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List: scilab-users
Subject: [Scilab-users] Scilab and gmsh to plot surfaces
From: "Carrico, Paul" <paul.carrico () auxitrolweston ! com>
Date: 2019-06-27 13:50:23
Message-ID: 3A6B7233274DB449A2A0053A47684F953FFAF91F () BGS-EX01 ! auxitrol ! ad
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Dear All
After a tesselation using cgal library (delaunay_2), I used gmsh (http://gmsh.info/) \
to plot the triangles ... just an idea of sharing about 2 powerful tools :-) (useful \
with a huge amount of nodes)
A basic "saddle" surface has been used to test it
Hope it help
Paul
###############################################################################
clc, mode(0), clear
PATH = get_absolute_file_path("saddle.sce");
fich = mopen(PATH + "/saddle.msh","w");
// saddle surface
function [z]=saddle(x, y)
z = x^2 - y^2
endfunction
n = 100;
x = linspace(-2,2,n)'; // (n,1) matrix
y = linspace(-1,3,n)'; // (n,1) matrix
i = (1:n)'; j = ones(n,1);
X = x .*. j;
Y = j .*. y;
Z = saddle(X,Y);
// ### plot in gmsh ###
// Surface number
SurfaceNumber = 1;
//tri = delaunay_2(X,Y);
triangles = delaunay_2(X',Y');
NumberOfTriangles = size(triangles,"r");
mfprintf(fich,"$MeshFormat\n");
mfprintf(fich,"2.2 0 8\n");
mfprintf(fich,"$EndMeshFormat\n");
// Nodes
mfprintf(fich,"$Nodes\n");
mfprintf(fich,"%d\n",n*n);
i = (1:n*n)';
mfprintf(fich,"%d %g %g %g\n",i,X(i),Y(i),Z(i));
mfprintf(fich,"$EndNodes\n");
// elements
mfprintf(fich,"$Elements\n")
mfprintf(fich,"%d\n",NumberOfTriangles);
i = (1 : NumberOfTriangles)';
SurfaceNumber = SurfaceNumber*ones(NumberOfTriangles,1);
mfprintf(fich,"%d 2 2 %d %d %d %d \
%d\n",i,SurfaceNumber,SurfaceNumber,triangles(i,1),triangles(i,2),triangles(i,3)); \
mfprintf(fich,"$EndElements\n") mclose(fich);
// ### plot in scilab ###
scf(0);
drawlater();
f = gcf();
f.figure_size = [1000, 1000];
f.background = color(255,255,255);
a = gca();
a.font_size = 2;
a.x_label.text = '$X$';
a.x_label.font_size = 4;
a.y_label.text = '$Y$';
a.Y_label.font_size = 4;
a.z_label.text = "$\sigma$";
a.z_label.font_size = 4;
plot3d(x, y, feval(x, y, saddle));
drawnow();
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<div class="WordSection1">
<p class="MsoNormal">Dear All<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US">After a tesselation using cgal library \
(delaunay_2), I used gmsh (</span><a href="http://gmsh.info/"><span \
lang="EN-US">http://gmsh.info/</span></a><span lang="EN-US">) to plot the triangles \
… just an idea of sharing about 2 powerful \
tools :-)<o:p></o:p></span></p> <p class="MsoNormal"><span lang="EN-US">(useful \
with a huge amount of nodes)<o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US"><o:p> </o:p></span></p> <p class="MsoNormal"><span lang="EN-US">A \
basic “saddle” surface has been used to test it<o:p></o:p></span></p> <p \
class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p> <p \
class="MsoNormal"><span lang="EN-US">Hope it help<o:p></o:p></span></p> <p \
class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p> <p \
class="MsoNormal"><span lang="EN-US">Paul<o:p></o:p></span></p> <p \
class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p> <p \
class="MsoNormal"><span \
lang="EN-US">###############################################################################<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">clc</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#32B9B9">mode</span><span style="color:#4A55DB">(</span><span \
style="color:rosybrown">0</span><span style="color:#4A55DB">)</span><span \
style="color:black">,</span> <span \
style="color:#32B9B9">clear</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">PATH</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span \
style="color:#32B9B9">get_absolute_file_path</span><span \
style="color:#4A55DB">(</span><span \
style="color:rosybrown">"saddle.sce"</span><span \
style="color:#4A55DB">)</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">mopen</span><span \
style="color:#4A55DB">(</span><span style="color:black">PATH</span> <span \
style="color:#5C5C5C">+</span> <span \
style="color:rosybrown">"/saddle.msh"</span><span \
style="color:black">,</span><span style="color:rosybrown">"w"</span><span \
style="color:#4A55DB">)</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR">// \
saddle surface</span></i><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#B01813;mso-fareast-language:FR">function</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#4A55DB">[</span><b><span style="color:#834310">z</span></b><span \
style="color:#4A55DB">]</span><span style="color:#5C5C5C">=</span><u><span \
style="color:black">saddle</span></u><span style="color:#4A55DB">(</span><b><span \
style="color:#834310">x</span></b><span style="color:black">, </span><b><span \
style="color:#834310">y</span></b><span \
style="color:#4A55DB">)</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<b><span style="color:#834310">z</span></b> <span style="color:#5C5C5C">=</span> <b>
<span style="color:#834310">x</span></b><span style="color:#5C5C5C">^</span><span \
style="color:rosybrown">2</span> <span style="color:#5C5C5C">-</span> <b><span \
style="color:#834310">y</span></b><span style="color:#5C5C5C">^</span><span \
style="color:rosybrown">2</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#B01813;mso-fareast-language:FR">endfunction</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">n</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">100</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">x</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <u><span \
style="color:#AE5CB0">linspace</span></u><span style="color:#4A55DB">(</span><span \
style="color:#5C5C5C">-</span><span style="color:rosybrown">2</span><span \
style="color:black">,</span><span style="color:rosybrown">2</span><span \
style="color:black">,n</span><span style="color:#4A55DB">)</span><span \
style="color:#5C5C5C">'</span><span style="color:black">;</span> <i><span \
style="color:#64AE64">// (n,1) matrix</span></i><o:p></o:p></span></p> <p \
class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">y</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <u><span \
style="color:#AE5CB0">linspace</span></u><span style="color:#4A55DB">(</span><span \
style="color:#5C5C5C">-</span><span style="color:rosybrown">1</span><span \
style="color:black">,</span><span style="color:rosybrown">3</span><span \
style="color:black">,n</span><span style="color:#4A55DB">)</span><span \
style="color:#5C5C5C">'</span><span style="color:black">;</span> <i><span \
style="color:#64AE64">// (n,1) matrix</span></i><o:p></o:p></span></p> <p \
class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">i</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">(</span><span \
style="color:rosybrown">1</span><span style="color:#FFAA00">:</span><span \
style="color:black">n</span><span style="color:#4A55DB">)</span><span \
style="color:#5C5C5C">'</span><span style="color:black">;</span> <span \
style="color:black">j</span> <span style="color:#5C5C5C">=</span> <span \
style="color:#32B9B9"> ones</span><span style="color:#4A55DB">(</span><span \
style="color:black">n,</span><span style="color:rosybrown">1</span><span \
style="color:#4A55DB">)</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">X</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:black">x</span> <span \
style="color:#5C5C5C">
.*.</span> <span style="color:black">j;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">Y</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:black">j</span> <span \
style="color:#5C5C5C">
.*.</span> <span style="color:black">y;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">Z</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <u><span \
style="color:black">saddle</span></u><span style="color:#4A55DB">(</span><span \
style="color:black">X,Y</span><span style="color:#4A55DB">)</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR">// \
### plot in gmsh ###</span></i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR">// \
Surface number </span></i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">SurfaceNumber</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">1</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR">//tri \
= delaunay_2(X,Y);</span></i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">triangles</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span \
style="color:#32B9B9">delaunay_2</span><span style="color:#4A55DB">(</span><span \
style="color:black">X</span><span style="color:#5C5C5C">'</span><span \
style="color:black">,Y</span><span style="color:#5C5C5C">'</span><span \
style="color:#4A55DB">)</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">NumberOfTriangles</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">size</span><span \
style="color:#4A55DB">(</span><span style="color:black">triangles,</span><span \
style="color:rosybrown">"r"</span><span style="color:#4A55DB">)</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif&qu \
ot;;color:rosybrown;mso-fareast-language:FR">"$MeshFormat\n"</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">"2.2
0 8\n"</span><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif&qu \
ot;;color:rosybrown;mso-fareast-language:FR">"$EndMeshFormat\n"</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR">// \
Nodes</span></i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">"$Nodes\n"</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">"%d\n"</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,n</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">*</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">n</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">i</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">(</span><span \
style="color:rosybrown">1</span><span style="color:#FFAA00">:</span><span \
style="color:black">n</span><span style="color:#5C5C5C">*</span><span \
style="color:black">n</span><span style="color:#4A55DB">)</span><span \
style="color:#5C5C5C">'</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">"%d
%g %g %g\n"</span><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,i,X</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">i</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,Y</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">i</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,Z</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">i</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">))</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">"$EndNodes\n"</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR">// \
elements</span></i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">"$Elements\n"</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">"%d\n"</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,NumberOfTriangles</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">i</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">(</span><span \
style="color:rosybrown">1</span> <span style="color:#FFAA00">:</span> <span \
style="color:black">NumberOfTriangles</span><span style="color:#4A55DB">)</span><span \
style="color:#5C5C5C">'</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">SurfaceNumber</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span \
style="color:black">SurfaceNumber</span><span style="color:#5C5C5C">*</span><span \
style="color:#32B9B9">ones</span><span style="color:#4A55DB">(</span><span \
style="color:black">NumberOfTriangles,</span><span \
style="color:rosybrown">1</span><span style="color:#4A55DB">)</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">"%d
2 2 %d %d %d %d %d\n"</span><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,i,SurfaceNumber,SurfaceNumber,triangles</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">i,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">1</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,triangles</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">i,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">2</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,triangles</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">i,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">3</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">))</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mfprintf</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich,</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif&qu \
ot;;color:rosybrown;mso-fareast-language:FR">"$EndElements\n"</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mclose</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">fich</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR">// \
### plot in scilab ###</span></i><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><u><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">scf</span></u><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">0</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">drawlater</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">()</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">f</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <u><span \
style="color:#AE5CB0">gcf</span></u><span style="color:#4A55DB">()</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">f</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">figure_size</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">[</span><span \
style="color:rosybrown">1000</span><span style="color:black">,</span> <span \
style="color:rosybrown">1000</span><span style="color:#4A55DB">]</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">f</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">background</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">color</span><span \
style="color:#4A55DB">(</span><span style="color:rosybrown">255</span><span \
style="color:black">,</span><span style="color:rosybrown">255</span><span \
style="color:black">,</span><span style="color:rosybrown">255</span><span \
style="color:#4A55DB">)</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">a</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <u><span \
style="color:#AE5CB0">gca</span></u><span style="color:#4A55DB">()</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">a</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">font_size</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">2</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">a</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">x_label</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">text</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">'$X$'</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">a</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">x_label</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">font_size</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">4</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">a</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">y_label</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">text</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">'$Y$'</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">a</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">Y_label</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">font_size</span><span \
lang="EN-US" style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">4</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">a</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">z_label</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">text</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span \
style="color:rosybrown">"$\sigma$"</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">a</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">z_label</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">.</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#AAAAAA;mso-fareast-language:FR">font_size</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">4</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">plot3d</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">x,</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">y,</span> <span style="color:#32B9B9">feval</span><span \
style="color:#4A55DB">(</span><span style="color:black">x,</span> <span \
style="color:black">y,</span> <u><span style="color:black">saddle</span></u><span \
style="color:#4A55DB">))</span><span \
style="color:black">;</span><o:p></o:p></span></p> <p class="MsoNormal"><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">drawnow</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">()</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span \
style="font-size:10.0pt;font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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