doc/luamesh-doc.tex

   1 % luamesh: compute and draw meshes with lua, luamplib and tikz
   2 %
   3 % Originally written by Maxime Chupin <mc@melusine.eu.org>,
   4 % 2010.
   5 %
   6 % Distributed under the terms of the GNU free documentation licence:
   7 %   http://www.gnu.org/licenses/fdl.html
   8 % without any invariant section or cover text.
   9
  10 \documentclass{lltxdoc}
  11 \usepackage{tcolorbox}
  12 \usepackage{xargs}
  13 \usepackage{enumitem}
  14 \usepackage[tikz]{bclogo}
  15 \usepackage{wrapfig}
  16 \title{\Verb+luamesh+: compute and draw meshes with \lualatex}
  17 \author{Maxime Chupin \email{mc@melusine.eu.org}}
  18 \date{\today}
  19
  20
  21 \definecolor{darkred}{rgb}{0.8,0.1,0.1}
  22
  23
  24 \newcommand*\commande{\noindent\hspace{-30pt}%
  25   \SaveVerb[aftersave={%
  26    \UseVerb{Vitem}
  27   }%
  28   ]{Vitem}}
  29
  30 \newcommand*\textme[1]{\textcolor{black}{\rmfamily\textit{#1}}}
  31 \newcommand*\meta[1]{% % meta
  32   \textme{\ensuremath{\langle}#1\ensuremath{\rangle}}}
  33 \newcommand*\optstar{% % optional star
  34   \meta{\ensuremath{*}}\xspace}
  35 \DefineShortVerb{\|}
  36
  37 \setlength{\fboxsep}{2pt}
  38 \fvset{%
  39   codes={\catcode`\«\active \catcode`\×\active },
  40   defineactive={\makefancyog\makefancytimes},
  41   formatcom=\color{darkred},
  42   frame=single
  43 }
  44 % rendre «...» équivalent à \meta{...}
  45 {\catcode`\«\active
  46   \newcommandx\makefancyog[0][addprefix=\global]{%
  47     \def«##1»{\meta{##1}}}}
  48 % rendre × équivalent à \optstar
  49 {\catcode`\×\active
  50   \newcommandx\makefancytimes[0][addprefix=\global]{%
  51     \def×{\optstar{}}}}
  52
  53
  54 \tcbuselibrary{listings,breakable}
  55
  56 \definecolor{vert}{rgb}{0.1,0.4,0.1}
  57 \definecolor{bleu}{rgb}{0.1,0.1,0.4}
  58 \lstset{
  59   numberstyle=\footnotesize\color{vert},
  60   keywordstyle=\ttfamily\bfseries\color{blue},
  61   basicstyle=\ttfamily\footnotesize,
  62   commentstyle=\itshape\color{vert},
  63   stringstyle=\ttfamily,
  64   showstringspaces=false,
  65   language=[LaTeX]TeX,
  66   breaklines=true,
  67   breakindent=30pt,
  68   defaultdialect=[LaTeX]TeX,
  69   morekeywords={buildMeshBW,buildMeshBWinc,drawPointsMesh,
  70     drawPointsMeshinc, meshAddPointBW, meshAddPointBWinc}% frame=tb
  71 }
  72
  73 \lstdefinelanguage{lua}
  74 {morekeywords={for,end,function,do,if,else,elseif,then,
  75     tex.print,tex.sprint,io.read,io.open,string.find,string.explode,require},
  76   morecomment=[l]{--},
  77   morecomment=[s]{--[[}{]]},
  78   morestring=[b]''
  79 }
  80
  81 \newtcblisting{Exemple}{%
  82   arc=0pt,outer arc=0pt,
  83   colback=red!2!white,
  84   colframe=red!75!black,
  85   breakable,
  86   boxsep=0pt,left=5pt,right=5pt,top=5pt,bottom=5pt, bottomtitle =
  87   3pt, toptitle=3pt,
  88   boxrule=0pt,bottomrule=0.5pt,toprule=0.5pt, toprule at break =
  89   0pt, bottomrule at break = 0pt,
  90   listing options={breaklines},
  91 }
  92
  93 \newtcblisting{commandshell}{colback=black,colupper=white,colframe=black,
  94   arc=0pt,
  95   listing only,boxsep=0pt,listing
  96   options={style=tcblatex,language=sh},
  97   every listing line={\textcolor{red}{\small\ttfamily\bfseries user \$> }}}
  98
  99 \newtcblisting{latexcode}{
 100   arc=0pt,outer arc=0pt,
 101   colback=red!2!white,
 102   colframe=red!75!black,
 103   breakable,
 104   boxsep=0pt,left=5pt,right=5pt,top=5pt,bottom=5pt, bottomtitle =
 105   3pt, toptitle=3pt,
 106   boxrule=0pt,bottomrule=0.5pt,toprule=0.5pt, toprule at break =
 107   0pt, bottomrule at break = 0pt,
 108   listing only,boxsep=0pt,listing
 109   options={breaklines}
 110 }
 111
 112
 113 \newcommand\luamesh{\Verb+luamesh+\xspace}
 114
 115 \newenvironment{optionsenum}[1][]
 116 {\begin{description}[font=\color{darkred}\ttfamily]}
 117   {\end{description}}
 118
 119 \newenvironment{warning}{%
 120   \setlength{\logowidth}{24pt}
 121   \tcbset{%
 122     arc=0pt,outer arc=0pt,colback=gray!10!white,colframe=gray!60!white,
 123     boxsep=0pt,left=5pt,right=5pt,top=5pt,bottom=5pt, bottomtitle = 3pt, toptitle=3pt,
 124     boxrule=0pt,bottomrule=0.5pt,toprule=0.5pt}
 125   \medskip
 126   \begin{tcolorbox}%
 127     \begin{wrapfigure}[2]{L}{17pt}%
 128       % \raisebox{-5pt}{
 129       \vspace*{-0.55cm}
 130       \bcinfo
 131       % }%
 132     \end{wrapfigure}
 133   }%
 134   {\end{tcolorbox}\medskip}
 135
 136 \lstset{moredelim=*[s][\color{red}\rmfamily\itshape]{<}{>}}
 137 \lstset{moredelim=*[s][\color{blue}\rmfamily\itshape]{<<}{>>}}
 138
 139 \begin{document}
 140 %% === Page de garde ===================================================
 141 \thispagestyle{empty}
 142 \begin{tikzpicture}[remember picture, overlay]
 143   \node[below right, shift={(-4pt,4pt)}] at (current page.north west) {%
 144     \includegraphics{fond.pdf}%
 145   };
 146 \end{tikzpicture}%
 147
 148 \noindent
 149 \includegraphics{luamesh-title}\\
 150 {\large compute and draw meshes with \lualatex}\\[1cm]
 151 \parbox{0.6\textwidth}{
 152   \meshAddPointBW[
 153   mode=ext,step=badtriangles,
 154   colorNew =green!20!red,
 155   colorBack=red!10,
 156   colorCircle = blue,
 157   bbox = show,
 158   colorBbox = black!30
 159   ]
 160   {meshgarde.txt}{7}
 161 }\hfill
 162 \parbox{0.4\textwidth}{\Large\raggedleft
 163   \textbf{Contributor}\\
 164   Maxime \textsc{Chupin}
 165 }
 166 \vfill
 167 \begin{center}
 168   Version 0.1, 25 novembre 2016\\
 169   \url{http://melusine.eu.org/syracuse/G/delaunay/}
 170 \end{center}
 171 %% == Page de garde ====================================================
 172 \newpage
 173
 174 \maketitle
 175
 176 \begin{abstract}
 177   The package \Verb|luamesh| allows to compute and draw 2D Delaunay
 178   triangulation. The algorithm is written with lua, and depending on the
 179   choice of the ``engine'', the drawing is done by MetaPost (with
 180   \Verb|luamplib|) or by \Verb|tikz|.
 181
 182   The Delaunay triangulation algorithm is the Bowyer and Watson
 183   algorithm. Several macros are provided to draw the global mesh, the
 184   set of points, or a particular step of the algorithm.
 185 \end{abstract}
 186
 187 I would like to thank Jean-Michel Sarlat, who hosts the development
 188 with a git project on the \Verb+melusine+ machine:
 189 \begin{center}
 190   \url{https://melusine.eu.org/syracuse/G/delaunay/}
 191 \end{center}
 192 I would also like to thank the first user, an intensive
 193 \emph{test} user, and a very kind English corrector: Nicole Spillane.
 194
 195 \section{Installation}
 196
 197
 198 Of course, you can just put the two files \Verb+luamesh.lua+ and
 199 \Verb+luamesh.sty+ in the working directory, but this is not
 200 recommended.
 201
 202
 203 \subsection{With \TeX live and Linux or Mac OSX}
 204
 205 To install \luamesh with \TeX live, you have to create the local
 206 \Verb+texmf+ directory in your \Verb+home+.
 207
 208 \begin{commandshell}
 209 mkdir ~/texmf
 210 \end{commandshell}
 211
 212 Then place the files in the correct directories. First, the
 213 \Verb+luamesh.sty+ file must be in the directory:
 214 \begin{center}
 215   \Verb+~/texmf/tex/latex/luamesh/+
 216 \end{center}
 217 and secondly, the \Verb+luamesh.lua+ must be in the directory:
 218 \begin{center}
 219   \Verb+~/texmf/scripts/luamesh/+
 220 \end{center}
 221
 222 Once you have done this, \luamesh can be included in your document
 223 with
 224 \begin{latexcode}
 225 \usepackage{luamesh}
 226 \end{latexcode}
 227
 228 \subsection{With Mik\TeX{} and Windows}
 229
 230 We do not know these two systems, so we refer to the
 231 documentation for integrating local additions to Mik\TeX:
 232 \begin{center}
 233   \url{http://docs.miktex.org/manual/localadditions.html}
 234 \end{center}
 235
 236
 237 \subsection{A \lualatex package}
 238
 239 If you want to use this package, you must compile your document with
 240 \Verb+lualatex+:
 241
 242 \begin{commandshell}
 243   lualatex mylatexfile.tex
 244 \end{commandshell}
 245
 246
 247 \subsection{Dependencies}
 248
 249 This package is built upon two main existing packages to draw the
 250 triangulations :
 251 \begin{enumerate}
 252 \item \Verb+luamplib+ to use MetaPost via the \luatex library
 253   \Verb+mplib+;
 254 \item and \Verb+tikz+.
 255 \end{enumerate}
 256 We will see how to choose between these two \emph{drawing engines}.
 257
 258 Moreover, the following packages are necessary:
 259 \begin{enumerate}
 260 \item \Verb+xkeyval+ to manage the optional arguments;
 261 \item \Verb+xcolor+ to use colors (needed by \Verb+luamplib+);
 262 \item \Verb+ifthen+ to help the programming with \TeX.
 263 \end{enumerate}
 264
 265
 266 \section{The Basic Macros}
 267
 268 Let us recall that this package provides macros to draw two
 269 dimensional triangulations (or meshes).
 270
 271 \subsection{Draw a Complete Mesh}\label{sec:buildMesh}
 272
 273 \commande|\buildMeshBW[«options»]{«list of points» or «file name»}|\medskip
 274
 275 This macro produces the Delaunay triangulation (using the Bowyer and
 276 Watson algorithm) of the given \meta{list of points}. The list of
 277 points must be given in the following way :
 278 \begin{center}
 279   \verb+(x1,y1);(x2,y2);(x3,y3);...;(xn,yn)+
 280 \end{center}
 281
 282 \begin{Exemple}
 283   \buildMeshBW{(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)}
 284 \end{Exemple}
 285
 286 \subsubsection{The Options}
 287
 288 There are several options to customize the drawing.
 289 \begin{optionsenum}
 290 \item[mode = int (default) \textme{or} ext:] this option allows to
 291   use either the previously described set of points in the argument, or
 292   a file, containing, line by line (2 columns), the points. Such a
 293   file looks like :
 294 \begin{verbatim}
 295 x1  y1
 296 x2  y2
 297 x3  y3
 298 ...
 299 xn yn
 300 \end{verbatim}
 301 \item[bbox = none (default) \textme{or} show:] this option allows to draw the
 302   added points to form a \emph{bounding box}\footnote{The bounding
 303     box is defined by four points place at 15\% around the box
 304     defined by $(x_{\min},y_{\min})$, $(x_{\min},y_{\max})$,
 305     $(x_{\max},y_{\max})$, and $(x_{\min},y_{\max})$. It is used by
 306     the algorithm and will be computed in any case.} and the corresponding
 307   triangulation. By default, these triangles are removed at the end of
 308   the algorithm.
 309 \item[color = \meta{value} (default: black):] The color of the
 310   drawing.
 311 \item[colorBbox = \meta{value} (default: black):] The color of the
 312   drawing for the elements (points and triangles) belonging to the
 313   bounding box.
 314 \item[print = none (default) \textme{or} points:] To label the vertices of the
 315   triangulation. This also adds a \emph{dot} at each vertex.
 316 \item[meshpoint = \meta{value} (default: P):] The letter(s) used to
 317   label the vertices of the triangulation. It is included in the math
 318   mode delimiters \Verb+$...$+. The bounding box points are labeled
 319   with numbers 1 to 4 and with a star exponent.
 320 \item[tikz (boolean, default:false):] By default, this boolean is set
 321   to \Verb+false+, and MetaPost (with \Verb+luamplib+) is used to draw
 322   the picture. With this option, \Verb+tikz+ becomes the \textit{drawing
 323     engine}.
 324 \item[scale = \meta{value} (default: 1cm):] The scale option defines
 325   the scale at which the picture is drawn (the same for both
 326   axes). It must contain the unit of length (cm,
 327   pt, etc.).
 328 \end{optionsenum}
 329
 330 To illustrate the options, let us show you an example. We consider a
 331 file \Verb+mesh.txt+:
 332 \begin{verbatim}
 333 0.3    0.3
 334 1.5    1
 335 4      0
 336 4.5    2.5
 337 1.81   2.14
 338 2.5    0.5
 339 2.8    1.5
 340 \end{verbatim}
 341 \begin{Exemple}
 342   \buildMeshBW[%
 343   tikz,
 344   mode = ext,
 345   bbox = show,
 346   color = red,
 347   colorBbox = blue!30,
 348   print = points,
 349   meshpoint = x,
 350   scale = 1.3cm,
 351   ]{mesh.txt}
 352 \end{Exemple}
 353
 354 \begin{warning}
 355 The drawing engine is not very relevant here, but it is useful to
 356 understand how the drawing is made. However, the engine will be
 357 relevant to
 358 the so called \emph{inc} macros (section~\ref{sec:inc}), for adding
 359 code before and after the one generated by
 360 \luamesh.
 361 \end{warning}
 362
 363 \subsection{Draw the Set of Points}
 364
 365 \commande|\drawPointsMesh[«options»]{«list of points» or «file name»}|\medskip
 366
 367 With the \Verb+\drawPointsMesh+, we plot the set of (user chosen) points from
 368 which the Bowyer and Watson algorithm computes the triangulation.
 369
 370 The use of this macro is quite similar to
 371 \Verb+\buildMeshBW+. Here is an example of the basic uses.
 372 \begin{Exemple}
 373   \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)}
 374 \end{Exemple}
 375
 376
 377 \subsubsection{The Options}
 378
 379 There are several options (exactly the same as for the
 380 \Verb+\buildMeshBW+) to customize the drawing.
 381 \begin{optionsenum}
 382 \item[mode = int (default) \textme{or} ext:] this option allows to
 383   use either the previously described set of points as the argument, or
 384   a file, containing, line by line (2 columns), the points. Such a
 385   file looks like :
 386 \begin{verbatim}
 387 x1  y1
 388 x2  y2
 389 x3  y3
 390 ...
 391 xn yn
 392 \end{verbatim}
 393 \item[bbox = none (default) \textme{or} show:] this option allows to draw the
 394   added points to form a \emph{bounding box} and the corresponding
 395   triangulation. By default, these triangles are removed at the end of
 396   the algorithm. \emph{Here, because we plot only the vertices of the
 397     mesh, there are no triangles, only dots.}
 398 \item[color = \meta{value} (default: black):] The color of the
 399   drawing.
 400 \item[colorBbox = \meta{value} (default: black):] The color of the
 401   drawing for the elements (points and triangles) belonging to the
 402   bounding box.
 403 \item[print = none (default) \textme{or} points:] To label the vertices of the
 404   triangulation. This also adds a \emph{dot} at each vertex. Without
 405   label, there is still the dot.
 406 \item[meshpoint = \meta{value} (default: P):] The letter(s) used to
 407   label the vertices of the triangulation. It is included in the math
 408   mode delimiters \Verb+$...$+. The bounding box points are labeled
 409   with numbers 1 to 4 and with a star exponent.
 410 \item[tikz (boolean, default:false):] By default, this boolean is set
 411   to \Verb+false+, and MetaPost (with \Verb+luamplib+) is used to draw
 412   the picture. With this option, \Verb+tikz+ becomes the \textit{drawing
 413     engine}.
 414 \item[scale = \meta{value} (default: 1cm):] The scale option defines
 415   the scale at which the picture is drawn (the same for both
 416   axes). It must contain the unit of length (cm,
 417   pt, etc.).
 418 \end{optionsenum}
 419 With the same external mesh point file presented in
 420 section~\ref{sec:buildMesh}, we illustrate the different options.
 421
 422 \begin{Exemple}
 423   \drawPointsMesh[%
 424   tikz,
 425   mode = ext,
 426   bbox = show,
 427   color = blue,
 428   colorBbox = red,
 429   print = points,
 430   meshpoint = y,
 431   scale = 1.3cm,
 432   ]{mesh.txt}
 433 \end{Exemple}
 434
 435
 436 \subsection{Draw a Step of the Bowyer and Watson Algorithm}
 437
 438 \commande|\meshAddPointBW[«options»]{«list of points» or «file name»}{«point» or «number of line»}|\medskip
 439
 440 This command allows to plot the steps within the addition of a
 441 point in a Delaunay triangulation, by the Bowyer and Watson
 442 algorithm.
 443
 444 This macro produces the Delaunay triangulation (using the Bowyer and
 445 Watson algorithm) of the given \meta{list of points} and shows a step
 446 of the algorithm when the \meta{point} is added. The list of
 447 points must be given in the following way:
 448 \begin{center}
 449   \verb+(x1,y1);(x2,y2);(x3,y3);...;(xn,yn)+
 450 \end{center}
 451 and the point is of the form \verb+(x,y)+. The \meta{file name}
 452 and \meta{number of line}  will be explained in the option
 453 description.
 454
 455 One can use the macro as fallows:
 456 \begin{Exemple}
 457   \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)}
 458   \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)}
 459   \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)}
 460 \end{Exemple}
 461 The default value for \Verb+step+ is
 462 \Verb+badtriangles+. Consequently, the first
 463 line is equivalent to
 464 \begin{latexcode}
 465 \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)}
 466 \end{latexcode}
 467
 468 \subsubsection{The Options}
 469
 470 There are several options (some of them are the same as for
 471 \Verb+\buildMeshBW+) to customize the drawing.
 472 \begin{optionsenum}
 473 \item[mode = int (default) \textme{or} ext:] this option allows to
 474   use either the previously described set of point in the first
 475   argument, or
 476   a file containing, line by line (2 columns), the points. Such a
 477   file looks like :
 478 \begin{verbatim}
 479 x1  y1
 480 x2  y2
 481 x3  y3
 482 ...
 483 xn yn
 484 \end{verbatim}
 485 For the second argument of the macro, if we are in the
 486 \Verb+mode = ext+, the argument must be the \emph{line number} of the file
 487 corresponding to the point we want to add. The algorithm will stop the
 488 line before to build the initial triangulation for which it will add
 489 the point corresponding to the line. The subsequent lines in the file are
 490 ignored.
 491 \item[bbox = none (default) \textme{or} show:] this option allows to draw the
 492   added points to form a \emph{bounding box} and the corresponding
 493   triangulation. By default, these triangles are removed at the end of
 494   the algorithm.
 495 \item[color = \meta{value} (default: black):] The color of the
 496   drawing.
 497 \item[colorBbox = \meta{value} (default: black):] The color of the
 498   drawing for the elements (points and triangles) belonging to the
 499   bounding box.
 500 \item[colorNew = \meta{value} (default: red):] The color of the
 501   drawing of the ``new'' elements which are the point to add, the
 502   polygon of the cavity, and the new triangles.
 503 \item[colorBack = \meta{value} (default: black!20):] The color for the
 504   filling of the region concerned by the addition of the new point.
 505 \item[colorCircle = \meta{value} (default: green):] The color for
 506   the circumcircle of the triangles containing the point to add.
 507 \item[meshpoint = \meta{value} (default: P):] The letter(s) used to
 508   label the vertices of the triangulation. It is included in the math
 509   mode delimiters \Verb+$...$+. The bounding box points are labeled
 510   with numbers 1 to 4 and with a star exponent.
 511 \item[step = badtriangles (default) \textme{or} cavity \textme{or}
 512   newtriangles:] To choose the step we want to draw, corresponding to
 513   the steps of the Bowyer and Watson algorithm.
 514 \item[newpoint = \meta{value} (default: P):] The letter(s) used to
 515   label the new point of the triangulation. It is include in the math
 516   mode delimiters \Verb+$...$+.
 517 \item[tikz (boolean, default:false):] By default, this boolean is set
 518   to \Verb+false+, and MetaPost (with \Verb+luamplib+) is used to draw
 519   the picture. With this option, \Verb+tikz+  is the \textit{drawing
 520     engine}.
 521 \item[scale = \meta{value} (default: 1cm):] The scale option defines
 522   the scale at which the picture is draw (the same for the two
 523   axis). It must contain the unit of length (cm,
 524   pt, etc.).
 525 \end{optionsenum}
 526
 527 Here is an example of customizing the drawing. First, recall that
 528 the external file \Verb+mesh.txt+ is:
 529 \begin{verbatim}
 530 0.3    0.3
 531 1.5    1
 532 4      0
 533 4.5    2.5
 534 1.81   2.14
 535 2.5    0.5
 536 2.8    1.5
 537 \end{verbatim}
 538 We draw the addition of the 6th point. The 7th line will be ignored.
 539 \begin{Exemple}
 540   \meshAddPointBW[
 541   tikz,
 542   mode = ext,
 543   color = blue!70,
 544   meshpoint = \alpha,
 545   newpoint = y,
 546   colorBack=red!10,
 547   colorNew = green!50!red,
 548   colorCircle = blue,
 549   colorBbox = black!20,
 550   bbox = show,
 551   scale=1.4cm,
 552   step=badtriangles]
 553   {mesh.txt}{6}
 554 \end{Exemple}
 555
 556 \section{The \emph{inc} Macros}\label{sec:inc}
 557
 558 The three macros presented in the above sections have complementary
 559 macros, with the suffix \Verb+inc+ that allow the user to add code
 560 (MetaPost or \Verb+tikz+, depending of the drawing engine) before and
 561 after the code generated by \luamesh.
 562
 563 The three macros are:
 564
 565 \commande|\buildMeshBWinc[«options»]{«list of points» or «file name»}{«code before»}{«code after»}|\medskip
 566
 567 \commande|\drawPointsMeshinc[«options»]{«list of points» or «file name»}{«code before»}{«code after»}|\medskip
 568
 569 \commande|\meshAddPointBWinc[«options»]{«list of points» or «file  name»}%|
 570
 571 \commande|                           {«point» or «number of line»}{«code before»}{«code after»}|\medskip
 572
 573 \subsection{With MetaPost}
 574
 575 We consider the case where the drawing engine is MetaPost (through the
 576 \Verb+luamplib+ package).
 577
 578 We describe the feature taking one macro in example but the mechanism
 579 and the possibilities are exactly the same for all the macros.
 580
 581 When we use the MetaPost drawing engine, the macros previously
 582 described produced a code of the form
 583 \begin{latexcode}
 584 \begin{luamplib}
 585   u:=<scale>;
 586   beginfig(0);
 587   <code for the drawing>
 588   endfig;
 589 \end{luamplib}
 590 \end{latexcode}
 591
 592 Then, the arguments \meta{code before} and \meta{code after} are
 593 inserted as follows:
 594 \begin{latexcode}
 595 \begin{luamplib}
 596   u:=<scale>;
 597   <<code before>>
 598   <code for the drawing>
 599   <<code after>>
 600 \end{luamplib}
 601 \end{latexcode}
 602 \begin{warning}
 603 With the \emph{inc} macros, the user has to add the \Verb+beginfig();+
 604 and \Verb+endfig;+ commands to produce a picture. Indeed, this allows
 605 to use the \Verb+\everymplib+ command from the \Verb+\luamplib+ package.
 606 \end{warning}
 607
 608 \subsubsection{The \LaTeX{} Colors Inside the MetaPost Code}
 609
 610 The configurable colors
 611 of the \LaTeX{} macro are accessible inside the MetaPost code. For
 612 \Verb+\buildMeshBWinc+ and \Verb+\drawPointsMeshinc+, we have
 613 \Verb+\luameshmpcolor+,
 614 and \Verb+\luameshmpcolorBbox+.
 615 For the macro \Verb+\meshAddPointBWinc+ we have three additional
 616 colors : \Verb+\luameshmpcolorBack+, \Verb+\luameshmpcolorNew+, and
 617 \Verb+\luameshmpcolorCircle+. Of course, we can define MetoPost
 618 colors as well. Finally, the \Verb+luamplib+ mechanism of
 619 \Verb+\mpcolor+ is also available.
 620
 621 \subsubsection{The Mesh Points with MetaPost}
 622
 623 At the beginning of the automatically generated code, a list of
 624 MetaPost \Verb+pair+s are defined corresponding to all the vertices of
 625 the mesh (when the option \Verb+bbox=show+, the last 4 points are the
 626 \emph{bounding box points}). The points are available with the
 627 \Verb+MeshPoints[]+ table of variables. The \Verb+MeshPoints[i]+ are
 628 defined using the unit length \Verb+u+.
 629
 630 \subsubsection{Examples}
 631
 632 Here is three examples for the different macros.
 633 \begin{Exemple}
 634 \drawPointsMeshinc[
 635 color = blue!50,
 636 print = points,
 637 meshpoint = x,
 638 scale=0.8cm,
 639 ]{(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)}%
 640 {% code before
 641   beginfig(0);
 642 }%
 643 {% code after
 644   label(btex Mesh $\mathbb{T}$ etex, (0,2u)) withcolor \luameshmpcolor;
 645   endfig;
 646 }
 647 \buildMeshBWinc[%
 648 bbox = show,
 649 color = red,
 650 colorBbox = blue!30,
 651 print = points,
 652 meshpoint = x,
 653 scale=0.8cm
 654 ]{(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)}%
 655 {% code before
 656   beginfig(0);
 657 }
 658 {% code after
 659   drawdblarrow MeshPoints[3] -- MeshPoints[9] withpen pencircle scaled 1pt
 660   withcolor (0.3,0.7,0.2);
 661   endfig;
 662 }
 663 \meshAddPointBWinc[
 664 meshpoint = \alpha,
 665 newpoint = y,
 666 colorBack=red!10,
 667 colorNew = green!50!red,
 668 colorCircle = blue,
 669 colorBbox = black!20,
 670 bbox = show,
 671 scale=0.8cm,
 672 step=badtriangles]
 673 {(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)}%
 674 {%code before
 675   picture drawing;
 676   drawing := image(
 677 }{%code after
 678   );
 679   beginfig(0);
 680   fill MeshPoints[7]--MeshPoints[8]--MeshPoints[9]--MeshPoints[10]--cycle
 681   withcolor \mpcolor{blue!10};
 682   draw drawing;
 683   endfig;
 684 }
 685 \end{Exemple}
 686 \begin{warning}
 687   The variables \Verb+MeshPoints[]+ are not defined for the argument
 688   corresponding to the code to place before the code generated by
 689   \luamesh. Hence, to use such variables, we have to define a
 690   \Verb+picture+ as shown in the third example above.
 691 \end{warning}
 692
 693
 694 \subsection{With TikZ}
 695
 696
 697
 698 \section{Gallery of Examples}
 699
 700 \end{document}
 701
 702
 703
 704 %%% Local Variables:
 705 %%% flyspell-mode: 1
 706 %%% ispell-local-dictionary: "american"
 707 %%% End: