
Binary files /dev/null and b/Lectures/Figures/CompleteCoveragePrinciple.png differ
diff --git a/Lectures/Figures/ControlGraphRules.png b/Lectures/Figures/ControlGraphRules.png
new file mode 100644
index 0000000000000000000000000000000000000000..d159c6e12a7f57123181b3ac548dcfa2e1d1f04c
Binary files /dev/null and b/Lectures/Figures/ControlGraphRules.png differ
diff --git a/Lectures/Figures/EuclidsAlgorithm.png b/Lectures/Figures/EuclidsAlgorithm.png
new file mode 100644
index 0000000000000000000000000000000000000000..84fe1f286f6dcbf619f1d32ef91cb032fba4711f
Binary files /dev/null and b/Lectures/Figures/EuclidsAlgorithm.png differ
diff --git a/Lectures/Figures/EuclidsAlgorithmNoGraph.png b/Lectures/Figures/EuclidsAlgorithmNoGraph.png
new file mode 100644
index 0000000000000000000000000000000000000000..c265229e536b97deda032362fa4d36fb696d504e
Binary files /dev/null and b/Lectures/Figures/EuclidsAlgorithmNoGraph.png differ
diff --git a/Lectures/Figures/ExampleStatementCoverage.png b/Lectures/Figures/ExampleStatementCoverage.png
new file mode 100644
index 0000000000000000000000000000000000000000..98b8bf23d646858d2101a9193125651924d92eaa
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diff --git a/Lectures/Figures/ExampleStatementCoverageOnlyCode.png b/Lectures/Figures/ExampleStatementCoverageOnlyCode.png
new file mode 100644
index 0000000000000000000000000000000000000000..9045b71c393fc0c431f031932ee48c2e607e959f
Binary files /dev/null and b/Lectures/Figures/ExampleStatementCoverageOnlyCode.png differ
diff --git a/Lectures/Figures/Simplification.png b/Lectures/Figures/Simplification.png
new file mode 100644
index 0000000000000000000000000000000000000000..19c715fed88dee10790ced6aef0c2166a2065f46
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diff --git a/Lectures/Figures/SoftwareLifecycle.png b/Lectures/Figures/SoftwareLifecycle.png
new file mode 100644
index 0000000000000000000000000000000000000000..ecbfe6a70374881d5533fa8b77182aab62ba251b
Binary files /dev/null and b/Lectures/Figures/SoftwareLifecycle.png differ
diff --git a/Lectures/Figures/WeaknessConditionCoverage.png b/Lectures/Figures/WeaknessConditionCoverage.png
new file mode 100644
index 0000000000000000000000000000000000000000..d363baf43f9fe04cfd84d78f131fff7586e550bf
Binary files /dev/null and b/Lectures/Figures/WeaknessConditionCoverage.png differ
diff --git a/Lectures/Figures/WeaknessEdgeCoverage.png b/Lectures/Figures/WeaknessEdgeCoverage.png
new file mode 100644
index 0000000000000000000000000000000000000000..54121b5f80ebe6c3f024922106ae16b5f7dfa142
Binary files /dev/null and b/Lectures/Figures/WeaknessEdgeCoverage.png differ
diff --git a/Lectures/Figures/WeaknessStatementCoverage.png b/Lectures/Figures/WeaknessStatementCoverage.png
new file mode 100644
index 0000000000000000000000000000000000000000..b0a85fdec068da6b9fa66dff5d6277bbf7946e02
Binary files /dev/null and b/Lectures/Figures/WeaknessStatementCoverage.png differ
diff --git a/Lectures/Figures/WeaknessStatementCoverageOnlyCode.png b/Lectures/Figures/WeaknessStatementCoverageOnlyCode.png
new file mode 100644
index 0000000000000000000000000000000000000000..1e6d029dc9edc962b31d5bf0c15aaf673bc46f12
Binary files /dev/null and b/Lectures/Figures/WeaknessStatementCoverageOnlyCode.png differ
diff --git a/Lectures/L09_VerificationAndValidation/CondCovExample.java b/Lectures/L09_VerificationAndValidation/CondCovExample.java
new file mode 100644
index 0000000000000000000000000000000000000000..e83ce3e23f13acc860371cbb4c74191b111f9081
--- /dev/null
+++ b/Lectures/L09_VerificationAndValidation/CondCovExample.java
@@ -0,0 +1,14 @@
+if c1 and c2 then
+ st;
+else
+ sf;
+
+// equivalent to
+
+if c1 then
+ if c2 then
+ st;
+ else
+ sf;
+else
+ sf;
diff --git a/Lectures/L09_VerificationAndValidation/DeleteCorrect.java b/Lectures/L09_VerificationAndValidation/DeleteCorrect.java
new file mode 100644
index 0000000000000000000000000000000000000000..e1fd95834b8c976c5ebc924445b2a48fbd4b6f15
--- /dev/null
+++ b/Lectures/L09_VerificationAndValidation/DeleteCorrect.java
@@ -0,0 +1,11 @@
+ public static void del(int i)
+ {
+ int j;
+
+ for (j = i; j < (length - 1); j++)
+ {
+ s[j] = s[j+1];
+ }
+
+ length = length - 1;
+ }
\ No newline at end of file
diff --git a/Lectures/L09_VerificationAndValidation/DeleteIncorrect.java b/Lectures/L09_VerificationAndValidation/DeleteIncorrect.java
new file mode 100644
index 0000000000000000000000000000000000000000..df93cf93810c7ef369da3077b4826741a582865e
--- /dev/null
+++ b/Lectures/L09_VerificationAndValidation/DeleteIncorrect.java
@@ -0,0 +1,11 @@
+ public static void del(int i)
+ {
+ int j;
+
+ for (j = i; j <= (length - 1); j++)
+ {
+ s[j] = s[j+1];
+ }
+
+ length = length - 1;
+ }
\ No newline at end of file
diff --git a/Lectures/L09_VerificationAndValidation/VerificAndValid.pdf b/Lectures/L09_VerificationAndValidation/VerificAndValid.pdf
index 20cf1b5b423d00e509cf1d2345eadc22e6a47ef0..fde513631576c4fd4348d69cda088e18612f22f9 100644
Binary files a/Lectures/L09_VerificationAndValidation/VerificAndValid.pdf and b/Lectures/L09_VerificationAndValidation/VerificAndValid.pdf differ
diff --git a/Lectures/L09_VerificationAndValidation/VerificAndValid.tex b/Lectures/L09_VerificationAndValidation/VerificAndValid.tex
index f0fac85f7aaa6057c2c3b42163708ac34da90e4f..ccc4c1ea395e92652b767a842a822fbd4b9a0bfa 100755
--- a/Lectures/L09_VerificationAndValidation/VerificAndValid.tex
+++ b/Lectures/L09_VerificationAndValidation/VerificAndValid.tex
@@ -15,6 +15,7 @@
urlcolor=blue,
unicode=false}
\urlstyle{same}
+\usepackage{listings}
\bibliographystyle{plain}
@@ -44,7 +45,16 @@
\bi
\item Administrative details
\item Questions?
-\item License and copyright
+\item 741 workflow
+\item Testing from SE perspective
+\item Testing from SC perspective
+\item V\&V template
+\item V\&V examples
+\bi
+\item SWHS
+\item Mesh Gen
+\item Rogue Reborn
+\ei
\ei
\end{frame}
@@ -54,7 +64,20 @@
\frametitle{Administrative Details}
\bi
+\item SRS Presentation grades on Avenue
\item GitHub issues for colleagues
+\bi
+\item Assigned 1 colleague (see \texttt{Repos.xlsx} in repo)
+\item Provide at least 5 issues on their SRS
+\item Grading
+\bi
+\item Not enough issues, or poor issues 0/2
+\item Enough issues, but shallow 1/2
+\item Enough issues and deep (not surface) 2/2
+\ei
+\item Due by Tuesday, Oct 10, 11:59 pm
+\ei
+\item Reading week next week, no 741 classes
\ei
\end{frame}
@@ -66,6 +89,7 @@
~\newline
\begin{tabular}{l l l}
\textbf{SRS} & Week 05 & Oct 4\\
+\textbf{SRS Issues} & Reading week & Oct 10\\
\textbf{V\&V Present} & Week 06 & Week of Oct 16\\
\textbf{V\&V Plan} & Week 07 & Oct 25\\
MG Present & Week 08 & Week of Oct 30\\
@@ -86,18 +110,18 @@ Final Documentation & Week 13 & Dec 6\\
\bi
\item V\&V Present
\bi
-\item Tuesday: Steven, Alexandre P., Alexander S.
-\item Friday: Geneva, Jason, Yuzhi
+\item \textbf{Tuesday: Steven, Alexandre P., Alexander S.}
+\item \textbf{Friday: Geneva, Jason, Yuzhi}
\ei
\item MG Present
\bi
-\item Tuesday: Xiaoye, Shushen, Devi, Keshav, Alex P, Paul
+\item Tuesday: Xiaoye, Shusheng, Devi, Keshav, Alex P, Paul
\item Friday: Yuzhi, Jason, Geneva, Alex S, Isobel, Steven
\ei
\item MIS Present
\bi
\item Tuesday: Isobel, Keshav, Paul
-\item Friday: Shushen, Xiaoye, Devi
+\item Friday: Shusheng, Xiaoye, Devi
\ei
\item Impl.\ Present
\bi
@@ -114,12 +138,1188 @@ Final Documentation & Week 13 & Dec 6\\
\begin{frame}
\frametitle{Questions?}
\begin{itemize}
-\item Questions about ...
+\item Questions about SRS?
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
+\frametitle{``Faked'' Rational Design Process}
+
+\begin{center}
+\includegraphics[scale=0.7]{../Figures/OverviewOfProcess.pdf}
+\end{center}
+
+%See Parnas and Clements 1986 about ``Faking It''
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Outline of Verification Topics}
+
+\begin{itemize}
+
+\item What are the goals of verification?
+\item What are the main approaches to verification?
+\begin{itemize}
+\item What kind of assurance do we get through testing?
+\item \structure{Can testing prove correctness?}
+\item How can testing be done systematically?
+\item How can we remove defects (debugging)?
+\end{itemize}
+\item What are the main approaches to software analysis?
+\item Informal versus formal analysis
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Incorrect Version of Delete}
+
+Using \texttt{s = new T[MAX\_SIZE]}, for some type \texttt{T}
+
+\lstset{language=java,breaklines=true,showspaces=false,showstringspaces=false,breakatwhitespace=true}
+\noindent \lstinputlisting{DeleteIncorrect.java}
+
+\bi
+\item \structure{What is the error?}
+\item \structure{What test case would highlight the error?}
+\ei
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Correct Version of Delete}
+
+\lstset{language=java,breaklines=true,showspaces=false,showstringspaces=false,breakatwhitespace=true}
+\noindent \lstinputlisting{DeleteCorrect.java}
+
+Avoids potential ArrayIndexOutOfBoundsException Exception
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Verification Versus Validation}
+
+\begin{itemize}
+
+\item \structure{What is the difference between verification and
+ validation?}
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Verification Versus Validation}
+
+\begin{itemize}
+
+\item Verification - Are we building the product right? Are we implementing the
+ requirements correctly (internal)
+\item Validation - Are we building the right product? Are we getting the right
+ requirements (external)
+\item According to
+ \href{https://en.wikipedia.org/wiki/Software_verification_and_validation}{Capability
+ Maturity Model (CMM)}
+\bi
+\item
+ Software Verification: The process of evaluating software to determine
+ whether the products of a given development phase satisfy the conditions
+ imposed at the start of that phase. [IEEE-STD-610]
+ \item Software Validation: The process of evaluating software during or at the
+ end of the development process to determine whether it satisfies specified
+ requirements. [IEEE-STD-610]
+\ei
+\item We will focus on verification
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Verification Activities}
+
+\begin{center}
+\includegraphics[scale=0.55]{../Figures/SoftwareLifecycle.png}
+\end{center}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\begin{frame}
+\frametitle{Need for Verification}
+
+\begin{itemize}
+
+\item Designers are fallible even if they are skilled and follow sound principles
+\item We need to build confidence in the software
+\item Everything must be verified, every required functionality, every required
+ quality, every process, every product, every document
+\item For every work product covered in this class we have discussed its verification
+\item Even verification itself must be verified
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Properties of Verification}
+
+From \cite{GhezziEtAl2003}
+
+\begin{itemize}
+
+\item May not be binary (OK, not OK)
+\begin{itemize}
+\item Severity of defect is important
+\item Some defects may be tolerated
+\item Our goal is typically acceptable reliability, not correctness
+\end{itemize}
+\item May be subjective or objective - for instance, usability, generic level of
+ maintainability or portability
+\bi
+\item \structure{How might we make usability objective?}
+\ei
+\item Even implicit qualities should be verified
+\begin{itemize}
+\item Because requirements are often incomplete
+\item For instance robustness, maintainability
+\end{itemize}
+\item \structure{What is better than implicitly specified
+ qualities?} % explicit!
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Approaches to Verification}
+
+\begin{itemize}
+
+\item \structure{What are some approaches to verification?}
+\item \structure{How can we categorize these approaches?}
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Approaches to Verification}
+
+\begin{itemize}
+
+\item Experiment with behaviour of product
+\begin{itemize}
+\item Sample behaviours via testing
+\item Goal is to find ``counter examples''
+\item \structure{Dynamic} technique
+\item Examples: unit testing, integration testing, acceptance testing, white box
+ testing, stress testing, etc.
+\end{itemize}
+\item Analyze product to deduce its adequacy
+\begin{itemize}
+\item Analytic study of properties
+\item \structure{Static} technique
+\item Examples: Code walk-throughs, code inspections, correctness proof, etc.
+\end{itemize}
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Does our Engineering Analogy Fail?}
+
+\begin{itemize}
+
+\item \structure{If a bridge can hold 512 kN, can it hold 499 kN?}
+\item \structure{If our software works for the input 512, will it work for 499?}
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Verification in Engineering}
+
+\begin{itemize}
+
+\item Example of bridge design
+\item One test assures infinite correct situations
+\item In software a small change in the input may result in significantly different behaviour
+\item There are also chaotic systems in nature, but products of engineering
+ design are usually stable and well-behaved
+% consider the examples of weather, bifurcation in engineering, chaos theory for traffic, etc.
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Modified Version Works for 512, but not 499}
+
+\includegraphics[scale=0.5]{../Figures/BinarySearch.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Testing and Lack of ``Continuity''}
+
+\begin{itemize}
+
+\item Testing samples behaviours by examining ``test cases''
+\item Impossible to extrapolate behaviour of software from a finite set of test cases
+\item No continuity of behaviour - it can exhibit correct behaviour in
+ infinitely many cases, but may still be incorrect in some cases
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Goals of Testing}
+
+\begin{itemize}
+
+\item \structure{If our code passes all test cases, is it now guaranteed to be
+ error free?}
+\item \structure{Are 5000 random tests always better than 5 carefully selected
+ tests?}
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Goals of Testing}
+
+\begin{itemize}
+
+\item To show the \structure{presence} of bugs (Dijkstra, 1972)
+\item If tests do not detect failures, we cannot conclude that software is defect-free
+\item Still, we need to do testing - driven by sound and systematic principles
+\begin{itemize}
+\item Random testing is often not a systematic principle to use
+% look at the example from the text, or divide by zero within a circular range
+\item Need a test plan
+\end{itemize}
+\item Should help isolate errors - to facilitate debugging
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Goals of Testing Continued}
+
+\begin{itemize}
+\item Should be repeatable
+\begin{itemize}
+\item Repeating the same experiment, we should get the same results
+\item Repeatability may not be true because of the effect of the execution
+ environment on testing
+\item Repeatability may not occur if there are uninitialized variables
+\item Repeatability may not happen when there is nondeterminism
+\end{itemize}
+
+\item Should be accurate
+\begin{itemize}
+\item Accuracy increases reliability
+\item Part of the motivation for formal specification
+\end{itemize}
+
+\item \structure{Is a \structure{successful} test case one that passes the test, or one
+ that shows a failure?}
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Test (V\&V) Plan}
+
+\begin{itemize}
+
+\item \structure{Given that no single verification technique can prove
+ correctness, the practical approach is to use ALL verification techniques.
+ Is this statement True or False?}
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Test (V\&V) Plan}
+
+\begin{itemize}
+
+\item Testing can uncover errors and build confidence in the software
+\item Resources of time, people, facilities are limited
+\item Need to plan how the software will be tested
+\item You know in advance that the software is unlikely to be perfect
+\item You need to put resources into the most important parts of the project
+\item A risk analysis can determine where to put your limited resources
+\item A risk is a condition that can result in a loss
+\item Risk analysis involves looking at how bad the loss can be and at the
+ probability of the loss occurring
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{White Box Versus Black Box Testing}
+\begin{itemize}
+\item \structure{Do you know (or can you guess) the difference between white box
+ and black box testing?}
+\item \structure{What if they were labelled transparent box and opaque box
+ testing, respectively?}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{White Box Versus Black Box Testing}
+\begin{itemize}
+\item White box testing is derived from the program's internal structure
+\item Black box testing is derived from a description of the program's function
+\item Should perform both white box and black box testing
+\item Black box testing
+\begin{itemize}
+\item Uncovers errors that occur in implementing requirements or design specifications
+\item Not concerned with how processing occurs, but with the results
+\item Focuses on functional requirements for the system
+\item Focuses on normal behaviour of the system
\end{itemize}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{White Box Testing}
+
+\begin{itemize}
+\item Uncovers errors that occur during implementation of the program
+\item Concerned with how processing occurs
+\item Evaluates whether the structure is sound
+%\item Focuses on the nonfunctional requirements for the system
+\item Focuses on abnormal or extreme behaviour of the system
+\end{itemize}
+
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
+\frametitle{Dynamic Testing}
+\begin{itemize}
+\item \structure{Is there a dynamic testing technique that can guarantee
+ correctness?}
+\item \structure{If so, what is the technique?}
+\item \structure{Is this technique practical?}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Dynamic Versus Static Testing}
+\begin{itemize}
+\item Another classification of verification techniques, as previously discussed
+\item Use a combination of dynamic and static testing
+\item Dynamic analysis
+\begin{itemize}
+\item Requires the program to be executed
+\item Test cases are run and results are checked against expected behaviour
+\item Exhaustive testing is the only dynamic technique that guarantees program
+validity
+\item Exhaustive testing is usually impractical or impossible
+\item Reduce number of test cases by finding criteria for choosing representative test cases
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Static Testing Continued}
+\begin{itemize}
+\item Static analysis
+\begin{itemize}
+\item Does not involve program execution
+\item Testing techniques simulate the dynamic environment
+\item Includes syntax checking
+\item Generally static testing is used in the requirements and design stage, where there is no code to execute
+\item Document and code walkthroughs
+\item Document and code inspections
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Manual Versus Automated Testing}
+\begin{itemize}
+\item \structure{What is the difference between manual and automated testing?}
+\item \structure{What are the advantages of automated testing?}
+\item \structure{What is regression testing?}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Manual Versus Automated Testing}
+\begin{itemize}
+\item Manual testing
+\begin{itemize}
+\item Has to be conducted by people
+\item Includes by-hand test cases, structured walkthroughs, code inspections
+\end{itemize}
+\item Automated testing
+\begin{itemize}
+\item The more automated the development process, the easier to automate testing
+\item Less reliance on people
+\item Necessary for \structure{regression testing}
+\item Test tools can assist, such as Junit, Cppunit, CuTest etc.
+\item Can be challenging to automate GUI tests
+\item Test suite for Maple has 2 000 000 test cases, run on 14 platforms, every
+ night, automated reporting
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% \begin{frame}
+% \frametitle{Automated Testing at MapleSoft}
+% \begin{itemize}
+% \item Three steps
+% \begin{itemize}
+% \item Write the problem description
+% \item result := solver(problem)
+% \item assert(result == expected)
+% \end{itemize}
+% \item Assert writes out code to reproduce any failures
+% \item Track failures
+% \begin{itemize}
+% \item Source code management (like CVS or Subversion)
+% \item Database of test cases, functions called
+% \item Database of source files, functions defined
+% \item Database of 40 days of timings and resources used
+% \end{itemize}
+% \item Automatically sends an e-mail to the programmer and his/her boss
+% \end{itemize}
+% \end{frame}
+
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Continuous Integration Testing}
+\begin{itemize}
+\item \structure{What is continuous integration testing?}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Continuous Integration Testing}
+\begin{itemize}
+\item Information available on
+ \href{https://en.wikipedia.org/wiki/Continuous_integration}{Wikipedia}
+\item Developers integrate their code into a shared repo frequently (multiple
+ times a day)
+\item Each integration is automatically accompanied by regression tests and
+ other build tasks
+\item Build server
+\bi
+\item Unit tests
+\item Integration tests
+\item Static analysis
+\item Profile performance
+\item Extract documentation
+\item Update project web-page
+\item Portability tests
+\item etc.
+\ei
+\item Avoids potentially extreme problems with integration when the baseline and
+ a developer's code greatly differ
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Continuous Integration Tools}
+\begin{itemize}
+\item Gitlab
+\bi
+\item Example at
+ \href{https://gitlab.cas.mcmaster.ca/andrem5/RogueReborn/pipelines}{Rogue
+ Reborn}
+\ei
+\item Jenkins
+\item Travis
+\item \href{https://www.docker.com/}{Docker}
+\bi
+\item Eliminates the ``it works on my machine'' problem
+\item Package dependencies with your apps
+\item A container for lightweight virtualization
+\item Not a full VM
+\ei
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Sample Nonfunctional System Testing}
+\begin{itemize}
+\item Stress testing - Determines if the system can function when subject to large volumes
+\item Usability testing
+\item Performance measurement
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Functional System Testing}
+\begin{itemize}
+\item Requirements: Determines if the system can perform its function correctly and that the correctness can be
+sustained over a continuous period of time
+%\item Regression: Determines if changes to the system do not invalidate previous positive testing results
+\item Error Handling: Determines the ability of the system to properly process incorrect transactions
+\item Manual Support: Determines that the manual support procedures are documented and complete, where manual support
+involves procedures, interfaces between people and the system, and training procedures
+\item Inter-systems: Determines the that interconnections between systems function correctly
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Sample Functional System Testing}
+\begin{itemize}
+\item Requirements: Determines if the system can perform its function correctly and that the correctness can be
+sustained over a continuous period of time
+%\item Regression: Determines if changes to the system do not invalidate previous positive testing results
+\item Error Handling: Determines the ability of the system to properly process
+ incorrect transactions
+\item Manual Support: Determines that the manual support procedures are documented and complete, where manual support
+involves procedures, interfaces between people and the system, and training procedures
+\item Parallel: Determines the results of the new application are consistent with the processing of the previous
+application or version of the application
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Testing Phases}
+\begin{enumerate}
+\item Unit testing
+\item Integration testing
+\item System testing
+\item Acceptance testing
+\end{enumerate}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Theoretical Foundations Of Testing: Definitions}
+\begin{itemize}
+\item P (program), D (input domain), R (output domain)
+\bi
+\item P: D $\rightarrow$ R (may be partial)
+\ei
+\item Correctness defined by OR $\subseteq$ D $\times$ R
+\bi
+\item P(d) correct if $\langle$ d, P(d) $\rangle \in$ OR
+\item P correct if all P(d) are correct
+\ei
+\item Failure
+\bi
+\item P(d) is not correct
+\item May be undefined (error state) or may be the wrong result
+\ei
+\item Error (Defect)
+\bi
+\item Anything that may cause a failure
+\bi
+\item Typing mistake
+\item Programmer forgot to test ``x=0''
+\ei
+\ei
+\item Fault
+\bi
+\item Incorrect intermediate state entered by program
+\ei
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Definitions Questions}
+\begin{itemize}
+\item \structure{A test case t is an element of D or R?}
+\item \structure{A test set T is a finite subset of D or R?}
+\item \structure{How would we define whether a test is successful?}
+\item \structure{How would we define whether a test set is successful?}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Definitions Continued}
+\begin{itemize}
+\item Test case t: An element of D
+\item Test set T: A finite subset of D
+\item Test is successful if P(t) is correct
+\item Test set successful if P correct for all t in T
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Theoretical Foundations of Testing}
+
+\begin{itemize}
+\item Desire a test set $T$ that is a finite subset of $D$ that will uncover all errors
+\item Determining and ideal $T$ leads to several
+ \href{https://en.wikipedia.org/wiki/Undecidable_problem}{undecideable
+ problems}
+\item No algorithm exists:
+\bi
+\item To state if a test set will uncover all possible errors
+\item To derive a test set that would prove program correctness
+\item To determine whether suitable input exists to guarantee execution of a
+ given statement in a given program
+\item etc.
+\ei
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Empirical Testing}
+
+\begin{itemize}
+\item Need to introduce empirical testing principles and heuristics as a
+ compromise between the impossible and the inadequate
+\item Find a strategy to select \structure{significant} test cases
+\item Significant means the test cases have a high potential of uncovering the
+ presence of errors
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Complete-Coverage Principle}
+
+\begin{itemize}
+\item Try to group elements of $D$ into subdomains $D_1$, $D_2$, ..., $D_n$
+ where any element of each $D_i$ is likely to have similar behaviour
+\item $D = D_1 \cup D_2 \cup ... \cup D_n$
+\item Select one test as a representative of the subdomain
+\item If $D_j \cap D_k = \emptyset$ for all $j \neq k$, (partition), any element
+ can be chosen from each subdomain
+\item Otherwise choose representatives to minimize number of tests, yet
+ fulfilling the principle
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Complete-Coverage Principle}
+
+\includegraphics[scale=0.5]{../Figures/CompleteCoveragePrinciple.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{White-box Testing}
+
+\begin{itemize}
+\item \structure{Intuitively, after running your test suites, what percentage of
+ the lines of code in your program should be exercised?}
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{White-box Coverage Testing}
+
+\begin{itemize}
+\item (In)adequacy criteria - if significant parts of the program structure are not tested, testing is inadequate
+\item Control flow coverage criteria
+\begin{itemize}
+\item Statement coverage
+\item Edge coverage
+\item Condition coverage
+\item Path coverage
+\end{itemize}
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Statement-Coverage Criterion}
+
+\begin{itemize}
+\item Select a test set $T$ such that every elementary statement in $P$ is
+ executed at least once by some $d$ in $T$
+\item An input datum executes many statements - try to minimize the number of
+ test cases still preserving the desired coverage
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Example}
+
+\includegraphics[scale=0.5]{../Figures/ExampleStatementCoverageOnlyCode.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Example}
+
+\includegraphics[scale=0.5]{../Figures/ExampleStatementCoverage.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Weakness of the Criterion}
+
+\includegraphics[scale=0.6]{../Figures/WeaknessStatementCoverageOnlyCode.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Weakness of the Criterion}
+
+\includegraphics[scale=0.6]{../Figures/WeaknessStatementCoverage.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Edge-Coverage Criterion}
+
+\begin{itemize}
+\item Select a test set $T$ such that every edge (branch) of the control flow is
+ exercised at least once by some $d$ in $T$
+\item This requires formalizing the concept of the control graph and how to construct it
+\begin{itemize}
+\item Edges represent statements
+\item Nodes at the ends of an edge represent entry into the statement and exit
+\end{itemize}
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Control Graph Construction Rules}
+
+\includegraphics[scale=0.4]{../Figures/ControlGraphRules.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Simplification}
+
+A sequence of edges can be collapsed into just one edge\\
+~\newline
+
+\includegraphics[scale=0.5]{../Figures/Simplification.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Example: Euclid's Algorithm}
+
+\includegraphics[scale=0.5]{../Figures/EuclidsAlgorithmNoGraph.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Example: Euclid's Algorithm}
+
+\includegraphics[scale=0.5]{../Figures/EuclidsAlgorithm.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Weakness}
+
+\includegraphics[scale=0.4]{../Figures/WeaknessEdgeCoverage.png}\\
+\uncover<2->{\structure{Do not discover the error ($<$ instead of $\leq$)}}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+%\frametitle{Alternative View of Condition Coverage}
+
+\lstset{language=java,breaklines=true,showspaces=false,showstringspaces=false,breakatwhitespace=true}
+\noindent \lstinputlisting{CondCovExample.java}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Condition-Coverage Criterion}
+
+\begin{itemize}
+\item Select a test set $T$ such that every edge of $P$'s control flow is traversed and all possible values of the
+constituents of compound conditions are exercised at least once
+\item This criterion is finer than edge coverage
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Weakness}
+
+\includegraphics[scale=0.5]{../Figures/WeaknessConditionCoverage.png}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Path-Coverage Criterion}
+
+\begin{itemize}
+\item Select a test set $T$ that traverses all paths from the initial to the final node of $P$s control flow
+\item It is finer than the previous kinds of coverage
+\item However, number of paths may be too large, or even infinite (see while loops)
+\item Loops
+\begin{itemize}
+\item Zero times (or minimum number of times)
+\item Maximum times
+\item Average number of times
+\end{itemize}
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{The Infeasibility Problem}
+
+\begin{itemize}
+\item Syntactically indicated behaviours (statements, edges, etc.) are often impossible
+\item Unreachable code, infeasible edges, paths, etc.
+\item Adequacy criteria may be impossible to satisfy
+\begin{itemize}
+\item Manual justification for omitting each impossible test case
+\item Adequacy ``scores'' based on coverage - example 95 \% statement coverage
+\end{itemize}
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Further Problem}
+
+\begin{itemize}
+\item What if the code omits the implementation of some part of the specification?
+\item White box test cases derived from the code will ignore that part of the specification!
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Testing Boundary Conditions}
+
+\begin{itemize}
+
+\item Testing criteria partition input domain in classes, assuming that behavior
+ is ``similar'' for all data within a class
+\item Some typical programming errors, however, just happen to be at the
+ boundary between different classes
+\begin{itemize}
+\item Off by one errors
+\item $<$ instead of $\leq$
+\item equals zero
+\end{itemize}
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Criterion}
+
+\begin{itemize}
+
+\item After partitioning the input domain D into several classes, test the
+ program using input values not only ``inside'' the classes, but also at their
+ boundaries
+\item This applies to both white-box and black-box techniques
+\item In practice, use the different testing criteria in combinations
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{The Oracle Problem}
+
+\structure{When might it be difficult to know the ``expected''
+ output/behaviour?}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{The Oracle Problem}
+
+\begin{itemize}
+
+\item Given input test cases that cover the domain, what are the expected
+ outputs?
+\item Oracles are required at each stage of testing to tell us what the right
+ answer is
+\item Black-box criteria are better than white-box for building test oracles
+\item Automated test oracles are required for running large amounts of tests
+\item Oracles are difficult to design - no universal recipe
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{The Oracle Problem Continued}
+
+\begin{itemize}
+
+\item Determining what the right answer should be is not always easy
+\begin{itemize}
+%\item Air traffic control system
+\item Scientific computing
+\item Machine learning
+\item Artifical intelligence
+\end{itemize}
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{The Oracle Problem Continued}
+
+\structure{What are some strategies we can use when we do not have a test
+ oracle?}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Strategies Without An Oracle}
+
+\begin{itemize}
+
+\item Using an independent program to approximate the oracle (pseudo oracle)
+\item Method of manufactured solutions
+\item Properties of the expected values can be easier than stating the expected
+ output
+\bi
+\item \uncover<1>{\structure<1>{Examples?}}
+\item \uncover<2->{List is sorted}
+\item \uncover<2->{Number of entries in file matches number of inputs}
+\item \uncover<2->{Conservation of energy or mass}
+\item \uncover<2->{Expected trends in output are observed (metamorphic testing)}
+\item \uncover<2->{etc.}
+\ei
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Mutation Testing for SC}
+\begin{itemize}
+\item Generate changes to the source code, called mutants, which become code faults
+\item Mutants include changing an operation, modifying constants, changing the order of execution, etc.
+\item The adequacy of a set of tests is established by running the tests on all generated mutants
+\item Need to account for floating point approximations
+\item See Hook and Kelly, 2009
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Analysis of Units}
+\begin{itemize}
+\item Dynamic testing of units is not the only option
+\item Static testing (analysis) includes the following
+\begin{itemize}
+\item Informal inspection
+\item Systematic inspection
+\item Code walkthroughs, data flow analysis
+\item Correctness proofs (for instance using pre and post conditions)
+\item Complexity measures
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Challenges Specific to Scientific Computing}
+\begin{itemize}
+\item Unknown solution
+\item Approximation of real numbers
+\item Nonfunctional requirements
+\item Parallel computation
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Validation Testing Report for PMGT}
+\begin{itemize}
+\item Prepared by Wen Yu
+\item Do not know the correct solution, but know properties of the correct solution
+\item Automated correctness validation tests
+\begin{itemize}
+\item The area of each element is greater than zero
+\item The boundary of the mesh is closed
+\item Vertices in a clockwise order
+\item $nc + nv - ne = 1$
+\item ...
+\end{itemize}
+\item Visual correctness validation tests
+\begin{itemize}
+\item No vertex outside the input domain
+\item No vertex inside a cell
+\item No dangling edges
+\item All cells connected
+\item The mesh is conformal
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Validation Testing Report for PMGT (Continued)}
+\begin{itemize}
+\item List and description of test cases
+\item Test cases are labelled and numbered
+\item Traceability to SRS requirements
+\item Traceability to MG
+\item Summary of results
+\item Analysis of results
+\begin{itemize}
+\item Focus on nonfunctional requirements
+\item Speed
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
\begin{frame}[allowframebreaks]
\frametitle{References}
diff --git a/Lectures/L10_VnVContinued/VnVContinued.tex b/Lectures/L10_VnVContinued/VnVContinued.tex
new file mode 100755
index 0000000000000000000000000000000000000000..1703dc8c820933b7cd323d77356ae676d5f3ee06
--- /dev/null
+++ b/Lectures/L10_VnVContinued/VnVContinued.tex
@@ -0,0 +1,130 @@
+%\documentclass[handout]{beamer}
+\documentclass[t,12pt,numbers,fleqn]{beamer}
+%\documentclass[ignorenonframetext]{beamer}
+
+\newif\ifquestions
+%\questionstrue
+\questionsfalse
+
+\usepackage{pgfpages}
+\usepackage{hyperref}
+\hypersetup{colorlinks=true,
+ linkcolor=blue,
+ citecolor=blue,
+ filecolor=blue,
+ urlcolor=blue,
+ unicode=false}
+\urlstyle{same}
+
+\bibliographystyle{plain}
+
+%\usetheme{Iimenau}
+
+\useoutertheme{split} %so the footline can be seen, without needing pgfpages
+
+%\pgfpagesuselayout{resize to}[letterpaper,border shrink=5mm,landscape] %if this is uncommented, the hyperref links do not work
+
+\mode<presentation>{}
+
+\input{../def-beamer}
+
+\newcommand{\topic}{10 Verification and Validation Continued}
+
+\input{../titlepage}
+
+\begin{document}
+
+\input{../footline}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Verification and Validation Continued}
+
+\bi
+\item Administrative details
+\item Questions?
+\ei
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Administrative Details}
+
+\bi
+\item GitHub issues for colleagues
+\ei
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Administrative Details: Deadlines}
+~\newline
+\begin{tabular}{l l l}
+\textbf{V\&V Present} & Week 06 & Week of Oct 16\\
+\textbf{V\&V Plan} & Week 07 & Oct 25\\
+MG Present & Week 08 & Week of Oct 30\\
+MG & Week 09 & Nov 8\\
+MIS Present & Week 10 & Week of Nov 13\\
+MIS & Week 11 & Nov 22\\
+Impl.\ Present & Week 12 & Week of Nov 27\\
+Final Documentation & Week 13 & Dec 6\\
+\end {tabular}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Administrative Details: Presentation Schedule}
+
+\bi
+\item V\&V Present
+\bi
+\item \textbf{Tuesday: Steven, Alexandre P., Alexander S.}
+\item \textbf{Friday: Geneva, Jason, Yuzhi}
+\ei
+\item MG Present
+\bi
+\item Tuesday: Xiaoye, Shusheng, Devi, Keshav, Alex P, Paul
+\item Friday: Yuzhi, Jason, Geneva, Alex S, Isobel, Steven
+\ei
+\item MIS Present
+\bi
+\item Tuesday: Isobel, Keshav, Paul
+\item Friday: Shusheng, Xiaoye, Devi
+\ei
+\item Impl.\ Present
+\bi
+\item Tuesday: Alexander S., Steven, Alexandre P.
+\item Friday: Jason, Geneva, Yuzhi
+\ei
+
+\ei
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Questions?}
+\begin{itemize}
+\item Questions about ...
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[allowframebreaks]
+\frametitle{References}
+
+\bibliography{../../ReferenceMaterial/References}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\end{document}
\ No newline at end of file
diff --git a/Lectures/L11_VnVPresent1/VnVPresent1.tex b/Lectures/L11_VnVPresent1/VnVPresent1.tex
new file mode 100755
index 0000000000000000000000000000000000000000..f17f9c80dded2e3e61f31f3265c28b3a00e221bf
--- /dev/null
+++ b/Lectures/L11_VnVPresent1/VnVPresent1.tex
@@ -0,0 +1,53 @@
+%\documentclass[handout]{beamer}
+\documentclass[t,12pt,numbers,fleqn]{beamer}
+%\documentclass[ignorenonframetext]{beamer}
+
+\newif\ifquestions
+%\questionstrue
+\questionsfalse
+
+\usepackage{pgfpages}
+\usepackage{hyperref}
+\hypersetup{colorlinks=true,
+ linkcolor=blue,
+ citecolor=blue,
+ filecolor=blue,
+ urlcolor=blue,
+ unicode=false}
+\urlstyle{same}
+
+\bibliographystyle{plain}
+
+%\usetheme{Iimenau}
+
+\useoutertheme{split} %so the footline can be seen, without needing pgfpages
+
+%\pgfpagesuselayout{resize to}[letterpaper,border shrink=5mm,landscape] %if this is uncommented, the hyperref links do not work
+
+\mode<presentation>{}
+
+\input{../def-beamer}
+
+\newcommand{\topic}{11 Verification and Validation Presentations}
+
+\input{../titlepage}
+
+\begin{document}
+
+\input{../footline}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Verification and Validation Presentations}
+
+\bi
+\item Steven
+\item Alexandre P
+\item Alexander S
+\ei
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\end{document}
\ No newline at end of file
diff --git a/Lectures/L12_VnVPresent2/VnVPresent2.tex b/Lectures/L12_VnVPresent2/VnVPresent2.tex
new file mode 100755
index 0000000000000000000000000000000000000000..d086952e42bba3348a1cd81c817fb70893ab70c9
--- /dev/null
+++ b/Lectures/L12_VnVPresent2/VnVPresent2.tex
@@ -0,0 +1,53 @@
+%\documentclass[handout]{beamer}
+\documentclass[t,12pt,numbers,fleqn]{beamer}
+%\documentclass[ignorenonframetext]{beamer}
+
+\newif\ifquestions
+%\questionstrue
+\questionsfalse
+
+\usepackage{pgfpages}
+\usepackage{hyperref}
+\hypersetup{colorlinks=true,
+ linkcolor=blue,
+ citecolor=blue,
+ filecolor=blue,
+ urlcolor=blue,
+ unicode=false}
+\urlstyle{same}
+
+\bibliographystyle{plain}
+
+%\usetheme{Iimenau}
+
+\useoutertheme{split} %so the footline can be seen, without needing pgfpages
+
+%\pgfpagesuselayout{resize to}[letterpaper,border shrink=5mm,landscape] %if this is uncommented, the hyperref links do not work
+
+\mode<presentation>{}
+
+\input{../def-beamer}
+
+\newcommand{\topic}{12 Verification and Validation Presentations}
+
+\input{../titlepage}
+
+\begin{document}
+
+\input{../footline}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Verification and Validation Presentations}
+
+\bi
+\item Geneva
+\item Jason
+\item Yuzhi
+\ei
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\end{document}
\ No newline at end of file
diff --git a/Lectures/L13_ModularDesign/ModularDesign.tex b/Lectures/L13_ModularDesign/ModularDesign.tex
new file mode 100755
index 0000000000000000000000000000000000000000..d77c64c6d205887133eb2112ff00392917995a46
--- /dev/null
+++ b/Lectures/L13_ModularDesign/ModularDesign.tex
@@ -0,0 +1,133 @@
+%\documentclass[handout]{beamer}
+\documentclass[t,12pt,numbers,fleqn]{beamer}
+%\documentclass[ignorenonframetext]{beamer}
+
+\newif\ifquestions
+%\questionstrue
+\questionsfalse
+
+\usepackage{pgfpages}
+\usepackage{hyperref}
+\hypersetup{colorlinks=true,
+ linkcolor=blue,
+ citecolor=blue,
+ filecolor=blue,
+ urlcolor=blue,
+ unicode=false}
+\urlstyle{same}
+
+\bibliographystyle{plain}
+
+%\usetheme{Iimenau}
+
+\useoutertheme{split} %so the footline can be seen, without needing pgfpages
+
+%\pgfpagesuselayout{resize to}[letterpaper,border shrink=5mm,landscape] %if this is uncommented, the hyperref links do not work
+
+\mode<presentation>{}
+
+\input{../def-beamer}
+
+\newcommand{\topic}{13 Modular Design}
+
+\input{../titlepage}
+
+\begin{document}
+
+\input{../footline}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Modular Design}
+
+\bi
+\item Administrative details
+\item Questions?
+\item License and copyright
+\item Integration Testing %L34
+\ei
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Administrative Details}
+
+\bi
+\item GitHub issues for colleagues
+\ei
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Administrative Details: Deadlines}
+~\newline
+\begin{tabular}{l l l}
+\textbf{SRS} & Week 05 & Oct 4\\
+\textbf{V\&V Present} & Week 06 & Week of Oct 16\\
+\textbf{V\&V Plan} & Week 07 & Oct 25\\
+MG Present & Week 08 & Week of Oct 30\\
+MG & Week 09 & Nov 8\\
+MIS Present & Week 10 & Week of Nov 13\\
+MIS & Week 11 & Nov 22\\
+Impl.\ Present & Week 12 & Week of Nov 27\\
+Final Documentation & Week 13 & Dec 6\\
+\end {tabular}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Administrative Details: Presentation Schedule}
+
+\bi
+\item V\&V Present
+\bi
+\item Tuesday: Steven, Alexandre P., Alexander S.
+\item Friday: Geneva, Jason, Yuzhi
+\ei
+\item MG Present
+\bi
+\item Tuesday: Xiaoye, Shusheng, Devi, Keshav, Alex P, Paul
+\item Friday: Yuzhi, Jason, Geneva, Alex S, Isobel, Steven
+\ei
+\item MIS Present
+\bi
+\item Tuesday: Isobel, Keshav, Paul
+\item Friday: Shusheng, Xiaoye, Devi
+\ei
+\item Impl.\ Present
+\bi
+\item Tuesday: Alexander S., Steven, Alexandre P.
+\item Friday: Jason, Geneva, Yuzhi
+\ei
+
+\ei
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Questions?}
+\begin{itemize}
+\item Questions about ...
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[allowframebreaks]
+\frametitle{References}
+
+\bibliography{../../ReferenceMaterial/References}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\end{document}
\ No newline at end of file
diff --git a/Repos.xlsx b/Repos.xlsx
index 611bd59cba3dbd8209310054166800a792635d18..4bd32edf4838af32d32b90cd62347473affbdc38 100644
Binary files a/Repos.xlsx and b/Repos.xlsx differ