Examples/MeshGenToolbox/doc/testingApp.tex

+\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}

Examples/MeshGenToolbox/doc/uh.eps

+%!PS-Adobe-3.0 EPSF-3.0
+%%Title: (Slide 1)
+%%Version: 1 4
+%%Creator: Adobe Acrobat 6.0
+%%CreationDate: 13:37:41 12/26/06
+%%For: (Wen Yu)
+%%DocumentData: Clean7Bit
+%%BoundingBox: 29 62 747 599
+%%HiResBoundingBox: 29.0 62.0 747.0 599.0
+%%Pages: 0
+%%DocumentProcessColors: Black
+%%DocumentNeededResources: (atend)
+%%DocumentSuppliedResources:
+%%+ procset (Adobe Acrobat - PDF operators) 1.2 0
+%%+ procset (Adobe Acrobat - type operators) 1.2 0
+%%+ procset (Adobe Acrobat - general image support) 1.2 0
+%%+ procset (Adobe Acrobat - monochrome image support) 1.2 0
+%%+ procset (Adobe Acrobat - color image support) 1.2 0
+%%+ procset (Adobe Acrobat - indexed color image support) 1.2 0
+%%EndComments
+%%BeginProlog
+%%EndProlog
+%%BeginSetup
+%ADOPrintSettings: L1 W0 VM op crd os scsa T h EF bg ucr sf ef r b fa pr SEPS ttf HB  0
+%%BeginResource: file Pscript_T42Hdr PSVER
+userdict /ct_T42Dict 15 dict put
+ct_T42Dict begin
+/Is2015?
+{
+  version
+  cvi
+  2015
+  ge
+} bind def
+/AllocGlyphStorage
+{
+  Is2015?
+  {	
+		pop
+  } 
+  { 
+		{string} forall
+  } ifelse
+} bind def
+/Type42DictBegin
+{
+	25 dict begin
+  /FontName exch def
+  /CharStrings 256 dict 
+	begin
+		  /.notdef 0 def
+		  currentdict 
+	end def
+  /Encoding exch def
+  /PaintType 0 def
+  /FontType 42 def
+  /FontMatrix [1 0 0 1 0 0] def
+  4 array  astore cvx /FontBBox exch def
+  /sfnts
+} bind def
+/Type42DictEnd  
+{
+	 currentdict dup /FontName get exch definefont end
+	ct_T42Dict exch
+	dup /FontName get exch put
+} bind def
+/RD {string currentfile exch readstring pop} executeonly def
+/PrepFor2015
+{
+	Is2015?
+	{		  
+		 /GlyphDirectory 
+		 16
+		 dict def
+		 sfnts 0 get
+		 dup
+		 2 index
+		 (glyx)
+		 putinterval
+		 2 index  
+		 (locx)
+		 putinterval
+		 pop
+		 pop
+	}
+	{
+		 pop
+		 pop
+	} ifelse			
+} bind def
+/AddT42Char
+{
+	Is2015?
+	{
+		/GlyphDirectory get 
+		begin
+		def
+		end
+		pop
+		pop
+	}
+	{
+		/sfnts get
+		4 index
+		get
+		3 index
+	  2 index
+		putinterval
+		pop
+		pop
+		pop
+		pop
+	} ifelse
+} bind def
+end
+%%EndResource
+%%BeginResource: procset Adobe_CoolType_Utility_MAKEOCF 1.16 0
+%%Copyright: Copyright 1987-2003 Adobe Systems Incorporated.
+%%Version: 1.16 0
+systemdict /languagelevel known dup
+	{ currentglobal false setglobal }
+	{ false }
+ifelse
+exch
+userdict /Adobe_CoolType_Utility 2 copy known
+	{ 2 copy get dup maxlength 25 add dict copy }
+	{ 25 dict }
+ifelse put
+Adobe_CoolType_Utility
+	begin
+	/ct_Level2? exch def
+	/ct_Clone? 1183615869 internaldict dup
+			/CCRun known not
+			exch /eCCRun known not
+			ct_Level2? and or def
+ct_Level2?
+	{ globaldict begin currentglobal true setglobal }
+if
+	/ct_AddStdCIDMap
+		ct_Level2?
+			{ {
+			((Hex) 57 StartData
+			0615 1e27 2c39 1c60 d8a8 cc31 fe2b f6e0
+			7aa3 e541 e21c 60d8 a8c9 c3d0 6d9e 1c60
+			d8a8 c9c2 02d7 9a1c 60d8 a849 1c60 d8a8
+			cc36 74f4 1144 b13b 77) 0 () /SubFileDecode filter cvx exec
+			} }
+			{ {
+			<BAB431EA07F209EB8C4348311481D9D3F76E3D15246555577D87BC510ED54E
+		 118C39697FA9F6DB58128E60EB8A12FA24D7CDD2FA94D221FA9EC8DA3E5E6A1C
+			4ACECC8C2D39C54E7C946031DD156C3A6B4A09AD29E1867A> eexec
+			} }
+		ifelse bind def
+ct_Level2?
+	{ end setglobal }
+if
+	/ct_UseNativeCapability?  systemdict /composefont known def
+	/ct_MakeOCF 35 dict def
+	/ct_Vars 25 dict def
+	/ct_GlyphDirProcs 6 dict def
+	/ct_BuildCharDict 15 dict dup
+		begin
+		/charcode 2 string def
+		/dst_string 1500 string def
+		/nullstring () def
+		/usewidths? true def
+		end def
+	ct_Level2? { setglobal } { pop } ifelse
+	ct_GlyphDirProcs
+		begin
+		/GetGlyphDirectory
+			{
+			systemdict /languagelevel known
+				{ pop /CIDFont findresource /GlyphDirectory get }
+				{
+				1 index /CIDFont findresource /GlyphDirectory
+				get dup type /dicttype eq
+					{
+					dup dup maxlength exch length sub 2 index lt
+						{
+						dup length 2 index add dict copy 2 index
+						/CIDFont findresource/GlyphDirectory 2 index put
+						}
+					if
+					}
+				if
+				exch pop exch pop
+				}
+			ifelse
+			+
+			} def
+		/+
+			{
+			systemdict /languagelevel known
+				{
+				currentglobal false setglobal
+				3 dict begin
+					/vm exch def
+				}
+				{ 1 dict begin }
+			ifelse
+			/$ exch def
+			systemdict /languagelevel known
+				{
+				vm setglobal
+				/gvm currentglobal def
+				$ gcheck setglobal
+				}
+			if
+			? { $ begin } if
+			} def
+		/? { $ type /dicttype eq } def
+		/| {
+			userdict /Adobe_CoolType_Data known
+				{
+			Adobe_CoolType_Data /AddWidths? known
+				{
+				 currentdict Adobe_CoolType_Data
+					begin
+					  begin
+						AddWidths?
+								{
+								Adobe_CoolType_Data /CC 3 index put
+								? { def } { $ 3 1 roll put } ifelse
+								CC charcode exch 1 index 0 2 index 256 idiv put
+								1 index exch 1 exch 256 mod put
+								stringwidth 2 array astore
+								currentfont /Widths get exch CC exch put
+								}
+								{ ? { def } { $ 3 1 roll put } ifelse }
+							ifelse
+					end
+				end
+				}
+				{ ? { def } { $ 3 1 roll put } ifelse }	ifelse
+				}
+				{ ? { def } { $ 3 1 roll put } ifelse }
+			ifelse
+			} def
+		/!
+			{
+			? { end } if
+			systemdict /languagelevel known
+				{ gvm setglobal }
+			if
+			end
+			} def
+		/: { string currentfile exch readstring pop } executeonly def
+		end
+	ct_MakeOCF
+		begin
+		/ct_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
+		 /c5F/c60/c61/c62/c63/c64/c65/c66/c67/c68/c69/c6A/c6B/c6C/c6D/c6E/c6F/c70/c71
+		 /c72/c73/c74/c75/c76/c77/c78/c79/c7A/c7B/c7C/c7D/c7E/c7F/c80/c81/c82/c83/c84
+		 /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
+		/ct_CID_STR_SIZE 8000 def
+		/ct_mkocfStr100 100 string def
+		/ct_defaultFontMtx [.001 0 0 .001 0 0] def
+		/ct_1000Mtx [1000 0 0 1000 0 0] def
+		/ct_raise {exch cvx exch errordict exch get exec stop} bind def
+		/ct_reraise
+			{ cvx $error /errorname get (Error: ) print dup (						  ) cvs print
+					errordict exch get exec stop
+			} bind def
+		/ct_cvnsi
+			{
+			1 index add 1 sub 1 exch 0 4 1 roll
+				{
+				2 index exch get
+				exch 8 bitshift
+				add
+				}
+			for
+			exch pop
+			} bind def
+		/ct_GetInterval
+			{
+			Adobe_CoolType_Utility /ct_BuildCharDict get
+				begin
+				/dst_index 0 def
+				dup dst_string length gt
+					{ dup string /dst_string exch def }
+				if
+				1 index ct_CID_STR_SIZE idiv
+				/arrayIndex exch def
+				2 index arrayIndex  get
+				2 index
+				arrayIndex ct_CID_STR_SIZE mul
+				sub
+					{
+					dup 3 index add 2 index length le
+						{
+						2 index getinterval
+						dst_string  dst_index 2 index putinterval
+						length dst_index add /dst_index exch def
+						exit
+						}
+						{
+						1 index length 1 index sub
+						dup 4 1 roll
+						getinterval
+						dst_string  dst_index 2 index putinterval
+						pop dup dst_index add /dst_index exch def
+						sub
+						/arrayIndex arrayIndex 1 add def
+						2 index dup length arrayIndex gt
+							  { arrayIndex get }
+							  {
+							  pop
+							  exit
+							  }
+						ifelse
+						0
+						}
+					ifelse
+					}
+				loop
+				pop pop pop
+				dst_string 0 dst_index getinterval
+				end
+			} bind def
+		ct_Level2?
+			{
+			/ct_resourcestatus
+			currentglobal mark true setglobal
+				{ /unknowninstancename /Category resourcestatus }
+			stopped
+				{ cleartomark setglobal true }
+				{ cleartomark currentglobal not exch setglobal }
+			ifelse
+				{
+					{
+					mark 3 1 roll /Category findresource
+						begin
+						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
+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
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+/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
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+PDFVars/TermAll get exec end end
+%%PageTrailer
+%%Trailer
+%%DocumentNeededResources:
+%%+ font Arial-BoldMT
+%%EOF

Examples/MeshGenToolbox/mgt/Cell.h

+/*****************************************************************************/
+/*  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

Examples/MeshGenToolbox/mgt/Coarsening.cpp

+/*****************************************************************************/
+/*  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
+
+}

Examples/MeshGenToolbox/mgt/Coarsening.h

+/*****************************************************************************/
+/*  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);
+};
+}

Examples/MeshGenToolbox/mgt/Edge.h

+/*****************************************************************************/
+/*  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

Examples/MeshGenToolbox/mgt/Input.cpp

+/*****************************************************************************/
+/*  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);
+	}
+}
+

Examples/MeshGenToolbox/mgt/Input.h

+/*****************************************************************************/
+/*  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);
+};
+}
+
+

Examples/MeshGenToolbox/mgt/Mesh.cpp

+/*****************************************************************************/
+/*  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;
+		}
+	}
+
+
+//}
+}

Examples/MeshGenToolbox/mgt/Mesh.h

+/*****************************************************************************/
+/*  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_;
+
+
+};
+
+
+//}
+
+}

Examples/MeshGenToolbox/mgt/Output.cpp

+/*****************************************************************************/
+/*  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);
+	}
+
+}

Examples/MeshGenToolbox/mgt/Output.h

+/*****************************************************************************/
+/*  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);
+};
+}
+
+

Examples/MeshGenToolbox/mgt/Refining.cpp

+/*****************************************************************************/
+/*  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
+
+	}
+
+
+
+}

Examples/MeshGenToolbox/mgt/Refining.h

+/*****************************************************************************/
+/*  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);
+
+};
+}

Examples/MeshGenToolbox/mgt/Service.cpp

+/*****************************************************************************/
+/*  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;
+}
+
+
+}
+

Examples/MeshGenToolbox/mgt/Service.h

+/*****************************************************************************/
+/*  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);
+
+
+};
+}
+

Examples/MeshGenToolbox/mgt/Vertex.h

+/*****************************************************************************/
+/*  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

Examples/MeshGenToolbox/mgt/makefile

+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