\documentclass{lltxdoc}
\usepackage{tcolorbox}
-\usepackage{xargs}
\usepackage{enumitem}
\usepackage[tikz]{bclogo}
\usepackage{wrapfig}
+
+
\title{\Verb+luamesh+: compute and draw meshes with \lualatex}
\author{Maxime Chupin \email{mc@melusine.eu.org}}
\date{\today}
+
+\definecolor{darkred}{rgb}{0.8,0.1,0.1}
+
+
\newcommand*\commande{\noindent\hspace{-30pt}%
\SaveVerb[aftersave={%
\UseVerb{Vitem}
\fvset{%
codes={\catcode`\«\active \catcode`\×\active },
defineactive={\makefancyog\makefancytimes},
- formatcom=\color{red},
+ formatcom=\color{darkred},
frame=single
}
% rendre «...» équivalent à \meta{...}
\newcommand\luamesh{\Verb+luamesh+\xspace}
\newenvironment{optionsenum}[1][]
-{\begin{description}[font=\color{red}\ttfamily]}
+{\begin{description}[font=\color{darkred}\ttfamily]}
{\end{description}}
\newenvironment{warning}{%
}%
{\end{tcolorbox}\medskip}
-
-
+\lstset{moredelim=*[s][\color{red}\rmfamily\itshape]{<}{>}}
+\lstset{moredelim=*[s][\color{blue}\rmfamily\itshape]{<<}{>>}}
+\usepackage[colorlinks=true]{hyperref}
\begin{document}
%% === Page de garde ===================================================
\thispagestyle{empty}
\end{tikzpicture}%
\noindent
-\includegraphics{luamesh}\\
+\includegraphics{luamesh-title}\\
{\large compute and draw meshes with \lualatex}\\[1cm]
\parbox{0.6\textwidth}{
\meshAddPointBW[
\maketitle
\begin{abstract}
- The package \Verb|luamesh| allows to compute and draw 2D triangulation
- of Delaunay. The algorithm is written with lua, and depending of the
- choice of the ``engine'', the draw is done by MetaPost (with
+ The package \Verb|luamesh| allows to compute and draw 2D Delaunay
+ triangulation. The algorithm is written with lua, and depending on the
+ choice of the ``engine'', the drawing is done by MetaPost (with
\Verb|luamplib|) or by \Verb|tikz|.
The Delaunay triangulation algorithm is the Bowyer and Watson
algorithm. Several macros are provided to draw the global mesh, the
- set of points, a particular step of the algorithm.
+ set of points, or a particular step of the algorithm.
\end{abstract}
I would like to thank Jean-Michel Sarlat, who hosts the development
\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.
+I would also like to thank the first user, an intensive
+\emph{test} user, and a very kind English corrector: Nicole Spillane.
+
+\tableofcontents
\section{Installation}
Of course, you can just put the two files \Verb+luamesh.lua+ and
-\Verb+luamesh.sty+ in the working directory, but it is not
+\Verb+luamesh.sty+ in the working directory, but this is not
recommended.
mkdir ~/texmf
\end{commandshell}
-Then we have to files to place in the correct directories. First, the
+Then place the files in the correct directories. First, the
\Verb+luamesh.sty+ file must be in the directory:
\begin{center}
\Verb+~/texmf/tex/latex/luamesh/+
\subsection{Dependencies}
-This package is built upon two main packages to draw the
+This package is built upon two main existing packages to draw the
triangulations :
\begin{enumerate}
\item \Verb+luamplib+ to use MetaPost via the \luatex library
\commande|\buildMeshBW[«options»]{«list of points» or «file name»}|\medskip
-This macro produce the Delaunay triangulation (using the Bowyer and
+This macro produces the Delaunay triangulation (using the Bowyer and
Watson algorithm) of the given \meta{list of points}. The list of
points must be given in the following way :
\begin{center}
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 point in the argument, or
+ 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}
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 $(x_{\min},y_{\max})$.} and the corresponding
+ $(x_{\max},y_{\max})$, 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 triangles are removed at the end of
the algorithm.
\item[color = \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.
+ triangulation. This also adds a \emph{dot} at each vertex.
\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
- label the vertices of the triangulation. It is include in the math
+ label the vertices of the triangulation. It is included in the math
mode delimiters \Verb+$...$+. The bounding box points are labeled
- with a star exponent, and numbered from 1 to 4.
+ 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, it is \Verb+tikz+ the \textit{drawing
+ 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 draw (the same for the two
- axis). It must contain the unit of length (cm,
+ 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}
\end{Exemple}
\begin{warning}
-The drawing engine is not here very relevant. But it is useful to
-understand how the drawing is made. However, the engine will make sens
-for the so called \emph{inc} macros (section~\ref{sec:inc}), where we
-will be allowed to add code before and after the generated one by
+The drawing engine is not very relevant here, but it is useful to
+understand how the drawing is made. However, the engine will be
+relevant to
+the so called \emph{inc} macros (section~\ref{sec:inc}), for adding
+code before and after the one generated by
\luamesh.
\end{warning}
\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.
+With the \Verb+\drawPointsMesh+, we plot the set of (user chosen) points from
+which the Bowyer and Watson algorithm computes the triangulation.
-The use of this macro is quite similar to the
+The use of this macro is quite similar to
\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)}
\subsubsection{The Options}
-There are several options (exactly the same that for the
-\Verb+\buildMeshBW+)to customize the drawing.
+There are several options (exactly the same as 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
+ use either the previously described set of points as the argument, or
a file, containing, line by line (2 columns), the points. Such a
file looks like :
\begin{verbatim}
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.}
+ mesh, there are no triangles, 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.
+ triangulation. This also adds a \emph{dot} at each vertex. Without
+ label, there is still the dot.
\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
- label the vertices of the triangulation. It is include in the math
+ label the vertices of the triangulation. It is included in the math
mode delimiters \Verb+$...$+. The bounding box points are labeled
- with a star exponent, and numbered from 1 to 4.
+ 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, it is \Verb+tikz+ the \textit{drawing
+ 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 draw (the same for the two
- axis). It must contain the unit of length (cm,
+ 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}
With the same external mesh point file presented in
\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
+This command allows to plot the steps within the addition of a
+point in a Delaunay triangulation, by the Bowyer and Watson
algorithm.
-This macro produce the Delaunay triangulation (using the Bowyer and
+This macro produces 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:
and \meta{number of line} will be explained in the option
description.
-One can use the macro as fallow:
+One can use the macro as fallows:
\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
+The default value for \Verb+step+ is
+\Verb+badtriangles+. Consequently, the first
+line is 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}
\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
+ use either the previously described set of point in the first
+ argument, or
+ a file containing, line by line (2 columns), the points. Such a
file looks like :
\begin{verbatim}
x1 y1
\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
+the point corresponding to the line. The subsequent lines in 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
\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.
+ the circumcircle 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
+ label the vertices of the triangulation. It is included in the math
mode delimiters \Verb+$...$+. The bounding box points are labeled
- with a star exponent, and numbered from 1 to 4.
+ with numbers 1 to 4 and with a star exponent.
\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.
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
+ the picture. With this option, \Verb+tikz+ is 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
pt, etc.).
\end{optionsenum}
-Here is an example of customization of the drawing. First, recall that
+Here is an example of customizing the drawing. First, recall that
the external file \Verb+mesh.txt+ is:
\begin{verbatim}
0.3 0.3
tikz,
mode = ext,
color = blue!70,
- meshpoint = x,
+ meshpoint = \alpha,
newpoint = y,
colorBack=red!10,
- colorNew = green!20!red,
+ colorNew = green!50!red,
colorCircle = blue,
colorBbox = black!20,
bbox = show,
scale=1.4cm,
- step=cavity]
+ step=badtriangles]
{mesh.txt}{6}
\end{Exemple}
\section{The \emph{inc} Macros}\label{sec:inc}
+The three macros presented in the above sections have complementary
+macros, with the suffix \Verb+inc+ that allow the user to add code
+(MetaPost or \Verb+tikz+, depending of the drawing engine) before and
+after the code generated by \luamesh.
+
+The three macros are:\medskip
+
+
+\commande|\buildMeshBWinc[«options»]{«list of points» or «file name»}{«code before»}{«code after»}|\medskip
+
+\commande|\drawPointsMeshinc[«options»]{«list of points» or «file name»}{«code before»}{«code after»}|\medskip
+
+\commande|\meshAddPointBWinc[«options»]{«list of points» or «file name»}%|
+
+\commande| {«point» or «number of line»}{«code before»}{«code after»}|\medskip
+
\subsection{With MetaPost}
-%\subsection{With \Verb+tikz+}
+We consider the case where the drawing engine is MetaPost (through the
+\Verb+luamplib+ package).
+
+We describe the feature taking one macro in example but the mechanism
+and the possibilities are exactly the same for all the macros.
+
+When we use the MetaPost drawing engine, the macros previously
+described produced a code of the form
+\begin{latexcode}
+\begin{luamplib}
+ u:=<scale>;
+ beginfig(0);
+ <code for the drawing>
+ endfig;
+\end{luamplib}
+\end{latexcode}
+
+Then, the arguments \meta{code before} and \meta{code after} are
+inserted as follows:
+\begin{latexcode}
+\begin{luamplib}
+ u:=<scale>;
+ <<code before>>
+ <code for the drawing>
+ <<code after>>
+\end{luamplib}
+\end{latexcode}
+\begin{warning}
+With the \emph{inc} macros, the user has to add the \Verb+beginfig();+
+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}
+
+The configurable colors
+of the \LaTeX{} macro are accessible inside the MetaPost code. For
+\Verb+\buildMeshBWinc+ and \Verb+\drawPointsMeshinc+, we have
+\Verb+\luameshmpcolor+,
+and \Verb+\luameshmpcolorBbox+.
+For the macro \Verb+\meshAddPointBWinc+ we have three additional
+colors : \Verb+\luameshmpcolorBack+, \Verb+\luameshmpcolorNew+, and
+\Verb+\luameshmpcolorCircle+. Of course, we can define MetoPost
+colors as well. Finally, the \Verb+luamplib+ mechanism of
+\Verb+\mpcolor+ is also available.
+
+\subsubsection{The Mesh Points}
+
+At the beginning of the automatically generated code, a list of
+MetaPost \Verb+pair+s are defined corresponding to all the vertices of
+the mesh (when the option \Verb+bbox=show+, the last 4 points are the
+\emph{bounding box points}). The points are available with the
+\Verb+MeshPoints[]+ table of variables. The \Verb+MeshPoints[i]+ are
+defined using the unit length \Verb+u+.
+
+\subsubsection{Examples}
+
+Here is three examples for the different macros.
+\begin{Exemple}
+\drawPointsMeshinc[
+color = blue!50,
+print = points,
+meshpoint = x,
+scale=0.8cm,
+]{(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)}%
+{% code before
+ beginfig(0);
+}%
+{% code after
+ label(btex Mesh $\mathbb{T}$ etex, (0,2u)) withcolor \luameshmpcolor;
+ endfig;
+}
+\buildMeshBWinc[%
+bbox = show,
+color = red,
+colorBbox = blue!30,
+print = points,
+meshpoint = x,
+scale=0.8cm
+]{(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)}%
+{% code before
+ beginfig(0);
+}
+{% code after
+ drawdblarrow MeshPoints[3] -- MeshPoints[9] withpen pencircle scaled 1pt
+ withcolor (0.3,0.7,0.2);
+ endfig;
+}
+\meshAddPointBWinc[
+meshpoint = \alpha,
+newpoint = y,
+colorBack=red!10,
+colorNew = green!50!red,
+colorCircle = blue,
+colorBbox = black!20,
+bbox = show,
+scale=0.8cm,
+step=badtriangles]
+{(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)}%
+{%code before
+ picture drawing;
+ drawing := image(
+}{%code after
+ );
+ beginfig(0);
+ fill MeshPoints[7]--MeshPoints[8]--MeshPoints[9]--MeshPoints[10]--cycle
+ withcolor \mpcolor{blue!10};
+ draw drawing;
+ endfig;
+}
+\end{Exemple}
+\begin{warning}
+ The variables \Verb+MeshPoints[]+ are not defined for the argument
+ corresponding to the code to place before the code generated by
+ \luamesh. Hence, to use such variables, we have to define a
+ \Verb+picture+ as shown in the third example above.
+\end{warning}
+
+
+\subsection{With TikZ}
+
+If we have chosen \Verb+tikz+ as the engine drawing, the added code
+will be written in \Verb+tikz+. In that case, the two arguments
+\meta{code before} and \meta{code after} will be inserted as follows:
+\begin{latexcode}
+\noindent
+\begin{tikzpicture}[x=<scale>,y=<scale>]
+ <<code before>>
+ <generated code>
+ <<code after>>
+\end{tikzpicture}
+\end{latexcode}
+
+Because the engine is \Verb+tikz+ their is no issue with colors, the
+\LaTeX{} colors (e.g.: \Verb+xcolor+) can be directly used.
+
+\subsubsection{The Mesh Points}
+
+The points of the mesh are defined here as \Verb+tikz+
+\Verb+\coordinate+ named as follows
+\begin{latexcode}
+\coordinate (MeshPoints1) at (...,...);
+\coordinate (MeshPoints2) at (...,...);
+\coordinate (MeshPoints3) at (...,...);
+%etc.
+\end{latexcode}
+
+Once again these coordinates are not yet defined for the \meta{code
+ before} argument.
+
+\subsubsection{Examples}
+
+\begin{Exemple}
+ \drawPointsMeshinc[
+ tikz,
+ color = blue!50,
+ print = points,
+ meshpoint = x,
+ scale=0.8cm,
+ ]{(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)}%
+ {% code before
+ }%
+ {% code after
+ \node[color = blue!50] at (0,2) {Mesh $\mathbb{T}$} ;
+ }
+ \buildMeshBWinc[%
+ tikz,
+ bbox = show,
+ color = red,
+ colorBbox = blue!30,
+ print = points,
+ meshpoint = x,
+ scale=0.8cm
+ ]{(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)}%
+ {% code before
+ }
+ {% code after
+ \draw[<->,thick, color=green] (MeshPoints3) -- (MeshPoints9);
+ }
+\end{Exemple}
-\section{Gallery of Examples}
+\input{dum.bbl}
\end{document}
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