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
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  43 }
  44 % rendre «...» équivalent à \meta{...}
  45 {\catcode`\«\active
  46   \newcommandx\makefancyog[0][addprefix=\global]{%
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  48 % rendre × équivalent à \optstar
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  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]{--},
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  78   morestring=[b]''
  79 }
  80
  81 \newtcblisting{Exemple}{%
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  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},
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  98
  99 \newtcblisting{latexcode}{
 100   arc=0pt,outer arc=0pt,
 101   colback=red!2!white,
 102   colframe=red!75!black,
 103   breakable,
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 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,
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 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
 137 \begin{document}
 138 %% === Page de garde ===================================================
 139 \thispagestyle{empty}
 140 \begin{tikzpicture}[remember picture, overlay]
 141   \node[below right, shift={(-4pt,4pt)}] at (current page.north west) {%
 142     \includegraphics{fond.pdf}%
 143   };
 144 \end{tikzpicture}%
 145
 146 \noindent
 147 \includegraphics{luamesh-title}\\
 148 {\large compute and draw meshes with \lualatex}\\[1cm]
 149 \parbox{0.6\textwidth}{
 150   \meshAddPointBW[
 151   mode=ext,step=badtriangles,
 152   colorNew =green!20!red,
 153   colorBack=red!10,
 154   colorCircle = blue,
 155   bbox = show,
 156   colorBbox = black!30
 157   ]
 158   {meshgarde.txt}{7}
 159 }\hfill
 160 \parbox{0.4\textwidth}{\Large\raggedleft
 161   \textbf{Contributor}\\
 162   Maxime \textsc{Chupin}
 163 }
 164 \vfill
 165 \begin{center}
 166   Version 0.1, 25 novembre 2016\\
 167   \url{http://melusine.eu.org/syracuse/G/delaunay/}
 168 \end{center}
 169 %% == Page de garde ====================================================
 170 \newpage
 171
 172 \maketitle
 173
 174 \begin{abstract}
 175   The package \Verb|luamesh| allows to compute and draw 2D Delaunay
 176   triangulation. The algorithm is written with lua, and depending on the
 177   choice of the ``engine'', the drawing is done by MetaPost (with
 178   \Verb|luamplib|) or by \Verb|tikz|.
 179
 180   The Delaunay triangulation algorithm is the Bowyer and Watson
 181   algorithm. Several macros are provided to draw the global mesh, the
 182   set of points, or a particular step of the algorithm.
 183 \end{abstract}
 184
 185 I would like to thank Jean-Michel Sarlat, who hosts the development
 186 with a git project on the \Verb+melusine+ machine:
 187 \begin{center}
 188   \url{https://melusine.eu.org/syracuse/G/delaunay/}
 189 \end{center}
 190 I would also like to thank the first user, an intensive
 191 \emph{test} user, and a very kind English corrector: Nicole Spillane.
 192
 193 \section{Installation}
 194
 195
 196 Of course, you can just put the two files \Verb+luamesh.lua+ and
 197 \Verb+luamesh.sty+ in the working directory, but this is not
 198 recommended.
 199
 200
 201 \subsection{With \TeX live and Linux or Mac OSX}
 202
 203 To install \luamesh with \TeX live, you have to create the local
 204 \Verb+texmf+ directory in your \Verb+home+.
 205
 206 \begin{commandshell}
 207 mkdir ~/texmf
 208 \end{commandshell}
 209
 210 Then place the files in the correct directories. First, the
 211 \Verb+luamesh.sty+ file must be in the directory:
 212 \begin{center}
 213   \Verb+~/texmf/tex/latex/luamesh/+
 214 \end{center}
 215 and secondly, the \Verb+luamesh.lua+ must be in the directory:
 216 \begin{center}
 217   \Verb+~/texmf/scripts/luamesh/+
 218 \end{center}
 219
 220 Once you have done this, \luamesh can be included in your document
 221 with
 222 \begin{latexcode}
 223 \usepackage{luamesh}
 224 \end{latexcode}
 225
 226 \subsection{With Mik\TeX{} and Windows}
 227
 228 We do not know these two systems, so we refer to the
 229 documentation for integrating local additions to Mik\TeX:
 230 \begin{center}
 231   \url{http://docs.miktex.org/manual/localadditions.html}
 232 \end{center}
 233
 234
 235 \subsection{A \lualatex package}
 236
 237 If you want to use this package, you must compile your document with
 238 \Verb+lualatex+:
 239
 240 \begin{commandshell}
 241   lualatex mylatexfile.tex
 242 \end{commandshell}
 243
 244
 245 \subsection{Dependencies}
 246
 247 This package is built upon two main existing packages to draw the
 248 triangulations :
 249 \begin{enumerate}
 250 \item \Verb+luamplib+ to use MetaPost via the \luatex library
 251   \Verb+mplib+;
 252 \item and \Verb+tikz+.
 253 \end{enumerate}
 254 We will see how to choose between these two \emph{drawing engines}.
 255
 256 Moreover, the following packages are necessary:
 257 \begin{enumerate}
 258 \item \Verb+xkeyval+ to manage the optional arguments;
 259 \item \Verb+xcolor+ to use colors (needed by \Verb+luamplib+);
 260 \item \Verb+ifthen+ to help the programming with \TeX.
 261 \end{enumerate}
 262
 263
 264 \section{The Basic Macros}
 265
 266 Let us recall that this package provides macros to draw two
 267 dimensional triangulations (or meshes).
 268
 269 \subsection{Draw a Complete Mesh}\label{sec:buildMesh}
 270
 271 \commande|\buildMeshBW[«options»]{«list of points» or «file name»}|\medskip
 272
 273 This macro produces the Delaunay triangulation (using the Bowyer and
 274 Watson algorithm) of the given \meta{list of points}. The list of
 275 points must be given in the following way :
 276 \begin{center}
 277   \verb+(x1,y1);(x2,y2);(x3,y3);...;(xn,yn)+
 278 \end{center}
 279
 280 \begin{Exemple}
 281   \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)}
 282 \end{Exemple}
 283
 284 \subsubsection{The Options}
 285
 286 There are several options to customize the drawing.
 287 \begin{optionsenum}
 288 \item[mode = int (default) \textme{or} ext:] this option allows to
 289   use either the previously described set of points in the argument, or
 290   a file, containing, line by line (2 columns), the points. Such a
 291   file looks like :
 292 \begin{verbatim}
 293 x1  y1
 294 x2  y2
 295 x3  y3
 296 ...
 297 xn yn
 298 \end{verbatim}
 299 \item[bbox = none (default) \textme{or} show:] this option allows to draw the
 300   added points to form a \emph{bounding box}\footnote{The bounding
 301     box is defined by four points place at 15\% around the box
 302     defined by $(x_{\min},y_{\min})$, $(x_{\min},y_{\max})$,
 303     $(x_{\max},y_{\max})$, and $(x_{\min},y_{\max})$. It is used by
 304     the algorithm and will be computed in any case.} and the corresponding
 305   triangulation. By default, these triangles are removed at the end of
 306   the algorithm.
 307 \item[color = \meta{value} (default: black):] The color of the
 308   drawing.
 309 \item[colorBbox = \meta{value} (default: black):] The color of the
 310   drawing for the elements (points and triangles) belonging to the
 311   bounding box.
 312 \item[print = none (default) \textme{or} points:] To label the vertices of the
 313   triangulation. This also adds a \emph{dot} at each vertex.
 314 \item[meshpoint = \meta{value} (default: P):] The letter(s) used to
 315   label the vertices of the triangulation. It is included in the math
 316   mode delimiters \Verb+$...$+. The bounding box points are labeled
 317   with numbers 1 to 4 and with a star exponent.
 318 \item[tikz (boolean, default:false):] By default, this boolean is set
 319   to \Verb+false+, and MetaPost (with \Verb+luamplib+) is used to draw
 320   the picture. With this option, \Verb+tikz+ becomes the \textit{drawing
 321     engine}.
 322 \item[scale = \meta{value} (default: 1cm):] The scale option defines
 323   the scale at which the picture is drawn (the same for both
 324   axes). It must contain the unit of length (cm,
 325   pt, etc.).
 326 \end{optionsenum}
 327
 328 To illustrate the options, let us show you an example. We consider a
 329 file \Verb+mesh.txt+:
 330 \begin{verbatim}
 331 0.3    0.3
 332 1.5    1
 333 4      0
 334 4.5    2.5
 335 1.81   2.14
 336 2.5    0.5
 337 2.8    1.5
 338 \end{verbatim}
 339 \begin{Exemple}
 340   \buildMeshBW[%
 341   tikz,
 342   mode = ext,
 343   bbox = show,
 344   color = red,
 345   colorBbox = blue!30,
 346   print = points,
 347   meshpoint = x,
 348   scale = 1.3cm,
 349   ]{mesh.txt}
 350 \end{Exemple}
 351
 352 \begin{warning}
 353 The drawing engine is not very relevant here, but it is useful to
 354 understand how the drawing is made. However, the engine will be
 355 relevant to
 356 the so called \emph{inc} macros (section~\ref{sec:inc}), for adding
 357 code before and after the one generated by
 358 \luamesh.
 359 \end{warning}
 360
 361 \subsection{Draw the Set of Points}
 362
 363 \commande|\drawPointsMesh[«options»]{«list of points» or «file name»}|\medskip
 364
 365 With the \Verb+\drawPointsMesh+, we plot the set of (user chosen) points from
 366 which the Bowyer and Watson algorithm computes the triangulation.
 367
 368 The use of this macro is quite similar to
 369 \Verb+\buildMeshBW+. Here is an example of the basic uses.
 370 \begin{Exemple}
 371   \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)}
 372 \end{Exemple}
 373
 374
 375 \subsubsection{The Options}
 376
 377 There are several options (exactly the same as for the
 378 \Verb+\buildMeshBW+) to customize the drawing.
 379 \begin{optionsenum}
 380 \item[mode = int (default) \textme{or} ext:] this option allows to
 381   use either the previously described set of points as the argument, or
 382   a file, containing, line by line (2 columns), the points. Such a
 383   file looks like :
 384 \begin{verbatim}
 385 x1  y1
 386 x2  y2
 387 x3  y3
 388 ...
 389 xn yn
 390 \end{verbatim}
 391 \item[bbox = none (default) \textme{or} show:] this option allows to draw the
 392   added points to form a \emph{bounding box} and the corresponding
 393   triangulation. By default, these triangles are removed at the end of
 394   the algorithm. \emph{Here, because we plot only the vertices of the
 395     mesh, there are no triangles, only dots.}
 396 \item[color = \meta{value} (default: black):] The color of the
 397   drawing.
 398 \item[colorBbox = \meta{value} (default: black):] The color of the
 399   drawing for the elements (points and triangles) belonging to the
 400   bounding box.
 401 \item[print = none (default) \textme{or} points:] To label the vertices of the
 402   triangulation. This also adds a \emph{dot} at each vertex. Without
 403   label, there is still the dot.
 404 \item[meshpoint = \meta{value} (default: P):] The letter(s) used to
 405   label the vertices of the triangulation. It is included in the math
 406   mode delimiters \Verb+$...$+. The bounding box points are labeled
 407   with numbers 1 to 4 and with a star exponent.
 408 \item[tikz (boolean, default:false):] By default, this boolean is set
 409   to \Verb+false+, and MetaPost (with \Verb+luamplib+) is used to draw
 410   the picture. With this option, \Verb+tikz+ becomes the \textit{drawing
 411     engine}.
 412 \item[scale = \meta{value} (default: 1cm):] The scale option defines
 413   the scale at which the picture is drawn (the same for both
 414   axes). It must contain the unit of length (cm,
 415   pt, etc.).
 416 \end{optionsenum}
 417 With the same external mesh point file presented in
 418 section~\ref{sec:buildMesh}, we illustrate the different options.
 419
 420 \begin{Exemple}
 421   \drawPointsMesh[%
 422   tikz,
 423   mode = ext,
 424   bbox = show,
 425   color = blue,
 426   colorBbox = red,
 427   print = points,
 428   meshpoint = y,
 429   scale = 1.3cm,
 430   ]{mesh.txt}
 431 \end{Exemple}
 432
 433
 434 \subsection{Draw a Step of the Bowyer and Watson Algorithm}
 435
 436 \commande|\meshAddPointBW[«options»]{«list of points» or «file name»}{«point» or «number of line»}|\medskip
 437
 438 This command allows to plot the steps within the addition of a
 439 point in a Delaunay triangulation, by the Bowyer and Watson
 440 algorithm.
 441
 442 This macro produces the Delaunay triangulation (using the Bowyer and
 443 Watson algorithm) of the given \meta{list of points} and shows a step
 444 of the algorithm when the \meta{point} is added. The list of
 445 points must be given in the following way:
 446 \begin{center}
 447   \verb+(x1,y1);(x2,y2);(x3,y3);...;(xn,yn)+
 448 \end{center}
 449 and the point is of the form \verb+(x,y)+. The \meta{file name}
 450 and \meta{number of line}  will be explained in the option
 451 description.
 452
 453 One can use the macro as fallows:
 454 \begin{Exemple}
 455   \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)}
 456   \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)}
 457   \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)}
 458 \end{Exemple}
 459 The default value for \Verb+step+ is
 460 \Verb+badtriangles+. Consequently, the first
 461 line is equivalent to
 462 \begin{latexcode}
 463 \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)}
 464 \end{latexcode}
 465
 466 \subsubsection{The Options}
 467
 468 There are several options (some of them are the same as for
 469 \Verb+\buildMeshBW+) to customize the drawing.
 470 \begin{optionsenum}
 471 \item[mode = int (default) \textme{or} ext:] this option allows to
 472   use either the previously described set of point in the first
 473   argument, or
 474   a file containing, line by line (2 columns), the points. Such a
 475   file looks like :
 476 \begin{verbatim}
 477 x1  y1
 478 x2  y2
 479 x3  y3
 480 ...
 481 xn yn
 482 \end{verbatim}
 483 For the second argument of the macro, if we are in the
 484 \Verb+mode = ext+, the argument must be the \emph{line number} of the file
 485 corresponding to the point we want to add. The algorithm will stop the
 486 line before to build the initial triangulation for which it will add
 487 the point corresponding to the line. The subsequent lines in the file are
 488 ignored.
 489 \item[bbox = none (default) \textme{or} show:] this option allows to draw the
 490   added points to form a \emph{bounding box} and the corresponding
 491   triangulation. By default, these triangles are removed at the end of
 492   the algorithm.
 493 \item[color = \meta{value} (default: black):] The color of the
 494   drawing.
 495 \item[colorBbox = \meta{value} (default: black):] The color of the
 496   drawing for the elements (points and triangles) belonging to the
 497   bounding box.
 498 \item[colorNew = \meta{value} (default: red):] The color of the
 499   drawing of the ``new'' elements which are the point to add, the
 500   polygon of the cavity, and the new triangles.
 501 \item[colorBack = \meta{value} (default: black!20):] The color for the
 502   filling of the region concerned by the addition of the new point.
 503 \item[colorCircle = \meta{value} (default: green):] The color for
 504   the circumcircle of the triangles containing the point to add.
 505 \item[meshpoint = \meta{value} (default: P):] The letter(s) used to
 506   label the vertices of the triangulation. It is included in the math
 507   mode delimiters \Verb+$...$+. The bounding box points are labeled
 508   with numbers 1 to 4 and with a star exponent.
 509 \item[step = badtriangles (default) \textme{or} cavity \textme{or}
 510   newtriangles:] To choose the step we want to draw, corresponding to
 511   the steps of the Bowyer and Watson algorithm.
 512 \item[newpoint = \meta{value} (default: P):] The letter(s) used to
 513   label the new point of the triangulation. It is include in the math
 514   mode delimiters \Verb+$...$+.
 515 \item[tikz (boolean, default:false):] By default, this boolean is set
 516   to \Verb+false+, and MetaPost (with \Verb+luamplib+) is used to draw
 517   the picture. With this option, \Verb+tikz+  is the \textit{drawing
 518     engine}.
 519 \item[scale = \meta{value} (default: 1cm):] The scale option defines
 520   the scale at which the picture is draw (the same for the two
 521   axis). It must contain the unit of length (cm,
 522   pt, etc.).
 523 \end{optionsenum}
 524
 525 Here is an example of customizing the drawing. First, recall that
 526 the external file \Verb+mesh.txt+ is:
 527 \begin{verbatim}
 528 0.3    0.3
 529 1.5    1
 530 4      0
 531 4.5    2.5
 532 1.81   2.14
 533 2.5    0.5
 534 2.8    1.5
 535 \end{verbatim}
 536 We draw the addition of the 6th point. The 7th line will be ignored.
 537 \begin{Exemple}
 538   \meshAddPointBW[
 539   tikz,
 540   mode = ext,
 541   color = blue!70,
 542   meshpoint = \alpha,
 543   newpoint = y,
 544   colorBack=red!10,
 545   colorNew = green!50!red,
 546   colorCircle = blue,
 547   colorBbox = black!20,
 548   bbox = show,
 549   scale=1.4cm,
 550   step=badtriangles]
 551   {mesh.txt}{6}
 552 \end{Exemple}
 553
 554 \section{The \emph{inc} Macros}\label{sec:inc}
 555
 556 The three macros presented in the above sections have complementary
 557 macros, with the suffix \Verb+inc+ that allow the user to add code
 558 (MetaPost or \Verb+tikz+, depending of the drawing engine) before and
 559 after the code generated by \luamesh.
 560
 561 The three macros are:
 562
 563 \commande|\buildMeshBWinc[«options»]{«list of points» or «file name»}{«code before»}{«code after»}|\medskip
 564
 565 \commande|\drawPointsMeshinc[«options»]{«list of points» or «file name»}{«code before»}{«code after»}|\medskip
 566
 567 \commande|\meshAddPointBWinc[«options»]{«list of points» or «file  name»}%|
 568
 569 \commande|                           {«point» or «number of line»}{«code before»}{«code after»}|\medskip
 570
 571 \subsection{With MetaPost}
 572
 573 We consider the case where the drawing engine is MetaPost (through the
 574 \Verb+luamplib+ package).
 575
 576 We describe the feature taking one macro in example but the mechanism
 577 and the possibilities are exactly the same for all the macros.
 578
 579 When we use the MetaPost drawing engine, the macros previously
 580 described produced a code of the form
 581 \begin{latexcode}
 582 \begin{luamplib}
 583
 584 \end{luamplib}
 585 \end{latexcode}
 586
 587
 588
 589 \subsection{With TikZ}
 590
 591 \section{Gallery of Examples}
 592
 593 \end{document}
 594
 595
 596
 597 %%% Local Variables:
 598 %%% flyspell-mode: 1
 599 %%% ispell-local-dictionary: "american"
 600 %%% End: