X-Git-Url: https://melusine.eu.org/syracuse/G/git/?p=delaunay.git;a=blobdiff_plain;f=doc%2Fluamesh-doc.tex;fp=doc%2Fluamesh-doc.tex;h=75a12510d1a7cdab12fb8c5de13a4d7ae1d67d1d;hp=80469eb7bedb79cce110f2f480f440c8868771d4;hb=1b7b34394c35546e9ae75eb3d61e71626922a82c;hpb=b8c8621a9a46ea7e87e0684988471eee782c9368

diff --git a/doc/luamesh-doc.tex b/doc/luamesh-doc.tex
index 80469eb..75a1251 100644
--- a/doc/luamesh-doc.tex
+++ b/doc/luamesh-doc.tex
@@ -12,7 +12,7 @@
 \usepackage{enumitem}
 \usepackage[tikz]{bclogo}
 \usepackage{wrapfig}
-
+\usepackage{animate}
 
 \title{\Verb+luamesh+: compute and draw meshes with \lualatex}
 \author{Maxime Chupin \email{mc@melusine.eu.org}}
@@ -609,7 +609,7 @@ and \Verb+endfig;+ commands to produce a picture. Indeed, this allows
 to use the \Verb+\everymplib+ command from the \Verb+\luamplib+ package.
 \end{warning}
 
-\subsubsection{The \LaTeX{} Colors Inside the MetaPost Code}
+\subsubsection{The \LaTeX{} Colors Inside the MetaPost Code}\label{sec:mpcolor}
 
 The configurable colors
 of the \LaTeX{} macro are accessible inside the MetaPost code. For
@@ -757,6 +757,323 @@ Once again these coordinates are not yet defined for the \meta{code
   }
 \end{Exemple}
 
+\section{Voronio Diagrams}
+
+Another interesting concept of Delaunay triangulation is that it is
+\emph{dual} to it so-called Voronio diagram. For a finite set of
+points $\{p_{1},\ldots, p_{n}\}$ in the Euclidean plane, for all
+$p_{k}$, it corresponds a Voronoi cell $R_{k}$ consisting of
+every point in the Euclidean plane whose distance to $p_{k}$ is less
+than
+or equal to its distance to any other $p_{k'}$.\bigskip
+
+
+\commande|\buildVoronoiBW[«options»]{«list of points» or «file  name»}|\medskip
+
+This macro produce the Voronio diagram dual to the Delaunay
+triangulation (computed by the Bowyer and Watson
+algorithm) of the given \meta{list of points}. Once again, the
+list of
+points must be given in the following way :
+\begin{center}
+  \verb+(x1,y1);(x2,y2);(x3,y3);...;(xn,yn)+
+\end{center}
+
+\begin{Exemple}
+  \buildVoronoiBW{(0.3,0.3);(1.5,1);(4,0);(4.5,2.5);(1.81,2.14);(2.5,0.5);(2.8,1.5);(0.1,2);(1.5,-0.3)}
+\end{Exemple}
+
+\subsection{The Options}\label{sec:voronoiOptions}
+
+
+There are several options to customize the drawing.
+\begin{optionsenum}
+\item[mode = int (default) \textme{or} ext:] this option allows to
+  use either the previously described set of points in the argument, or
+  a file, containing, line by line (2 columns), the points. Such a
+  file looks like :
+\begin{verbatim}
+x1  y1
+x2  y2
+x3  y3
+...
+xn yn
+\end{verbatim}
+\item[bbox = none (default) \textme{or} show:] this option allows to draw the
+  added points to form a \emph{bounding box}\footnote{The bounding
+    box is defined by four points place at 15\% around the box
+    defined by $(x_{\min},y_{\min})$, $(x_{\min},y_{\max})$,
+    $(x_{\max},y_{\max})$, and $(x_{\min},y_{\max})$. It is used by
+    the algorithm and will be computed in any case.} and the corresponding
+  triangulation. By default, these points are removed at the end of
+  the algorithm.
+\item[color = \meta{value} (default: black):] The color of the
+  drawing.
+\item[colorBbox = \meta{value} (default: black):] The color of the
+  drawing for the elements (points and triangles) belonging to the
+  bounding box.
+\item[colorVoronoi = \meta{value} (default: black):] The color of the
+  drawing for the elements (points and polygons) belonging to the
+  Voronoi diagram.
+\item[print = none (default) \textme{or} points:] To label the vertices of the
+  triangulation. Contrary to the previous macros, where
+  \Verb+print=none+,  a \emph{dot} is produced at each vertex (of the
+  set of points and on the circumcircle center which are the nodes of
+  the Voronoi diagram).
+\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
+  label the vertices of the triangulation. It is included in the math
+  mode delimiters \Verb+$...$+. The bounding box points are labeled
+  with numbers 1 to 4 and with a star exponent.
+\item[circumpoint = \meta{value} (default: P):] The letter(s) used to
+  label the vertices of the Voronoi diagram. It is included in the math
+  mode delimiters \Verb+$...$+.
+\item[tikz (boolean, default:false):] By default, this boolean is set
+  to \Verb+false+, and MetaPost (with \Verb+luamplib+) is used to draw
+  the picture. With this option, \Verb+tikz+ becomes the \textit{drawing
+    engine}.
+\item[scale = \meta{value} (default: 1cm):] The scale option defines
+  the scale at which the picture is drawn (the same for both
+  axes). It must contain the unit of length (cm,
+  pt, etc.).
+\end{optionsenum}
+
+
+\subsection{The \emph{inc} variant}
+
+Once again, a variant of the macros is available allowing the user to
+add code before and after the code produced by \luamesh. We refer to
+the section~\ref{sec:inc} because it works the same way.
+
+Let us note that:
+\begin{itemize}
+\item with MetaPost, the circumcenters are defined using
+  \Verb+pair CircumPoints[];+, and so, are accessible.
+\item With \Verb+tikz+, there are new coordinates defined as follows
+  \begin{latexcode}
+    \coordinate (CircumPoints1) at (...,...);
+    \coordinate (CircumPoints2) at (...,...);
+    \coordinate (CircumPoints3) at (...,...);
+    % etc.
+  \end{latexcode}
+\end{itemize}
+
+Finally, when the MetaPost drawing engine is used, another color is
+available (see~\ref{sec:mpcolor}): \Verb+\luameshmpcolorVoronoi+.
+
+
+\section{With Gmsh}
+
+Gmsh is a open source efficient software that produces meshes. The
+exporting format is the \emph{MSH ASCII file format} and can be easily
+read by a Lua program. \luamesh provides the user with dedicated
+macros to read and draw meshes coming from a Gmsh exportation.\bigskip
+
+\commande|\drawGmsh[«options»]{«file  name»}|\medskip
+
+This macro draw the triangulation produced by Gmsh and exported in the
+\Verb+msh+ format. The argument is the name of the file to read
+(e.g.: \Verb+maillage.msh+).
+
+\begin{Exemple}
+\drawGmsh{maillage.msh}
+\end{Exemple}
+
+There are several options to customize the drawing.
+\begin{optionsenum}
+\item[color = \meta{value} (default: black):] The color of the
+  drawing.
+\item[print = none (default) \textme{or} points:] To label the vertices of the
+  triangulation. Contrary to the previous macros, where
+  \Verb+print=none+,  a \emph{dot} is produced at each vertex (of the
+  set of points and on the circumcircle center which are the nodes of
+  the Voronoi diagram).
+\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
+  label the vertices of the triangulation. It is included in the math
+  mode delimiters \Verb+$...$+. The bounding box points are labeled
+  with numbers 1 to 4 and with a star exponent.
+\item[tikz (boolean, default:false):] By default, this boolean is set
+  to \Verb+false+, and MetaPost (with \Verb+luamplib+) is used to draw
+  the picture. With this option, \Verb+tikz+ becomes the \textit{drawing
+    engine}.
+\item[scale = \meta{value} (default: 1cm):] The scale option defines
+  the scale at which the picture is drawn (the same for both
+  axes). It must contain the unit of length (cm,
+  pt, etc.).
+\end{optionsenum}
+Here is an example:
+\begin{Exemple}
+  \drawGmsh[scale=2cm,print=points, color=blue!30]{maillage.msh}
+\end{Exemple}
+
+\subsection{Gmsh and Voronoi Diagrams}
+
+Because Gmsh generates Delaunay triangulations, we can plot the
+Voronoi diagram associated. This is done by the following macro:\bigskip
+
+\commande|\gmshVoronoi[«options»]{«file name»}|\medskip
+
+\begin{Exemple}
+  \gmshVoronoi{maillage.msh}
+\end{Exemple}
+
+We refer to the section~\ref{sec:voronoiOptions} for the list of the options.
+
+\subsection{The \emph{inc} variants}
+
+Once again, there exists \emph{inc} variant macros:\bigskip
+
+\commande|\drawGmshinc[«options»]{«file name»}{«code before»}{«code after»}|\medskip
+
+\commande|\gmshVoronoiinc[«options»]{«file name»}{«code before»}{«code after»}|\medskip
+
+We refer to the previous sections for explanations.
+
+\section{Gallery}
+\subsection{With Animate}
+
+If you use \emph{adobe acrobat reader}, you can easily produce an
+animation of the Bowyer and Watson algorithm with the package
+\Verb+animate+.
+
+For example, the following code (in a file name \Verb+animation.tex+):
+\begin{latexcode}
+  \documentclass{article}
+  %% lualatex compilation
+  \usepackage[margin=2.5cm]{geometry}
+  \usepackage{luamesh}
+  \usepackage{fontspec}
+  \usepackage{multido}
+  \pagestyle{empty}
+
+  \def\drawPath{draw (-2,-2)*u--(8,-2)*u--(8,6)*u--(-2,6)*u--cycle  withcolor 0.99white;}
+  \def\clipPath{clip currentpicture to (-2,-2)*u--(8,-2)*u--(8,6)*u--(-2,6)*u--cycle;}
+
+  \begin{document}
+
+  \drawPointsMeshinc[
+  mode=ext,
+  bbox = show,
+  colorBbox = blue!20,
+  print=points
+  ]
+  {mesh.txt}%
+  {%
+    beginfig(0);
+    \drawPath
+  }%
+  {%
+    \clipPath
+    endfig;
+  }
+  \newpage
+  \buildMeshBWinc[
+  mode=ext,
+  bbox = show,
+  colorBbox = blue!20,
+  print=points
+  ]
+  {meshInit.txt}%
+  {%
+    beginfig(0);
+    \drawPath
+  }%
+  {%
+    \clipPath
+    endfig;
+  }
+  \multido{\ii=5+1}{4}{%
+    \newpage
+    \meshAddPointBWinc[
+    mode=ext,step=badtriangles,
+    colorNew =green!20!red,
+    colorBack=red!10,
+    colorCircle = blue,
+    bbox = show,
+    colorBbox = blue!20
+    ]
+    {mesh.txt}{\ii}%
+    {%
+      beginfig(0);
+      \drawPath
+    }%
+    {%
+      \clipPath
+      endfig;
+    }   \newpage
+    \meshAddPointBWinc[
+    mode=ext,step=cavity,
+    colorNew =green!20!red,
+    colorBack=red!10,
+    colorCircle = blue,
+    bbox = show,
+    colorBbox = blue!20
+    ]
+    {mesh.txt}{\ii}%
+    {%
+      beginfig(0);
+      \drawPath
+    }%
+    {%
+      \clipPath
+      endfig;
+    }  \newpage
+    \meshAddPointBWinc[
+    mode=ext,step=newtriangles,
+    colorNew =green!20!red,
+    colorBack=red!10,
+    colorCircle = blue,
+    bbox = show,
+    colorBbox = blue!20]
+    {mesh.txt}{\ii}%
+    {%
+      beginfig(0);
+      \drawPath
+    }%
+    {%
+      \clipPath
+      endfig;
+    }
+  }
+  \newpage
+  \buildMeshBWinc[
+  mode=ext,
+  bbox = show,
+  colorBbox = blue!20,
+  print=points
+  ]
+  {mesh.txt}%
+  {%
+    beginfig(0);
+    \drawPath
+  }%
+  {%
+    \clipPath
+    endfig;
+  }
+  \newpage
+  \buildMeshBWinc[
+  mode=ext,
+  print=points
+  ]
+  {mesh.txt}%
+  {%
+    beginfig(0);
+    \drawPath
+  }%
+  {%
+    \clipPath
+    endfig;
+  }
+\end{document}
+\end{latexcode}
+produces a PDF with multiple pages. Using the \Verb+pdfcrop+ program,
+we crop the pages to the material, and then we can animate the PDF
+using the \Verb+animate+ package.
+
+%\begin{Exemple}
+%\animategraphics[controls]{1}{animation-crop}{}{}
+%\end{Exemple}
+
 \input{dum.bbl}
 
 \end{document}