summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/lualatex/luamesh/luamesh-doc.tex
blob: 07b6125f0fc9f985a954adcbe180d054807035e4 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
% luamesh: compute and draw meshes with lua, luamplib and tikz
%
% Originally written by Maxime Chupin <notezik@gmail.com>,
% 2017.
%
% Distributed under the terms of the GNU free documentation licence:
%   http://www.gnu.org/licenses/fdl.html
% without any invariant section or cover text.

\documentclass{luameshdoc}
\usepackage{tcolorbox}
\usepackage{enumitem}
\usepackage[tikz]{bclogo}
\usepackage{wrapfig}
\usepackage{animate}

\title{\Verb+luamesh+: compute and draw meshes with \lualatex}
\author{Maxime Chupin \email{notezik@gmail.com}}
\date{\today}


\definecolor{darkred}{rgb}{0.8,0.1,0.1}


\newcommand*\commande{\noindent\hspace{-30pt}%
  \SaveVerb[aftersave={%
   \UseVerb{Vitem}
  }%
  ]{Vitem}}

\newcommand*\textme[1]{\textcolor{black}{\rmfamily\textit{#1}}}
\newcommand*\meta[1]{% % meta
  \textme{\ensuremath{\langle}#1\ensuremath{\rangle}}}
\newcommand*\optstar{% % optional star
  \meta{\ensuremath{*}}\xspace}
\DefineShortVerb{\|}
\newcommand\R{\mathbf{R}}
\setlength{\fboxsep}{2pt}
\fvset{%
  codes={\catcode`\«\active \catcode`\×\active },
  defineactive={\makefancyog\makefancytimes},
  formatcom=\color{darkred},
  frame=single
}
% rendre «...» équivalent à \meta{...}
{\catcode`\«\active
  \newcommandx\makefancyog[0][addprefix=\global]{%
    \def«##1»{\meta{##1}}}}
% rendre × équivalent à \optstar
{\catcode`\×\active
  \newcommandx\makefancytimes[0][addprefix=\global]{%
    \def×{\optstar{}}}}


\tcbuselibrary{listings,breakable}

\definecolor{vert}{rgb}{0.1,0.4,0.1}
\definecolor{bleu}{rgb}{0.1,0.1,0.4}
\lstset{
  numberstyle=\footnotesize\color{vert},
  keywordstyle=\ttfamily\bfseries\color{blue},
  basicstyle=\ttfamily\footnotesize,
  commentstyle=\itshape\color{vert},
  stringstyle=\ttfamily,
  showstringspaces=false,
  language=[LaTeX]TeX,
  breaklines=true,
  breakindent=30pt,
  defaultdialect=[LaTeX]TeX,
  morekeywords={buildMeshBW,buildMeshBWinc,drawPointsMesh,buildVoronoiBW,buildVoronoiBWinc,
    drawPointsMeshinc, meshAddPointBW,
    meshAddPointBWinc,drawGmsh,drawGmshinc,gmshVoronoi,gmshVoronoiinc}% frame=tb
}

\lstdefinelanguage{lua}
{morekeywords={for,end,function,do,if,else,elseif,then,
    tex.print,tex.sprint,io.read,io.open,string.find,string.explode,require},
  morecomment=[l]{--},
  morecomment=[s]{--[[}{]]},
  morestring=[b]''
}

\newtcblisting{Exemple}{%
  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 options={breaklines},
}

\newtcblisting{commandshell}{colback=black,colupper=white,colframe=black,
  arc=0pt,
  listing only,boxsep=0pt,listing
  options={style=tcblatex,language=sh},
  every listing line={\textcolor{red}{\small\ttfamily\bfseries user \$> }}}

\newtcblisting{latexcode}{
  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={breaklines}
}


\newcommand\luamesh{\Verb+luamesh+\xspace}

\newenvironment{optionsenum}[1][]
{\begin{description}[font=\color{darkred}\ttfamily]}
  {\end{description}}

\newenvironment{warning}{%
  \setlength{\logowidth}{24pt}
  \tcbset{%
    arc=0pt,outer arc=0pt,colback=gray!10!white,colframe=gray!60!white,
    boxsep=0pt,left=5pt,right=5pt,top=5pt,bottom=5pt, bottomtitle = 3pt, toptitle=3pt,
    boxrule=0pt,bottomrule=0.5pt,toprule=0.5pt}
  \medskip
  \begin{tcolorbox}%
    \begin{wrapfigure}[2]{L}{17pt}%
      % \raisebox{-5pt}{
      \vspace*{-0.55cm}
      \bcinfo
      % }%
    \end{wrapfigure}
  }%
  {\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}
\begin{tikzpicture}[remember picture, overlay]
  \node[below right, shift={(-4pt,4pt)}] at (current page.north west) {%
    \includegraphics{fond.pdf}%
  };
\end{tikzpicture}%

\noindent
\includegraphics{luamesh-title}\\
{\large compute and draw meshes with \lualatex}\\[1cm]
\parbox{0.6\textwidth}{
  \meshAddPointBW[
  mode=ext,step=badtriangles,
  colorNew =green!20!red,
  colorBack=red!10,
  colorCircle = blue,
  bbox = show,
  colorBbox = black!30
  ]
  {meshgarde.txt}{7}
}\hfill
\parbox{0.4\textwidth}{\Large\raggedleft
  \textbf{Contributor}\\
  Maxime \textsc{Chupin}
}
\vfill
\begin{center}
  Version 0.6, 2020, June, 6th \\
  \url{https://plmlab.math.cnrs.fr/mchupin/luamesh}
\end{center}
%% == Page de garde ====================================================
\newpage

\maketitle

\begin{abstract}
  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, or 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}
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}

\luamesh is on the CTAN and can be installed with the package manager of
your distribution.

\begin{center}
  \url{https://www.ctan.org/pkg/luamesh}
\end{center}

Of course, you can just put the two files \Verb+luamesh.lua+ and
\Verb+luamesh.sty+ in the working directory but this 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+.

\begin{commandshell}
mkdir ~/texmf
\end{commandshell}

Then place the files in the correct directories. The
\Verb+luamesh.sty+ file must be in directory:
\begin{center}
  \Verb+~/texmf/tex/latex/luamesh/+
\end{center}
and the \Verb+luamesh.lua+, the \Verb+luamesh-tex.lua+ and the
\Verb-luamesh-polygon.lua+ files must be in directory:
\begin{center}
  \Verb+~/texmf/scripts/luamesh/+
\end{center}

Once you have done this, \luamesh can be included in your document
with
\begin{latexcode}
\usepackage{luamesh}
\end{latexcode}

\subsection{With Mik\TeX{} and Windows}

As these two systems are unknown to the contributor, 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 existing packages that one used to
draw the
triangulations :
\begin{enumerate}
\item \Verb+luamplib+ to use MetaPost via the \luatex library
  \Verb+mplib+;
\item \Verb+tikz+.
\end{enumerate}
We will see how to choose between these two \emph{drawing engines}.
Moreover, the following packages are necessary:
\begin{enumerate}
\item \Verb+xkeyval+ to manage the optional arguments;
\item \Verb+xcolor+ to use colors (required by \Verb+luamplib+);
\item \Verb+ifthen+ to help programming with \TeX.
\end{enumerate}


\section{The Basic Macros}

This package provides macros to draw two
dimensional triangulations (or meshes).

\subsection{Draw a Complete Mesh}\label{sec:buildMesh}

\commande|\buildMeshBW[«options»]{«list of points» or «file name»}|\medskip

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}
  \verb+(x1,y1);(x2,y2);(x3,y3);...;(xn,yn)+
\end{center}

\begin{Exemple}
  \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)}
\end{Exemple}

\subsubsection{The Options}

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 the points line by line (in 2 columns). 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
  points  added to form the \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
  triangles attached. 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[print = none (default) \textme{or} points \textme{or}
  dotpoints:] The \Verb+point+ value allows to label the vertices of the
  triangulation. This also adds a \emph{dot} at each vertex. The
  \Verb+dotpoints+ value only add a dot without the labeling.
\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}

To illustrate the options, let us show you an example. We consider a
file \Verb+mesh.txt+:
\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}
\begin{Exemple}
  \buildMeshBW[%
  tikz,
  mode = ext,
  bbox = show,
  color = red,
  colorBbox = blue!30,
  print = points,
  meshpoint = x,
  scale = 1.3cm,
  ]{mesh.txt}
\end{Exemple}

\begin{warning}
The drawing engine is not very relevant here, although it is useful to
understand how the drawing is produced. 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}

\subsection{Draw the Set of Points}

\commande|\drawPointsMesh[«options»]{«list of points» or «file name»}|\medskip

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
\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 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 points as the argument, or
  a file containing the points line by line (in 2 columns). 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
  points  added to form the \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
  triangles attached. By default, these triangles are removed at the end of
  the algorithm. \emph{Here, because we plot only the vertices of the
    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
  triangulation. This also adds a \emph{dot} at each vertex. With no
  label, the dot remains.
\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
  label the vertices of the triangulation. This 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}
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»}|\medskip

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 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:
\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 follows:
\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+. 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}

\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 points as the argument, or
  a file containing the points line by line (in 2 columns). 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
\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 at the
previous line to build the initial triangulation and proceed to add
the point corresponding to the line requested. The subsequent lines in
the file are
ignored.
\item[bbox = none (default) \textme{or} show:] this option allows to draw the
  added points that form the \emph{bounding box} and the triangles
  attached. Although they are always computed, 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 delimiting 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
  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 included in the math
  mode delimiters \Verb+$...$+. The bounding box points are labeled
  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.
\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, \Verb+tikz+  is 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
  axis). It must contain the unit of length (cm,
  pt, etc.).
\end{optionsenum}

Here is an example of customizing 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 = \alpha,
  newpoint = y,
  colorBack=red!10,
  colorNew = green!50!red,
  colorCircle = blue,
  colorBbox = black!20,
  bbox = show,
  scale=1.4cm,
  step=badtriangles]
  {mesh.txt}{6}
\end{Exemple}

\subsection{Mesh a Polygon}

\commande|\meshPolygon[«options»]{«list of points» or «file name»}|\medskip


With \luamesh, it is possible to mesh an object giving the
\emph{border}, \emph{i.e.}, one closed polygon. The polygon is given
as a list of points as above:
\begin{center}
  \verb+(x1,y1);(x2,y2);(x3,y3);...;(xn,yn)+
\end{center}
Once again we can also give a file of points using the \Verb+mode+
option.

This command allows to plot the steps within the building of a complete
mesh. The followed method is, given a parameter $h$:
\begin{itemize}
\item to build a squared grid of points with a unit distance equal to
  $h$;
\item to keep the grid points inside the polygon;
\item if necessary to add points along the polygon to respect the
  distance parameter;
\item to mesh the complete set of points (using the Bowyer and Watson
  algorithm).
\end{itemize}
One can use the macro as follows:
\begin{Exemple}
  \meshPolygon[step=polygon,scale=2cm]{(0,0);(1,0);(1,0.5);(0,0.5);(-0.20,0.35);(-0.25,0.25);(-0.20,0.15)}
  \meshPolygon[step=grid,scale=2cm]{(0,0);(1,0);(1,0.5);(0,0.5);(-0.20,0.35);(-0.25,0.25);(-0.20,0.15)}
  \meshPolygon[step=points,scale=2cm]{(0,0);(1,0);(1,0.5);(0,0.5);(-0.20,0.35);(-0.25,0.25);(-0.20,0.15)}
  \meshPolygon[step=mesh,scale=2cm]{(0,0);(1,0);(1,0.5);(0,0.5);(-0.20,0.35);(-0.25,0.25);(-0.20,0.15)}
\end{Exemple}

Note that if the points of the grid are too closed to the points of
the refined boundary, they are ejected.

\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 points as the argument, or
  a file containing the points line by line (in 2 columns). Such a
  file looks like :
\begin{verbatim}
x1  y1
x2  y2
x3  y3
...
xn yn
\end{verbatim}
\item[h = \meta{value} (default: 0.2):] The mesh parameter, it is the
  unit distance for the grid. If necessary, the boundary is refined to
  get points which respect the distance constrain.
\item[color = \meta{value} (default: black):] The color of the
  drawing (the grid point and the mesh).
\item[colorPolygon = \meta{value} (default: red):] The color of the
  drawing for the boundary polygon.
\item[print = none (default) \textme{or} points \textme{or}
  dotpoints:] The \Verb+point+ value allows to label the vertices of the
  triangulation. This also adds a \emph{dot} at each vertex. The
  \Verb+dotpoints+ value only add a dot without the labeling.
\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+$...$+.
\item[step = polygon  \textme{or} grid \textme{or}
  points \textme{or} mesh (default):] To choose the step we want to draw,
  see the description above.
\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+  is 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
  axis). It must contain the unit of length (cm,
  pt, etc.).
\item[gridpoints = rect (default)  \textme{or} perturb:] This option
  allows to specify the mode of generation of the grid points. The
  value \Verb+rect+ produces a simple rectangular grid, and the value
  \Verb+pertub+ randomly perturbs the rectangular grid.
\end{optionsenum}

Here is an example of customizing the drawing.
\begin{Exemple}
  \meshPolygon[
  tikz,
  color = blue!70,
  meshpoint = \alpha,
  colorPolygon=red!100,
  scale=4cm,
  step=mesh,
  print=points,
  gridpoints=perturb]
  {(0,0);(1,0);(1,0.5);(0,0.5);(-0.20,0.35);(-0.25,0.25);(-0.20,0.15)}
\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}

We consider the case where the drawing engine is MetaPost (through the
\Verb+luamplib+ package).

The feature is described for the \Verb+\buildMeshBWinc+ but the mechanism
and possibilities are exactly the same for all three macros.

When we use the MetaPost drawing engine, the macros previously
described produce 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}\label{sec:mpcolor}

The configurable colors
of the \LaTeX{} macro are accessible inside the MetaPost code. For
\Verb+\buildMeshBWinc+ and \Verb+\drawPointsMeshinc+,
\Verb+\luameshmpcolor+,
and \Verb+\luameshmpcolorBbox+ have been defined.
For the macro \Verb+\meshAddPointBWinc+ three additional
colors are present: \Verb+\luameshmpcolorBack+,
\Verb+\luameshmpcolorNew+, and
\Verb+\luameshmpcolorCircle+. For the macro \Verb+\meshPolygon+, the
color \Verb+\luameshmpcolorPoly+ is defined. Of course, MetaPost
colors can be defined as well. Finally, the \Verb+luamplib+ mechanism
\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 in
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+pair+s ($\R^{2}$ points)
\Verb+MeshPoints[i]+ are
defined using the unit length \Verb+u+.

With the \Verb+\meshPolygon+ macro, we have the points of the polygon
(refined) that are available with the
\Verb+polygon[]+ table of variables.

\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 placed \textbf{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 drawing engine, 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 used directly.

\subsubsection{The Mesh Points}

The mesh points  are defined here as \Verb+tikz+
\Verb+\coordinate+ and named as follows
\begin{latexcode}
\coordinate (MeshPoints1) at (...,...);
\coordinate (MeshPoints2) at (...,...);
\coordinate (MeshPoints3) at (...,...);
%etc.
\end{latexcode}

With the \Verb+\meshPolygon+ we have also the polygon points coordinates:
\begin{latexcode}
\coordinate (polygon1) at (...,...);
%etc.
\end{latexcode}

Once again these coordinates are not yet defined to be used in the
code given by \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{Voronoï Diagrams}

Another interesting feature of b Delaunay triangulation is that its
\emph{dual} is the so-called Voronoï diagram. More precisely, for a
finite set of
points $\{p_{1},\ldots, p_{n}\}$ in the Euclidean plane, the Voronoï
cell $R_{k}$ corresponding to $p_{k}$ is the set of
all points in the Euclidean plane $\R^{2}$ 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 Voronoï diagram  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 the points line by line (in 2 columns). 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
  Voronoï diagram.
\item[print = none (default) \textme{or} points:] To label the
  vertices in 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 at the circumcircle centers which are the nodes of
  the Voronoï diagram.
\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
  label the vertices of the triangulation. This is included in the math
  mode delimiters \Verb+$...$+. The bounding box points are labelled
  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 Voronoï diagram. This 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.).
\item[delaunay = none (default) \textme{or} show:] This option
  allows to draw the Delaunay triangulation under the Voronoï diagram.
\item[styleDelaunay = none (default) \textme{or} dashed:] This option
  allows to draw the Delaunay triangulation in dashed lines.
\item[styleVoronoi = none (default) \textme{or} dashed:] This option
  allows to draw the Voronoï edges in dashed lines.
\end{optionsenum}

\begin{Exemple}
  \buildVoronoiBW[tikz,delaunay=show,styleDelaunay=dashed]
  {(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 \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
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 they 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 an 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 draws the triangulation produced by Gmsh and exported in the
\Verb+msh+ format. The argument is the name of the file to be read
(e.g.: \Verb+maillage.msh+).

Since the version 0.6, \luamesh support both version 2 and 4 of the \emph{MSH ASCII file format}.


\begin{Exemple}
\drawGmsh{maillage.msh} % version 2.2 of MSH ASCII file format
\end{Exemple}


\begin{Exemple}
  \drawGmsh{maillagev4.msh} % version 4.1 of MSH ASCII file format
\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 some previous macros, when
  \Verb+print=none+  a \emph{dot} is produced at each vertex of the
  set of points and at the circumcircle centers (these are the nodes of
  the Voronoï diagram).
\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
  label the vertices of the triangulation. This 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 Voronoï Diagrams}

Because Gmsh generates Delaunay triangulations, we can plot the associated
Voronoï diagram. This is done by the following macro:\bigskip

\commande|\gmshVoronoi[«options»]{«file name»}|\medskip

\begin{Exemple}
  \gmshVoronoi{maillage.msh}
\end{Exemple}


\subsection{The Options}\label{sec:voronoiOptions}


There are several options to customize the drawing.
\begin{optionsenum}
\item[color = \meta{value} (default: black):] The color of the
  drawing.
\item[colorVoronoi = \meta{value} (default: black):] The color of the
  drawing for the elements (points and polygons) belonging to the
  Voronoï diagram.
\item[print = none (default) \textme{or} points:] To label the vertices of the
  triangulation. Contrary to some previous macros, when
  \Verb+print=none+,  a \emph{dot} is produced at each vertex of the
  set of points and at the circumcircle centers (these are the nodes of
  the Voronoï 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 Voronoï diagram. This 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.).
\item[delaunay = none (default) \textme{or} show] This option
  allows to draw the Delaunay triangulation overlapped with the
  Voronoï diagram.
\item[styleDelaunay = none (default) \textme{or} dashed] This option
  allows to draw the Delaunay triangulation in dashed lines.
\item[styleVoronoi = none (default) \textme{or} dashed] This option
  allows to draw the Voronoï edges in dashed lines.
\end{optionsenum}

\begin{Exemple}
  \gmshVoronoi[tikz,scale=3cm, delaunay=show,styleVoronoi=dashed]{maillagev4.msh}
\end{Exemple}


\subsection{The \emph{inc} variants}

Once again, there exist \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}


\section{History}

\begin{itemize}
\item June, 6th, 2020, v 0.6, correction of bug produced by the
  deleted \Verb+\mplibcolor+ function of \Verb+luamplib+ package.
\item June, 6th, 2020, v 0.6, add support of version 4 of the
  \emph{MSH ASCII file format}.
\end{itemize}


\input{dum.bbl}

\end{document}



%%% Local Variables:
%%% flyspell-mode: 1
%%% ispell-local-dictionary: "american"
%%% End: