From 30844d84fbfc8309bc2ef767bb9e4171c54d8c3c Mon Sep 17 00:00:00 2001
From: "Maxime Chupin (escudo)" <chupin@fougeriens.org>
Date: Tue, 15 Nov 2016 22:25:10 +0100
Subject: [PATCH] Luamplib et animate

---
 luamplibAnimate/LISTE.txt        |      3 +
 luamplibAnimate/Makefile         |      7 +
 luamplibAnimate/index.xml        |      7 +
 luamplibAnimate/mplibanimate.pdf | 151041 ++++++++++++++++++++++++++++
 luamplibAnimate/mplibanimate.tex |     92 +
 luamplibAnimate/page-html.tmpl   |     12 +
 luamplibAnimate/page.html        |    102 +
 luamplibAnimate/page.md          |    138 +
 8 files changed, 151402 insertions(+)
 create mode 100644 luamplibAnimate/LISTE.txt
 create mode 100644 luamplibAnimate/Makefile
 create mode 100644 luamplibAnimate/index.xml
 create mode 100644 luamplibAnimate/mplibanimate.pdf
 create mode 100644 luamplibAnimate/mplibanimate.tex
 create mode 100644 luamplibAnimate/page-html.tmpl
 create mode 100644 luamplibAnimate/page.html
 create mode 100644 luamplibAnimate/page.md

diff --git a/luamplibAnimate/LISTE.txt b/luamplibAnimate/LISTE.txt
new file mode 100644
index 0000000..914f4d4
--- /dev/null
+++ b/luamplibAnimate/LISTE.txt
@@ -0,0 +1,3 @@
+== Sources et pdf produit
+mplibanimate.pdf
+mplibanimate.tex
diff --git a/luamplibAnimate/Makefile b/luamplibAnimate/Makefile
new file mode 100644
index 0000000..e554521
--- /dev/null
+++ b/luamplibAnimate/Makefile
@@ -0,0 +1,7 @@
+TXT = $(wildcard *.md)
+HTM = $(patsubst %.md,%.html,$(TXT))
+TEX = $(patsubst %.text,%.tex,$(TXT))
+
+html: $(HTM)
+$(HTM) : %.html : %.md
+	pandoc -s  --template page-html.tmpl --email-obfuscation=references -f markdown -t html $< > $@
diff --git a/luamplibAnimate/index.xml b/luamplibAnimate/index.xml
new file mode 100644
index 0000000..c762cdb
--- /dev/null
+++ b/luamplibAnimate/index.xml
@@ -0,0 +1,7 @@
+<page encoding="UTF-8">
+  <titre>
+    Animation avec luamplib et animate
+  </titre>
+  <contenu date="fichier" f="page.html"/>
+  <auteur>Maxime Chupin</auteur>
+</page>
diff --git a/luamplibAnimate/mplibanimate.pdf b/luamplibAnimate/mplibanimate.pdf
new file mode 100644
index 0000000..1f7d33a
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+%%Title: CMMI10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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diff --git a/luamplibAnimate/mplibanimate.tex b/luamplibAnimate/mplibanimate.tex
new file mode 100644
index 0000000..41a0278
--- /dev/null
+++ b/luamplibAnimate/mplibanimate.tex
@@ -0,0 +1,92 @@
+\documentclass{article}
+\usepackage{animate}
+\usepackage{luamplib}
+
+\begin{document}
+
+
+\mplibcodeinherit{enable} % pour permettre la mémoire entre les
+                          % biginfig(i) produites
+\newcommand{\lemniscate}[1]{% #1: l'angle en degres
+  \begin{mplibcode}
+    if(#1=0):
+    u:=4cm;%
+    a:=2u;%
+    h:=a/4;%
+    s:=1.3;%
+    path lemn;%
+    path carre;%
+    carre = (0,0)--(1,0)--(1,1)--(0,1)--cycle;
+    fi;
+    beginfig(#1);
+    pickup pencircle scaled 0.6pt;
+    drawarrow (0,-s*u)--(0,s*u);
+    drawarrow (-s*u,0)--(s*u,0);
+    path cercle,hori,verti;
+    pair O,P,Q,R,M;
+    O:=(0,0);
+    cercle := fullcircle scaled (a);
+    pickup pencircle scaled 0.4pt;
+    draw cercle dashed evenly withcolor blue;
+    P:=(a/2*cosd(#1),a/2*sind(#1)); % chemin qui parcourt le cercle
+    Q:=(a/2*cosd(#1),0); %projection sur (Ox)
+    % projection de Q sur [O,P]
+    R = cosd(#1)*cosd(#1)*(a/2*cosd(#1),a/2*sind(#1));
+    % M sur [PQ] tel que QM = QR
+    QR := abs(R-Q);
+    if(sind(#1)>0.0):
+    M = Q + (0,QR);
+    else:
+    M = Q - (0,QR);
+    fi;
+
+    if #1=0:
+    lemn:=M;
+    else:
+    lemn:= lemn--M;
+    fi;
+
+    if ((#1>0) and (#1<90)) or ((#1>180) and (#1<270)):
+    draw carre scaled 6 rotated (angle(Q-P)+180) shifted Q;
+    draw carre scaled 6 rotated (angle(R-P)) shifted R;
+    fi;
+    if((#1>=90) and (#1<180)) or ((#1>=270) and (#1<360)):
+    draw carre scaled 6 rotated (angle(Q-P)+180) shifted Q;
+    draw carre scaled 6 rotated (angle(R-P)+180) shifted R;
+    fi;
+
+    draw O--P dashed evenly withcolor blue;
+    draw P--Q dashed evenly withcolor blue;
+    draw R--Q--M withcolor green;
+
+    label.lrt(btex $a$ etex, (a/2,0));
+    label.llft(btex $x$ etex, (s*u,0));
+    label.llft(btex $y$ etex, (0,s*u));
+    label(btex \itshape Lemniscate \par de Gerono etex, (-0.7u,1.15u));
+    label(btex $x^4=a^2(x^2-y^2)$ etex, (0.7u,-1.15u));
+
+
+    dotlabel.llft(btex $O$ etex, O);
+    dotlabel.urt(btex $M$ etex, M);
+    dotlabel.urt(btex $P$ etex, P);
+    dotlabel.urt(btex $Q$ etex, Q);
+    dotlabel.urt(btex $R$ etex, R);
+
+    pickup pencircle scaled 1pt;
+    draw lemn withcolor red;
+
+    clip currentpicture to (-s*u,-s*u)--(s*u,-s*u)--(s*u,s*u)--(-s*u,s*u)--cycle;
+    endfig;
+  \end{mplibcode}
+}
+
+
+\begin{center}
+  \begin{animateinline}[poster=last, controls]{24}
+    %
+    \multiframe{360}{i=0+1}{\lemniscate{\i}}
+  \end{animateinline}
+\end{center}
+
+Le PDF produit est à télécharger dans la liste plus haut.
+\end{document}
diff --git a/luamplibAnimate/page-html.tmpl b/luamplibAnimate/page-html.tmpl
new file mode 100644
index 0000000..288cc6e
--- /dev/null
+++ b/luamplibAnimate/page-html.tmpl
@@ -0,0 +1,12 @@
+<div>
+$body$
+</div>
+$if(toc)$
+<div id="TDM" class="tdm">
+<div style="text-align:center">
+  <a href="javascript:tdmgauche();">&larr;</a>&nbsp;<b>Sections</b>&nbsp;<a href="javascript:tdmdroite();">&rarr;</a>
+</div>
+ $toc$
+</div>
+$endif$
+<div style="clear:both"></div>
\ No newline at end of file
diff --git a/luamplibAnimate/page.html b/luamplibAnimate/page.html
new file mode 100644
index 0000000..b7a74e6
--- /dev/null
+++ b/luamplibAnimate/page.html
@@ -0,0 +1,102 @@
+<div>
+<div class="alert alert-info">
+<p>
+<p>Grâce à l'extension <code>luamplib</code> pour Lua(La)TeX et l'extension <code>animate</code>, on peut réaliser très facilement des animations avec MetaPost, lisibles dans an PDF avec <em>Acrobat Reader</em>. En effet, <code>luamplib</code> nous permet de créer des figures avec l'environnement <code>mplibcode</code> qu'on anime avec l'environnement <code>animateinline</code>.</p>
+<p>Les documentations des deux extensions utilisées :</p>
+<ul>
+<li><a href="http://mirror.hmc.edu/ctan/macros/luatex/generic/luamplib/luamplib.pdf%20%22lien%20vers%20le%20pdf%22"><code>luamplib</code></a></li>
+<li><a href="http://distrib-coffee.ipsl.jussieu.fr/pub/mirrors/ctan/macros/latex/contrib/animate/animate.pdf%20%22lien%20vers%20le%20pdf%22"><code>animate</code></a>.</li>
+</ul>
+</div>
+<ul>
+<li>La compilation se fait avec : <code>lualatex mplibanimate.tex</code>.</li>
+<li>Le code MetaPost est extrait de l'<a href="http://melusine.eu.org/syracuse/metapost/animations/gerono/" class="uri">http://melusine.eu.org/syracuse/metapost/animations/gerono/</a></li>
+</ul>
+<h2 id="explications">Explications</h2>
+<p>L’extension animate permet de générer des animations lisibles dans un PDF par le lecteur <em>Acrobat Reader</em>. Plusieurs options sont envisageables : soit produire l’animation à partir d’une séquence d’images pré-construites (sous différents formats, JPEG, ps, pdf, etc.), soit à partir d’image généré par du code LaTeX comme tikz , pstricks , etc. et... MetaPost ! C’est ce que nous présentons ici à partir de l'exemple d'<a href="http://melusine.eu.org/syracuse/metapost/animations/gerono/" class="uri">http://melusine.eu.org/syracuse/metapost/animations/gerono/</a>.</p>
+<p>Dans cet exemple, on paramétrise un certain point (P = (, )) à l’aide du paramètre d’angel () qui permet de construire le lemniscate de Gerono grâce à la recette suivante :</p>
+<div class="alert alert-info">
+<p>Soit (P) un point décrivant un cercle de centre (O) et de rayon (a). On projette (P) en (Q) sur l’axe ((Ox)), puis (Q) en (R) sur le segment ([OP]). Le lemniscate de Gerono est alors le lieu du point (M) de ([PQ]) tel que (QM = QN).</p>
+</div>
+<p>À partir de là, on construit la commande qui prend pour argument la valeur de l’angle, et qui construit l’image correspondante. On va ici utiliser l’<em>héritage</em> qui permet de garder en mémoire les unités et la courbe construite au fur et à mesure, à partir des étapes précédentes.</p>
+<p>On encapsule le code MetaPost dans un <em>macro</em> LaTeX grâce à l'environnement <code>mplibcode</code> de <code>luamplib</code>.</p>
+<div class="sourceCode"><pre class="sourceCode latex"><code class="sourceCode latex">\mplibcodeinherit{enable} <span class="co">% l&#39;héritage pour la mémoire entre les figures</span>
+\newcommand{\lemniscate}[1]{<span class="co">% #1: l&#39;angle en degres</span>
+  \begin{mplibcode}
+    if(#1=0):
+    u:=3cm;<span class="co">%</span>
+    a:=2u;<span class="co">%</span>
+    h:=a/4;<span class="co">%</span>
+    s:=1.3;<span class="co">%</span>
+    path lemn;<span class="co">%</span>
+    path carre;<span class="co">%</span>
+    carre = (0,0)--(1,0)--(1,1)--(0,1)--cycle;
+    fi;
+    beginfig(#1);
+    pickup pencircle scaled 0.6pt;
+    drawarrow (0,-s*u)--(0,s*u);
+    drawarrow (-s*u,0)--(s*u,0);
+    path cercle,hori,verti;
+    pair O,P,Q,R,M;
+    O:=(0,0);
+    cercle := fullcircle scaled (a);
+    pickup pencircle scaled 0.4pt;
+    draw cercle dashed evenly withcolor blue;
+    P:=(a/2*cosd(#1),a/2*sind(#1)); <span class="co">% chemin qui parcourt le cercle</span>
+    Q:=(a/2*cosd(#1),0); <span class="co">%projection sur (Ox)</span>
+    <span class="co">% projection de Q sur [O,P]</span>
+    R = cosd(#1)*cosd(#1)*(a/2*cosd(#1),a/2*sind(#1));
+    <span class="co">% M sur [PQ] tel que QM = QR</span>
+    QR := abs(R-Q);
+    if(sind(#1)&gt;0.0):
+    M = Q + (0,QR);
+    else:
+    M = Q - (0,QR);
+    fi;
+
+    if #1=0:
+    lemn:=M;
+    else:
+    lemn:= lemn--M;
+    fi;
+
+    if ((#1&gt;0) and (#1&lt;90)) or ((#1&gt;180) and (#1&lt;270)):
+    draw carre scaled 6 rotated (angle(Q-P)+180) shifted Q;
+    draw carre scaled 6 rotated (angle(R-P)) shifted R;
+    fi;
+    if((#1&gt;=90) and (#1&lt;180)) or ((#1&gt;=270) and (#1&lt;360)):
+    draw carre scaled 6 rotated (angle(Q-P)+180) shifted Q;
+    draw carre scaled 6 rotated (angle(R-P)+180) shifted R;
+    fi;
+
+    draw O--P dashed evenly withcolor blue;
+    draw P--Q dashed evenly withcolor blue;
+    draw R--Q--M withcolor green;
+
+    label.lrt(btex $a$ etex, (a/2,0));
+    label.llft(btex $x$ etex, (s*u,0));
+    label.llft(btex $y$ etex, (0,s*u));
+    label(btex \itshape Lemniscate \par de Gerono etex, (-0.7u,1.15u));
+    label(btex $x^4=a^2(x^2-y^2)$ etex, (0.7u,-1.15u));
+
+    dotlabel.llft(btex $O$ etex, O);
+    dotlabel.urt(btex $M$ etex, M);
+    dotlabel.urt(btex $P$ etex, P);
+    dotlabel.urt(btex $Q$ etex, Q);
+    dotlabel.urt(btex $R$ etex, R);
+
+    pickup pencircle scaled 1pt;
+    draw lemn withcolor red;
+
+    clip currentpicture to (-s*u,-s*u)--(s*u,-s*u)--(s*u,s*u)--(-s*u,s*u)--cycle;
+    endfig;
+  \end{mplibcode}
+}</code></pre></div>
+<p>Il suffit alors de construire l'animation avec l'extension <code>animate</code> et son environnement <code>animateinline</code>.</p>
+<div class="sourceCode"><pre class="sourceCode latex"><code class="sourceCode latex">\begin{center}
+\begin{animateinline}[poster=230, controls]{24}
+  \multiframe{360}{ii=0+1}{\lemniscate{\ii}}
+\end{animateinline}
+\end{center}</code></pre></div>
+</div>
+<div style="clear:both"></div>
\ No newline at end of file
diff --git a/luamplibAnimate/page.md b/luamplibAnimate/page.md
new file mode 100644
index 0000000..5be9269
--- /dev/null
+++ b/luamplibAnimate/page.md
@@ -0,0 +1,138 @@
+<div class="alert alert-info">
+<p>Grâce à l'extension `luamplib` pour Lua(La)TeX et
+l'extension `animate`, on peut réaliser très facilement des
+animations avec MetaPost, lisibles dans an PDF avec *Acrobat
+Reader*. En effet, `luamplib` nous permet de créer des
+figures avec l'environnement `mplibcode` qu'on anime avec
+l'environnement `animateinline`.
+
+Les documentations des deux
+extensions utilisées  :
+
+* [`luamplib`](http://mirror.hmc.edu/ctan/macros/luatex/generic/luamplib/luamplib.pdf
+"lien vers le pdf")
+* [`animate`](http://distrib-coffee.ipsl.jussieu.fr/pub/mirrors/ctan/macros/latex/contrib/animate/animate.pdf
+"lien vers le pdf").
+
+</div>
+
+* La compilation se fait avec : `lualatex mplibanimate.tex`.
+* Le code MetaPost est extrait de l'<http://melusine.eu.org/syracuse/metapost/animations/gerono/>
+
+## Explications
+
+L’extension animate permet de générer des animations lisibles dans un
+PDF par le lecteur *Acrobat Reader*. Plusieurs options sont
+envisageables : soit produire l’animation à partir d’une séquence
+d’images pré-construites (sous différents formats, JPEG, ps, pdf,
+etc.), soit à partir d’image généré par du code LaTeX comme tikz ,
+pstricks , etc. et... MetaPost ! C’est ce que nous présentons ici à
+partir de l'exemple
+d'<http://melusine.eu.org/syracuse/metapost/animations/gerono/>.
+
+Dans cet exemple, on paramétrise un certain point \(P = (\cos \theta,
+\sin \theta)\) à l’aide du paramètre d’angel \(\theta\) qui permet de
+construire le lemniscate de Gerono grâce à la recette suivante :
+
+
+<div class="alert alert-info">
+Soit \(P\) un point décrivant un cercle de centre \(O\) et de rayon
+\(a\). On projette \(P\) en \(Q\) sur l’axe \((Ox)\), puis \(Q\) en
+\(R\) sur le segment \([OP]\). Le lemniscate de Gerono est alors le
+lieu du point \(M\) de \([PQ]\) tel que \(QM = QN\).
+</div>
+
+À partir de là, on construit la commande qui prend pour argument la
+valeur de l’angle, et qui construit l’image correspondante. On va ici
+utiliser l’*héritage* qui permet de garder en mémoire les
+unités et la courbe construite au fur et à mesure, à partir des étapes
+précédentes.
+
+On encapsule le code MetaPost dans un *macro* LaTeX grâce à
+l'environnement `mplibcode` de `luamplib`.
+
+~~~~~~~ { .latex }
+\mplibcodeinherit{enable} % l'héritage pour la mémoire entre les figures
+\newcommand{\lemniscate}[1]{% #1: l'angle en degres
+  \begin{mplibcode}
+    if(#1=0):
+    u:=3cm;%
+    a:=2u;%
+    h:=a/4;%
+    s:=1.3;%
+    path lemn;%
+    path carre;%
+    carre = (0,0)--(1,0)--(1,1)--(0,1)--cycle;
+    fi;
+    beginfig(#1);
+    pickup pencircle scaled 0.6pt;
+    drawarrow (0,-s*u)--(0,s*u);
+    drawarrow (-s*u,0)--(s*u,0);
+    path cercle,hori,verti;
+    pair O,P,Q,R,M;
+    O:=(0,0);
+    cercle := fullcircle scaled (a);
+    pickup pencircle scaled 0.4pt;
+    draw cercle dashed evenly withcolor blue;
+    P:=(a/2*cosd(#1),a/2*sind(#1)); % chemin qui parcourt le cercle
+    Q:=(a/2*cosd(#1),0); %projection sur (Ox)
+    % projection de Q sur [O,P]
+    R = cosd(#1)*cosd(#1)*(a/2*cosd(#1),a/2*sind(#1));
+    % M sur [PQ] tel que QM = QR
+    QR := abs(R-Q);
+    if(sind(#1)>0.0):
+    M = Q + (0,QR);
+    else:
+    M = Q - (0,QR);
+    fi;
+
+    if #1=0:
+    lemn:=M;
+    else:
+    lemn:= lemn--M;
+    fi;
+
+    if ((#1>0) and (#1<90)) or ((#1>180) and (#1<270)):
+    draw carre scaled 6 rotated (angle(Q-P)+180) shifted Q;
+    draw carre scaled 6 rotated (angle(R-P)) shifted R;
+    fi;
+    if((#1>=90) and (#1<180)) or ((#1>=270) and (#1<360)):
+    draw carre scaled 6 rotated (angle(Q-P)+180) shifted Q;
+    draw carre scaled 6 rotated (angle(R-P)+180) shifted R;
+    fi;
+
+    draw O--P dashed evenly withcolor blue;
+    draw P--Q dashed evenly withcolor blue;
+    draw R--Q--M withcolor green;
+
+    label.lrt(btex $a$ etex, (a/2,0));
+    label.llft(btex $x$ etex, (s*u,0));
+    label.llft(btex $y$ etex, (0,s*u));
+    label(btex \itshape Lemniscate \par de Gerono etex, (-0.7u,1.15u));
+    label(btex $x^4=a^2(x^2-y^2)$ etex, (0.7u,-1.15u));
+
+    dotlabel.llft(btex $O$ etex, O);
+    dotlabel.urt(btex $M$ etex, M);
+    dotlabel.urt(btex $P$ etex, P);
+    dotlabel.urt(btex $Q$ etex, Q);
+    dotlabel.urt(btex $R$ etex, R);
+
+    pickup pencircle scaled 1pt;
+    draw lemn withcolor red;
+
+    clip currentpicture to (-s*u,-s*u)--(s*u,-s*u)--(s*u,s*u)--(-s*u,s*u)--cycle;
+    endfig;
+  \end{mplibcode}
+}
+~~~~~~~
+
+Il suffit alors de construire l'animation avec l'extension `animate`
+et son  environnement `animateinline`.
+
+~~~~~~~ { .latex }
+\begin{center}
+\begin{animateinline}[poster=230, controls]{24}
+  \multiframe{360}{ii=0+1}{\lemniscate{\ii}}
+\end{animateinline}
+\end{center}
+~~~~~~~
-- 
2.20.1