every listing line={\textcolor{red}{\small\ttfamily\bfseries user \$> }}}
\newtcblisting{latexcode}{
- arc=0pt,
+ arc=0pt,outer arc=0pt,
+ colback=red!2!white,
+ colframe=red!75!black,
+ breakable,
+ boxsep=0pt,left=5pt,right=5pt,top=5pt,bottom=5pt, bottomtitle =
+ 3pt, toptitle=3pt,
+ boxrule=0pt,bottomrule=0.5pt,toprule=0.5pt, toprule at break =
+ 0pt, bottomrule at break = 0pt,
listing only,boxsep=0pt,listing
- options={style=tcblatex}}
+ options={breaklines}
+}
\newcommand\luamesh{\Verb+luamesh+\xspace}
set of points, a particular step of the algorithm.
\end{abstract}
+I would like to thank Jean-Michel Sarlat, who hosts the development
+with a git project on the \Verb+melusine+ machine:
+\begin{center}
+ \url{https://melusine.eu.org/syracuse/G/delaunay/}
+\end{center}
+Then, I would like to thank the first user, and an intensive
+\emph{test} user: Nicole Spillane.
+
\section{Installation}
-\subsection{With Linux}
+
+Of course, you can just put the two files \Verb+luamesh.lua+ and
+\Verb+luamesh.sty+ in the working directory, but it is not
+recommended.
+
+
+\subsection{With \TeX live and Linux or Mac OSX}
To install \luamesh with \TeX live, you have to create the local
\Verb+texmf+ directory in your \Verb+home+.
\usepackage{luamesh}
\end{latexcode}
+\subsection{With Mik\TeX{} and Windows}
+
+We do not know these two systems, so we refer to the
+documentation for integrating local additions to Mik\TeX:
+\begin{center}
+ \url{http://docs.miktex.org/manual/localadditions.html}
+\end{center}
+
+
+\subsection{A \lualatex package}
+
+If you want to use this package, you must compile your document with
+\Verb+lualatex+:
+
+\begin{commandshell}
+ lualatex mylatexfile.tex
+\end{commandshell}
+
+
\subsection{Dependencies}
This package is built upon two main packages to draw the
\begin{enumerate}
\item \Verb+luamplib+ to use MetaPost via the \luatex library
\Verb+mplib+;
-\item or \Verb+tikz+.
+\item and \Verb+tikz+.
\end{enumerate}
We will see how to choose between these two \emph{drawing engines}.
\section{The Basic Macros}
-If you want to use this package, you must compile your document with
-\Verb+lualatex+:
-
-\begin{commandshell}
- lualatex mylatexfile.tex
-\end{commandshell}
-
Let us recall that this package provides macros to draw two
dimensional triangulations (or meshes).
-\subsection{Draw a Complete Mesh}
+\subsection{Draw a Complete Mesh}\label{sec:buildMesh}
\commande|\buildMeshBW[«options»]{«list of points» or «file name»}|\medskip
There are several options to customize the drawing.
\begin{optionsenum}
-\item[mode = int (default) or ext:] this option allows to
+\item[mode = int (default) \textme{or} ext:] this option allows to
use either the previously described set of point in the argument, or
a file, containing, line by line (2 columns), the points. Such a
file looks like :
...
xn yn
\end{verbatim}
-\item[bbox = none (default) or show:] this option allows to draw the
+\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 $(x_{\min},y_{\min})$, $(x_{\min},y_{\max})$,
\item[colorBbox = \meta{value} (default: black):] The color of the
drawing for the elements (points and triangles) belonging to the
bounding box.
-\item[print = none (default) or points:] To label the vertices of the
+\item[print = none (default) \textme{or} points:] To label the vertices of the
triangulations with an adding dot.
\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
label the vertices of the triangulation. It is include in the math
\subsection{Draw the Set of Points}
-\commande|\drawPointsMesh[«options»]{«list of points» or «file name»}|
+\commande|\drawPointsMesh[«options»]{«list of points» or «file name»}|\medskip
+
+With the \Verb+\drawPointsMesh+, we plot the set of the points from
+which the Browyer and Watson algorithm compute the triangulation.
+
+The use of this macro is quite similar to the
+\Verb+\buildMeshBW+. Here is an example of the basic uses.
+\begin{Exemple}
+ \drawPointsMesh{(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)}
+\end{Exemple}
+
+
+\subsubsection{The Options}
+
+There are several options (exactly the same that for the
+\Verb+\buildMeshBW+)to customize the drawing.
+\begin{optionsenum}
+\item[mode = int (default) \textme{or} ext:] this option allows to
+ use either the previously described set of point 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} and the corresponding
+ triangulation. By default, these triangles are removed at the end of
+ the algorithm. \emph{Here, because we plot only the vertices of the
+ mesh, there is no triangles, but only dots.}
+\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[print = none (default) \textme{or} points:] To label the vertices of the
+ triangulations with an adding dot. Without label, there is a dot.
+\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
+ label the vertices of the triangulation. It is include in the math
+ mode delimiters \Verb+$...$+. The bounding box points are labeled
+ with a star exponent, and numbered from 1 to 4.
+\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, it is \Verb+tikz+ the \textit{drawing
+ engine}.
+\item[scale = \meta{value} (default: 1cm):] The scale option defines
+ the scale at which the picture is draw (the same for the two
+ axis). It must contain the unit of length (cm,
+ pt, etc.).
+\end{optionsenum}
+With the same external mesh point file presented in
+section~\ref{sec:buildMesh}, we illustrate the different options.
+
+\begin{Exemple}
+ \drawPointsMesh[%
+ tikz,
+ mode = ext,
+ bbox = show,
+ color = blue,
+ colorBbox = red,
+ print = points,
+ meshpoint = y,
+ scale = 1.3cm,
+ ]{mesh.txt}
+\end{Exemple}
\subsection{Draw a Step of the Bowyer and Watson Algorithm}
-\commande|\meshAddPointBW[«options»]{«list of points» or «file name»}{«point» or «number of line»}|
+\commande|\meshAddPointBW[«options»]{«list of points» or «file name»}{«point» or «number of line»}|\medskip
+
+This command allows to plot the different step of the addition of a
+point in a Delaunay triangulation, using the Bowyer and Watson
+algorithm.
+
+This macro produce the Delaunay triangulation (using the Bowyer and
+Watson algorithm) of the given \meta{list of points} and shows a step
+of the algorithm when the \meta{point} is added. The list of
+points must be given in the following way:
+\begin{center}
+ \verb+(x1,y1);(x2,y2);(x3,y3);...;(xn,yn)+
+\end{center}
+and the point is of the form \verb+(x,y)+. The \meta{file name}
+and \meta{number of line} will be explained in the option
+description.
+
+One can use the macro as fallow:
+\begin{Exemple}
+ \meshAddPointBW[step=badtriangles]{(1.5,1);(4,0);(4.5,2.5);(1.81,2.14);(2.5,0.5);(2.8,1.5)}{(2.2,1.8)}
+ \meshAddPointBW[step=cavity]{(1.5,1);(4,0);(4.5,2.5);(1.81,2.14);(2.5,0.5);(2.8,1.5)}{(2.2,1.8)}
+ \meshAddPointBW[step=newtriangles]{(1.5,1);(4,0);(4.5,2.5);(1.81,2.14);(2.5,0.5);(2.8,1.5)}{(2.2,1.8)}
+\end{Exemple}
+The default value for \Verb+step+ is \Verb+badtriangles+. The first
+line is then equivalent to
+\begin{latexcode}
+\meshAddPointBW{(1.5,1);(4,0);(4.5,2.5);(1.81,2.14);(2.5,0.5);(2.8,1.5)}{(2.2,1.8)}
+\end{latexcode}
+
+\subsubsection{The Options}
+
+There are several options (some of them are the same as for
+\Verb+\buildMeshBW+) to customize the drawing.
+\begin{optionsenum}
+\item[mode = int (default) \textme{or} ext:] this option allows to
+ use either the previously described set of point in the argument
+ number one, 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}
+For the second argument of the macro, if we are in the
+\Verb+mode = ext+, the argument must be the \emph{line number} of the file
+corresponding to the point we want to add. The algorithm will stop the
+line before to build the initial triangulation for which it will add
+the point corresponding to the line. The other lines of the file are
+ignored.
+\item[bbox = none (default) \textme{or} show:] this option allows to draw the
+ added points to form a \emph{bounding box} and the corresponding
+ triangulation. By default, these triangles 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[colorNew = \meta{value} (default: red):] The color of the
+ drawing of the ``new'' elements which are the point to add, the
+ polygon of the cavity, and the new triangles.
+\item[colorBack = \meta{value} (default: black!20):] The color for the
+ filling of the region concerned by the addition of the new point.
+\item[colorCircle = \meta{value} (default: green):] The color for
+ circoncircle of the triangles containing the point to add.
+\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
+ label the vertices of the triangulation. It is include in the math
+ mode delimiters \Verb+$...$+. The bounding box points are labeled
+ with a star exponent, and numbered from 1 to 4.
+\item[step = badtriangles (default) \textme{or} cavity \textme{or}
+ newtriangles:] To choose the step we want to draw, corresponding to
+ the steps of the Bowyer and Watson algorithm.
+\item[newpoint = \meta{value} (default: P):] The letter(s) used to
+ label the new point of the triangulation. It is include 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, it is \Verb+tikz+ the \textit{drawing
+ engine}.
+\item[scale = \meta{value} (default: 1cm):] The scale option defines
+ the scale at which the picture is draw (the same for the two
+ axis). It must contain the unit of length (cm,
+ pt, etc.).
+\end{optionsenum}
+Here is an example of customization of the drawing. First, recall that
+the external file \Verb+mesh.txt+ is:
+\begin{verbatim}
+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
+\end{verbatim}
+We draw the addition of the 6th point. The 7th line will be ignored.
+\begin{Exemple}
+ \meshAddPointBW[
+ tikz,
+ mode = ext,
+ color = blue!70,
+ meshpoint = x,
+ newpoint = y,
+ colorBack=red!10,
+ colorNew = green!20!red,
+ colorCircle = blue,
+ colorBbox = black!20,
+ bbox = show,
+ scale=1.4cm,
+ step=cavity]
+ {mesh.txt}{6}
+\end{Exemple}
\section{The \emph{inc} Macros}\label{sec:inc}
+\subsection{With MetaPost}
+
+%\subsection{With \Verb+tikz+}
+
\section{Gallery of Examples}
\end{document}
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