texlive[72550] Master: mp-geom2d (14oct24)
commits+karl at tug.org
commits+karl at tug.org
Mon Oct 14 21:15:07 CEST 2024
Revision: 72550
https://tug.org/svn/texlive?view=revision&revision=72550
Author: karl
Date: 2024-10-14 21:15:06 +0200 (Mon, 14 Oct 2024)
Log Message:
-----------
mp-geom2d (14oct24)
Modified Paths:
--------------
trunk/Master/tlpkg/bin/tlpkg-ctan-check
trunk/Master/tlpkg/libexec/ctan2tds
trunk/Master/tlpkg/tlpsrc/collection-metapost.tlpsrc
Added Paths:
-----------
trunk/Master/texmf-dist/doc/metapost/mp-geom2d/
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Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/K001-2.dat
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/K001-2.dat (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/K001-2.dat 2024-10-14 19:15:06 UTC (rev 72550)
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Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/LICENSE
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/LICENSE (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/LICENSE 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,11 @@
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+ http://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX
+version 2005/12/01 or later.
+
+This work has the LPPL maintenance status “maintained”.
+
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/README.md
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/README.md (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/README.md 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,67 @@
+# MP-GEOM2D
+
+Flat geometry with MetaPost.
+
+
+
+
+
+## Purpose
+
+mp-geom2d was written with the aim of providing MetaPost macros for creating
+a geometry figure that closely matches an imperative description:
+
+- Let A be the point with coordinates (2,3).
+- Let B be the point with coordinates (4,5).
+- Draw the line (A, B).
+- ...
+
+## Documentation
+
+The documentation, in French, is in the form of a PDF file:
+
+* [mp-geom2d-doc.pdf](doc/mp-geom2d-doc.pdf)
+
+## Contact
+
+
+- Jean-Michel Sarlat, `jm.sarlat(at)gmail.com`
+- Maxime Chupin, `notezik(at)gmail.com`
+
+## License
+
+LATEX Project Public License 1.3c.
+
+# mp-geom2d (français)
+
+De la géométrie plane avec MetaPost.
+
+
+
+
+
+## Objectif
+
+mp-geom2d a été écrit avec le but de proposer des macros MetaPost permettant de réaliser
+une figure de géométrie en collant d’assez près à une description impérative :
+
+- Soit A le point de coordonnées (2,3).
+- Soit B le point de coordonnées (4,5).
+- Trace la droite (A, B).
+- ...
+
+## Documentation
+
+La documentation, en français, est sous forme d’un fichier PDF :
+
+* [mp-geom2d-doc.pdf](doc/mp-geom2d-doc.pdf)
+
+## Contact
+
+
+- Jean-Michel Sarlat, `jm.sarlat(at)gmail.com`
+- Maxime Chupin, `notezik(at)gmail.com`
+
+## Licence
+
+LATEX Project Public License 1.3c.
\ No newline at end of file
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--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/axessimilitude-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
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___________________________________________________________________
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+-19.76695 -54.49571 -19.92502 -54.87721 -19.92502 -55.27505 curveto
+-19.92502 -55.6729 -19.76695 -56.0544 -19.48566 -56.3357 curveto
+-19.20436 -56.61699 -18.82286 -56.77505 -18.42502 -56.77505 curveto
+-18.02718 -56.77505 -17.64568 -56.61699 -17.36438 -56.3357 curveto
+-17.08308 -56.0544 -16.92502 -55.6729 -16.92502 -55.27505 curveto closepath fill
+ 0 0 0 setrgbcolor
+newpath -16.92502 -55.27505 moveto
+-16.92502 -54.87721 -17.08308 -54.49571 -17.36438 -54.21442 curveto
+-17.64568 -53.93312 -18.02718 -53.77505 -18.42502 -53.77505 curveto
+-18.82286 -53.77505 -19.20436 -53.93312 -19.48566 -54.21442 curveto
+-19.76695 -54.49571 -19.92502 -54.87721 -19.92502 -55.27505 curveto
+-19.92502 -55.6729 -19.76695 -56.0544 -19.48566 -56.3357 curveto
+-19.20436 -56.61699 -18.82286 -56.77505 -18.42502 -56.77505 curveto
+-18.02718 -56.77505 -17.64568 -56.61699 -17.36438 -56.3357 curveto
+-17.08308 -56.0544 -16.92502 -55.6729 -16.92502 -55.27505 curveto closepath stroke
+ 0.545 0 0 setrgbcolor
+newpath 19.92474 -49.13376 moveto
+19.92474 -48.73592 19.76668 -48.35442 19.48538 -48.07312 curveto
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+18.0269 -47.63376 17.6454 -47.79182 17.3641 -48.07312 curveto
+17.08281 -48.35442 16.92474 -48.73592 16.92474 -49.13376 curveto
+16.92474 -49.5316 17.08281 -49.9131 17.3641 -50.1944 curveto
+17.6454 -50.4757 18.0269 -50.63376 18.42474 -50.63376 curveto
+18.82259 -50.63376 19.20409 -50.4757 19.48538 -50.1944 curveto
+19.76668 -49.9131 19.92474 -49.5316 19.92474 -49.13376 curveto closepath fill
+ 0 0 0 setrgbcolor
+newpath 19.92474 -49.13376 moveto
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+18.0269 -47.63376 17.6454 -47.79182 17.3641 -48.07312 curveto
+17.08281 -48.35442 16.92474 -48.73592 16.92474 -49.13376 curveto
+16.92474 -49.5316 17.08281 -49.9131 17.3641 -50.1944 curveto
+17.6454 -50.4757 18.0269 -50.63376 18.42474 -50.63376 curveto
+18.82259 -50.63376 19.20409 -50.4757 19.48538 -50.1944 curveto
+19.76668 -49.9131 19.92474 -49.5316 19.92474 -49.13376 curveto closepath stroke
+305.3278 7.49442 moveto
+(E) cmmi10 9.96265 fshow
+312.6822 6.00002 moveto
+(12) cmr7 6.97385 fshow
+28.95253 -123.35791 moveto
+(E) cmmi10 9.96265 fshow
+36.30693 -124.85231 moveto
+(31) cmr7 6.97385 fshow
+-63.17229 -160.20767 moveto
+(E) cmmi10 9.96265 fshow
+-55.81789 -161.70207 moveto
+(23) cmr7 6.97385 fshow
+-2.72421 7.49442 moveto
+(I) cmmi10 9.96265 fshow
+1.65518 6.00002 moveto
+(12) cmr7 6.97385 fshow
+-35.445 -66.28284 moveto
+(I) cmmi10 9.96265 fshow
+-31.06561 -67.77724 moveto
+(31) cmr7 6.97385 fshow
+22.62473 -60.14154 moveto
+(I) cmmi10 9.96265 fshow
+27.00412 -61.63594 moveto
+(23) cmr7 6.97385 fshow
+-79.49503 7.49442 moveto
+(C) cmmi10 9.96265 fshow
+-72.37453 6.00002 moveto
+(1) cmr7 6.97385 fshow
+49.4801 7.49442 moveto
+(C) cmmi10 9.96265 fshow
+56.6006 6.00002 moveto
+(2) cmr7 6.97385 fshow
+-5.79495 -86.50787 moveto
+(C) cmmi10 9.96265 fshow
+1.32555 -88.00227 moveto
+(3) cmr7 6.97385 fshow
+gsave [0.92719 0.3746 -0.3746 0.92719 128.9754 -70.6998 ] concat 0 0 moveto
+(Axe) cmr10 9.96263 fshow grestore
+gsave [0.92719 0.3746 -0.3746 0.92719 147.96304 -63.02837 ] concat 0 0 moveto
+(de) cmr10 9.96263 fshow grestore
+gsave [0.92719 0.3746 -0.3746 0.92719 160.2793 -58.05234 ] concat 0 0 moveto
+(similitude) cmr10 9.96263 fshow grestore
+grestore
+ 1 1 1 setrgbcolor 0 1 dtransform truncate idtransform setlinewidth pop
+ [] 0 setdash 1 setlinejoin 10 setmiterlimit
+newpath -184.25018 -184.25018 moveto
+-184.25018 128.97513 lineto
+350.07535 128.97513 lineto
+350.07535 -184.25018 lineto
+ closepath stroke
+showpage
+%%EOF
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/axessimilitude.1
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/axessimilitude.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/axessimilitude.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/axessimilitude.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,98 @@
+input geom2d;
+%%% depuis Drawing with Metapost de Toby Thurston
+labeloffset := 6;
+gddTaillePoint := 3;
+gddCouleurPoint := Yellow;
+gddU:=0.65cm;
+beginfig(1);
+ C1 = Cercle((-4,0),3);
+ C2 = Cercle((3,0),2);
+ C3 = Cercle((0,-4),1);
+
+ T1 = TangenteCommuneExterieure(C1,C2);
+ T2 = TangenteCommuneExterieure(C2,C1);
+ T3 = TangenteCommuneInterieure(C1,C2);
+ T4 = TangenteCommuneInterieure(C2,C1);
+
+ T5 = TangenteCommuneExterieure(C2,C3);
+ T6 = TangenteCommuneExterieure(C3,C2);
+ T7 = TangenteCommuneInterieure(C2,C3);
+ T8 = TangenteCommuneInterieure(C3,C2);
+
+ T9 = TangenteCommuneExterieure(C1,C3);
+ T10 = TangenteCommuneExterieure(C3,C1);
+ T11 = TangenteCommuneInterieure(C1,C3);
+ T12 = TangenteCommuneInterieure(C3,C1);
+
+ E12 = IntersectionDroites(T1,T2);
+ E23 = IntersectionDroites(T5,T6);
+ E31 = IntersectionDroites(T9,T10);
+ I12 = IntersectionDroites(T3,T4);
+ I23 = IntersectionDroites(T7,T8);
+ I31 = IntersectionDroites(T11,T12);
+
+ path t[];
+ t1 :=(gddTraceObjet T1) gddEnPlace;
+ t2 := (gddTraceObjet T2) gddEnPlace;
+ t3 := (-10*gddU,-10*gddU)--(-10gddU,10*gddU);
+ fill buildcycle(t1, t3,reverse t2) withcolor 1.4*LightSlateGrey;
+
+ t4 :=(gddTraceObjet T3) gddEnPlace;
+ t5 := (gddTraceObjet T4) gddEnPlace;
+ t6 := (1.5*gddU,-10*gddU)--(1.5*gddU,10*gddU);
+ fill buildcycle(t4, t5,reverse t6) withcolor 1.1*LightSlateGrey;
+
+ t7 :=(gddTraceObjet T3) gddEnPlace;
+ t8 := (gddTraceObjet T4) gddEnPlace;
+ t9 := (-1.5*gddU,-10*gddU)--(-1.5*gddU,10*gddU);
+ fill buildcycle(t7, t8,reverse t9) withcolor 1.1*LightSlateGrey;
+
+ drawoptions(withpen pencircle scaled 1pt withcolor LightSlateGrey);
+ colorie C1 withcolor white;
+ colorie C2 withcolor white;
+ colorie C3 withcolor white;
+ trace C1; trace C2; trace C3;
+
+ drawoptions();
+ trace Droite(Centre(C1),Centre(C2));
+ trace Droite(Centre(C3),Centre(C2));
+ trace Droite(Centre(C1),Centre(C3));
+
+ D_E = Droite(E12,E23);
+ trace D_E dashed evenly withcolor DarkBlue;
+
+ E_I = Segment(E12,I31);
+ trace E_I dashed evenly withcolor DarkRed;
+ I_E1 = Segment(I12,E31);
+ trace I_E1 dashed evenly withcolor DarkRed;
+ I_E2 = Segment(I12,E23);
+ trace I_E2 dashed evenly withcolor DarkRed;
+
+
+ drawoptions();
+ pointe Centre(C1);
+ pointe Centre(C2);
+ pointe Centre(C3);
+ gddCouleurPoint := DarkBlue;
+ pointe E12; pointe E31; pointe E23;
+ gddCouleurPoint := DarkRed;
+ pointe I12; pointe I31; pointe I23;
+
+ label.top(btex $E_{12}$ etex,PointTOPair(E12) gddEnPlace);
+ label.bot(btex $E_{31}$ etex,PointTOPair(E31) gddEnPlace);
+ label.bot(btex $E_{23}$ etex,PointTOPair(E23) gddEnPlace);
+
+ label.top(btex $I_{12}$ etex,PointTOPair(I12) gddEnPlace);
+ label.llft(btex $I_{31}$ etex,PointTOPair(I31) gddEnPlace);
+ label.lrt(btex $I_{23}$ etex,PointTOPair(I23) gddEnPlace);
+
+
+ label.top(btex $C_{1}$ etex,PointTOPair(Centre(C1)) gddEnPlace);
+ label.top(btex $C_{2}$ etex,PointTOPair(Centre(C2)) gddEnPlace);
+ label.bot(btex $C_{3}$ etex,PointTOPair(Centre(C3)) gddEnPlace);
+
+ draw textext("Axe de similitude") rotated (22) shifted (0.5[Pt(E23),Pt(E12)]
+ gddEnPlace +(0,3));
+ Fenetre(-10,-10,19,7);
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/axessimilitude.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1-1.png
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1-1.png
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1-1.png 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1-1.png 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1-1.png
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/octet-stream
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,37 @@
+input geom2d;
+
+labeloffset := 6;
+
+gddTaillePoint := 3;
+gddCouleurPoint := Yellow;
+
+beginfig(1);
+
+ Repere(9,9,4,5,0.8,0.8);
+ Axes;
+ Debut;
+ Graduations;
+ Unites(1);
+
+ C1 = Cercle((1,1),3);
+ C2 = Cercle((-1,-2),1);
+
+ P1 = IntersectionCercles(C1,C2);
+ P2 = IntersectionCercles(C2,C1);
+
+ drawoptions(withcolor LightSlateGrey);
+ trace C1;
+ trace C2;
+
+ drawoptions();
+ pointe Point(1,1);
+ pointe Point(-1,-2);
+ pointe P1;
+ pointe P2;
+ label.urt(textext("\(P_1\)"),PtR(P1));
+ label.top(textext("\(P_2\)"),PtR(P2));
+
+ Fin;
+
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles1.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2-1.png
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2-1.png
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2-1.png 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2-1.png 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2-1.png
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/octet-stream
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,34 @@
+input geom2d;
+
+labeloffset := 6;
+gddTaillePoint := 2;
+gddCouleurPoint := Yellow;
+
+beginfig(1);
+ Repere(9,9,4,5,0.8,0.8);
+ Axes;
+ Debut;
+ Axes;
+ Graduations; Unites(1);
+
+ C1 = Cercle((1,1),3);
+ C2 = Cercle((-1,-2),1);
+
+ T1 = TangenteCommuneExterieure(C1,C2);
+ T2 = TangenteCommuneExterieure(C2,C1);
+
+ drawoptions(withcolor LightSlateGrey);
+ trace C1;
+ trace C2;
+
+ drawoptions(withcolor Olive);
+ trace T1;
+ trace T2;
+
+ drawoptions();
+ pointe Point(1,1);
+ pointe Point(-1,-2);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles2.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-001.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-001.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-001.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-001.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-001.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-2.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-2.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-2.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-2.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3-2.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3.001
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3.001 (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3.001 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,76 @@
+%!PS
+%%BoundingBox: -1033 -2116 849 2051
+%%HiResBoundingBox: -1032.62207 -2115.02084 848.11754 2050.78284
+%%Creator: MetaPost 2.02
+%%CreationDate: 2023.11.19:1336
+%%Pages: 1
+%%BeginProlog
+%%EndProlog
+%%Page: 1 1
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+29.24107 27.82689 29.34645 28.08122 29.34645 28.34645 curveto closepath fill
+ 0 0 0 setrgbcolor
+newpath 29.34645 28.34645 moveto
+29.34645 28.61168 29.24107 28.86601 29.05354 29.05354 curveto
+28.86601 29.24107 28.61168 29.34645 28.34645 29.34645 curveto
+28.08122 29.34645 27.82689 29.24107 27.63936 29.05354 curveto
+27.45183 28.86601 27.34645 28.61168 27.34645 28.34645 curveto
+27.34645 28.08122 27.45183 27.82689 27.63936 27.63936 curveto
+27.82689 27.45183 28.08122 27.34645 28.34645 27.34645 curveto
+28.61168 27.34645 28.86601 27.45183 29.05354 27.63936 curveto
+29.24107 27.82689 29.34645 28.08122 29.34645 28.34645 curveto closepath stroke
+ 1 1 0 setrgbcolor
+newpath -84.03935 -85.03935 moveto
+-84.03935 -84.77412 -84.14473 -84.51979 -84.33226 -84.33226 curveto
+-84.51979 -84.14473 -84.77412 -84.03935 -85.03935 -84.03935 curveto
+-85.30458 -84.03935 -85.55891 -84.14473 -85.74644 -84.33226 curveto
+-85.93398 -84.51979 -86.03935 -84.77412 -86.03935 -85.03935 curveto
+-86.03935 -85.30458 -85.93398 -85.55891 -85.74644 -85.74644 curveto
+-85.55891 -85.93398 -85.30458 -86.03935 -85.03935 -86.03935 curveto
+-84.77412 -86.03935 -84.51979 -85.93398 -84.33226 -85.74644 curveto
+-84.14473 -85.55891 -84.03935 -85.30458 -84.03935 -85.03935 curveto closepath fill
+ 0 0 0 setrgbcolor
+newpath -84.03935 -85.03935 moveto
+-84.03935 -84.77412 -84.14473 -84.51979 -84.33226 -84.33226 curveto
+-84.51979 -84.14473 -84.77412 -84.03935 -85.03935 -84.03935 curveto
+-85.30458 -84.03935 -85.55891 -84.14473 -85.74644 -84.33226 curveto
+-85.93398 -84.51979 -86.03935 -84.77412 -86.03935 -85.03935 curveto
+-86.03935 -85.30458 -85.93398 -85.55891 -85.74644 -85.74644 curveto
+-85.55891 -85.93398 -85.30458 -86.03935 -85.03935 -86.03935 curveto
+-84.77412 -86.03935 -84.51979 -85.93398 -84.33226 -85.74644 curveto
+-84.14473 -85.55891 -84.03935 -85.30458 -84.03935 -85.03935 curveto closepath stroke
+showpage
+%%EOF
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,58 @@
+input geom2d;
+
+labeloffset := 6;
+
+gddTaillePoint := 2;
+gddCouleurPoint := Yellow;
+
+
+
+beginfig(1);
+
+
+ C1 = Cercle((1,1),3);
+ C2 = Cercle((-3,-3),1);
+
+ T1 = TangenteCommuneExterieure(C1,C2);
+ T2 = TangenteCommuneExterieure(C2,C1);
+ T3 = TangenteCommuneInterieure(C1,C2);
+ T4 = TangenteCommuneInterieure(C2,C1);
+
+
+ drawoptions(withcolor LightSlateGrey);
+ trace C1;
+ trace C2;
+
+ drawoptions(withcolor Olive);
+ trace T1;
+ trace T2;
+
+
+ drawoptions(withcolor DarkRed);
+ trace T3;
+ trace T4;
+
+ drawoptions();
+ pointe Centre(C1);
+ pointe Centre(C2);
+
+ a = angle((0,-1));
+ show a;
+
+endfig;
+
+beginfig(2);
+
+ A = Point(0,0);
+ B = Point(2,1);
+ C = Point(1,3);
+
+ K = CercleTroisPoints(A,B,C);
+
+ trace K;
+ pointe A;
+ pointe B;
+ pointe C;
+endfig;
+
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cercles/cercles3.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-2.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-2.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-2.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-2.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-2.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-3.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-3.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-3.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-3.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-3.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-4.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-4.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-4.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-4.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse-4.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,105 @@
+input geom2d;
+
+beginfig(1);
+ C = Point(3,2);
+ A = Point(5,1);
+ B = Point(3.5,3) ;
+ E = Ellipse(C,A,B);
+ F = EllipseF(C,A,2.5);
+ D = Centre(F);
+ pointe D;
+ trace E;
+ trace F;
+ pointe C;
+ pointe A;
+ pointe B;
+endfig;
+
+
+
+beginfig(2);
+ F1 = Point(3,1);
+ F2 = Point(1.5,0.5);
+ E := EllipseF(F1,F2,1.2);
+ trace E;
+
+ bboxmargin := 1cm;
+ path cadre; cadre = bbox currentpicture;
+
+ pair M;
+ M = point 3.5 of (gddTraceObjet(E)) ;
+ M' = PointImp(M);
+
+ d:=Longueur(M',F1)+Longueur(M',F2);
+ show d; % Pour vérifier que l'on obtient bien 2a
+
+ trace Segment(F1,M');
+ trace Segment(F2,M');
+ D := TangenteEllipse(E,M);
+ trace D;
+
+ gddTaillePoint := 1.5;
+ gddCouleurPoint := Yellow;
+ pointe M';
+ gddCouleurPoint := Gainsboro;
+ pointe F1;
+ pointe F2;
+
+ setbounds currentpicture to cadre;
+endfig;
+
+
+beginfig(3);
+ F1 := Point(3,1);
+ F2 := Point(1.5,0.5);
+ E := EllipseF(F1,F2,1.2);
+ trace E;
+
+ bboxmargin := 5cm;
+ path cadre; cadre = bbox currentpicture;
+ numeric M;
+ P = Point(1,-1);
+ C1 = CercleCP(P,F1);
+ trace C1;
+ C2 = Cercle(F2,2*DemiGrandAxe(E));
+ trace C2;
+ T1 = IntersectionCercles(C1,C2);
+ T2 = IntersectionCercles(C2,C1);
+ if(Longueur(F1,T1)<Longueur(F1,T2)):
+ U = T1;
+ else:
+ U = T2;
+ fi
+ DU = Segment(F2,U);
+ pair Ip;
+ Ip := (gddTraceObjet(DU)) intersectionpoint (gddTraceObjet(E));
+ M = PointImp(Ip);
+ trace DU;
+ marque.urt "M";
+ marque.urt "P";
+ marque.urt "F1";
+ marque.urt "F2";
+ marque.urt "T1";
+ marque.urt "T2";
+
+ setbounds currentpicture to cadre;
+endfig;
+beginfig(4);
+ F1 := Point(3,1);
+ F2 := Point(1.5,0.5);
+ E := EllipseF(F1,F2,1.2);
+ trace E;
+ P := Point(4,1);
+ bboxmargin := 5cm;
+ path cadre; cadre = bbox currentpicture;
+ T1 := TangenteExterieureEllipse(E,P,1);
+ trace T1;
+ T2 := TangenteExterieureEllipse(E,P,2);
+ trace T2;
+ marque.urt "P";
+ pointe gddB[T1];
+
+ pointe gddB[T2];
+ setbounds currentpicture to cadre;
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/ellipse.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/hyper-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/hyper-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/hyper-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/hyper-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/hyper-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/hyper.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/hyper.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/hyper.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,41 @@
+input geom2d;
+
+beginfig(1);
+ A = Point(0,0);
+ B = Point(3,2);
+ AB = Droite(A,B);
+ F_1 = Point(-1,1);
+ Hyper = HyperboleFD(F_1,AB,1.5);
+ O = Centre(Hyper);
+ F_2 = Foyer(Hyper,2);
+ Axe = Droite(F_1,F_2);
+ S_1 = Sommet(Hyper,1);
+ S_2 = Sommet(Hyper,2);
+
+ trace Axe dashed evenly;
+ C = CerclePrincipale(Hyper) ;
+ trace C avecCrayon(0.5,LightSlateGray) dashed evenly;
+ A_1 = AsymptoteHyperbole(Hyper,1);
+ A_2 = AsymptoteHyperbole(Hyper,2);
+ trace A_1 dashed evenly;
+ trace A_2 dashed evenly;
+
+ D_1 = Directrice(Hyper,1);
+ D_2 = Directrice(Hyper,2);
+
+ trace D_1 avecCrayon(1.1,CornflowerBlue);
+ trace D_2 avecCrayon(1.1,CornflowerBlue);
+ trace DemieHyperbole(Hyper,1) avecCrayon(1.5,Crimson);
+ trace DemieHyperbole(Hyper,2) avecCrayon(1.5,Crimson);
+
+ marque.lft "O";
+ marque.lft "S_1";
+ marque.lft "S_2";
+ marque.lft "F_1";
+ marque.lft "F_2";
+ label.lft(textext("\(\mathcal{C}\)"),Pt(PointDe(C,0.6)) gddEnPlace) withcolor LightSlateGray;
+ label.top(textext("\(\mathcal{D}_1\)"),Pt(PointDe(D_1,0.47)) gddEnPlace) withcolor CornflowerBlue;
+ label.top(textext("\(\mathcal{D}_2\)"),Pt(PointDe(D_2,0.46)) gddEnPlace) withcolor CornflowerBlue;
+ Fenetre(-4,-7,4,4);
+endfig;
+end.
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/coniques/hyper.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/construction/ogiveentiers-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/construction/ogiveentiers-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/construction/ogiveentiers-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/construction/ogiveentiers-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/construction/ogiveentiers-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/construction/ogiveentiers.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/construction/ogiveentiers.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/construction/ogiveentiers.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,126 @@
+input geom2d;
+
+beginfig(1);
+ % les points de base pour l’ogive
+ O = Point(0,0);
+ A = Point(-3,0);
+ A2 = Point(-4,0);
+ B = Point(3,0);
+ B2 = Point(4,0);
+ % la droite de base de l’ogive
+ AB = Droite(A,B);
+ % on se prend une droite quelconque
+ Ct = Point(0.8,-2); % point quelconque
+ AC = Droite(A,Ct); % droite quelconque
+ % on prend trois longueures égales sur la droite
+ longueurTier := 1.4;
+ C1 = ReportSurDroite(A,AC,longueurTier);
+ C2 = ReportSurDroite(C1,AC,longueurTier);
+ C3 = ReportSurDroite(C2,AC,longueurTier);
+ % on définit la droite qui passe par B et le dernier point
+ BC = Droite(B,C3);
+ % on construit une droite perpendiculaire à BC
+ D = Point(-4,0);
+ perpD = DroitePerpendiculaire(BC,D);
+ DD = IntersectionDroites(perpD,BC);
+ % on projette C2 et C1 sar la droite AB pour diviser [AB] en 3 parties
+ % égales
+ perpC2 = DroitePerpendiculaire(perpD,C2);
+ perpC1 = DroitePerpendiculaire(perpD,C1);
+ D1 = IntersectionDroites(AB,perpC1);
+ D2 = IntersectionDroites(AB,perpC2);
+ % on construit l’enveloppe de l’ogive
+ C_DA = CercleCP(D2,A);
+ C_DB = CercleCP(D1,B);
+ C_DA2 = CercleCP(D2,A2);
+ C_DB2 = CercleCP(D1,B2);
+ % on construit le point P pour la projection finale
+ C_AB = CercleCP(A,B);
+ C_BA = CercleCP(B,A);
+ P = IntersectionCercles(C_BA,C_AB);
+ % on prend 5 longueures égales sur la droite quelconque du début
+ longueurCinq :=0.8;
+ F1 = ReportSurDroite(A,AC,longueurCinq);
+ F2 = ReportSurDroite(F1,AC,longueurCinq);
+ F3 = ReportSurDroite(F2,AC,longueurCinq);
+ F4 = ReportSurDroite(F3,AC,longueurCinq);
+ F5 = ReportSurDroite(F4,AC,longueurCinq);
+ % on projette les points sur AB pour diviser [AB] en 5 parties égale
+ BF5 = Droite(B,F5);
+ perpF5 = DroitePerpendiculaire(BF5,A2);
+ CC = IntersectionDroites(BF5,perpF5);
+ perpF4 = DroitePerpendiculaire(perpF5,F4);
+ perpF3 = DroitePerpendiculaire(perpF5,F3);
+ perpF2 = DroitePerpendiculaire(perpF5,F2);
+ perpF1 = DroitePerpendiculaire(perpF5,F1);
+ G1 = IntersectionDroites(AB,perpF1);
+ G2 = IntersectionDroites(AB,perpF2);
+ G3 = IntersectionDroites(AB,perpF3);
+ G4 = IntersectionDroites(AB,perpF4);
+ % on projette les Gi sur l’ogive avec le point P
+ PG1 = Droite(P,G1);
+ PG2 = Droite(P,G2);
+ PG3 = Droite(P,G3);
+ PG4 = Droite(P,G4);
+ I1 = IntersectionDroiteCercle(PG1,C_DA,1);
+ I2 = IntersectionDroiteCercle(PG2,C_DA,2);
+ I3 = IntersectionDroiteCercle(PG3,C_DB,2);
+ I4 = IntersectionDroiteCercle(PG4,C_DB,2);
+ % à partir des 2 points issus de la division en 3 de [AB]
+ % on trace les séparations des pierres qui constituent l’ogive
+ Dvoute1 = Droite(D2,I1);
+ Dvoute2 = Droite(D2,I2);
+ Dvoute3 = Droite(D1,I3);
+ Dvoute4 = Droite(D1,I4);
+
+ % les tracés
+ drawoptions(withcolor 1.3*Grey);
+ trace perpC2; trace perpC1;
+ trace AB;
+ trace AC;
+ trace BC;
+ trace perpD;
+ trace SigneOrtho(B,DD,A2,0.2);
+
+ drawoptions(withcolor Bisque);
+ trace BF5;
+ trace perpF5;trace perpF4;trace perpF3;trace perpF2;trace perpF1;
+ trace SigneOrtho(B,CC,A2,0.2);
+
+ drawoptions(withcolor SteelBlue withpen pencircle scaled 0.85pt);
+ trace gddTraceArcDeCercle(C_DA,Pi/2,Pi);
+ trace gddTraceArcDeCercle(C_DA2,Pi/2,Pi);
+ trace gddTraceArcDeCercle(C_DB2,0,Pi/2);
+ trace gddTraceArcDeCercle(C_DB,0,Pi/2);
+
+ drawoptions();
+ trace gddTraceArcDeCercle(C_AB,0,-Pi/2) dashed evenly;
+ trace gddTraceArcDeCercle(C_BA,Pi,3Pi/2) dashed evenly;
+
+ drawoptions(withcolor DarkSalmon);
+ trace PG1; trace PG2; trace PG3; trace PG4;
+
+ drawoptions(withcolor SteelBlue withpen pencircle scaled 0.85pt);
+ trace Dvoute1; trace Dvoute2; trace Dvoute3; trace Dvoute4;
+ drawoptions();
+
+ gddCouleurPoint := DarkRed;
+ pointe O;
+ pointe A;
+ pointe B; pointe D;
+ pointe B2;
+
+ gddCouleurPoint := Bisque;
+ pointe F1; pointe F2; pointe F3; pointe F4; pointe F5;
+ pointe G1; pointe G2;pointe G3;pointe G4;
+ gddCouleurPoint := 1.3*Grey;
+ pointe DD;
+ pointe C1; pointe C2; pointe C3;
+ pointe D1; pointe D2;
+
+ gddCouleurPoint := DarkSalmon;
+ pointe P;
+ pointe I1; pointe I2; pointe I3; pointe I4;
+ Fenetre(-5,-7,5,5);
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/construction/ogiveentiers.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp01-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp01-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp01-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp01-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp01-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp01.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp01.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp01.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,38 @@
+input geom2d;
+
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef f(expr t) = 2*cos(t)*cos(t)*cos(t) enddef;
+vardef g(expr t) = 2*sin(t)*sin(t)*sin(t) enddef;
+
+
+beginfig(1);
+ Repere(8,8,4,4,1.8,1.8);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+ drawoptions(withpen pencircle scaled 0.5 withcolor LightSlateGrey);
+ trace ((-2,-2)--(-2,2)--(2,2)--(2,-2)--cycle);
+
+ nb = 80;
+ pas = 2*Pi/nb;
+ for i=0 upto nb: trace (0,2*sin(i*pas))--(2*cos(i*pas),0); endfor;
+
+ fleche Segment((2,0),(1.2,0)) avecCrayon(1,RoyalBlue);
+ fleche Segment((-2,0),(-1.2,0)) avecCrayon(1,RoyalBlue);
+ fleche Segment((0,2),(0,1.2)) avecCrayon(1,RoyalBlue);
+ fleche Segment((0,-2),(0,-1.2)) avecCrayon(1,RoyalBlue);
+
+ trace Courbe(f,g,0,2*Pi,500) avecCrayon(1.5,DarkOrange);
+
+ pointe Point(0,0);
+ pointe Point(2,0);
+ pointe Point(0,2);
+ pointe Point(0,-2);
+ pointe Point(-2,0);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp01.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp02-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp02-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp02-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp02-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp02-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp02.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp02.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp02.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,35 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef f(expr t) = sin(2*t+Pi/3) enddef;
+vardef g(expr t) = sin(3*t) enddef;
+
+beginfig(1);
+ Repere(8,8,4,4,3,3);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+
+ drawoptions(withcolor LightSlateGrey);
+ trace ((-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle);
+ trace ((-1,-1)--(1,1));
+ trace (1,-1)--(-1,1);
+ trace Cercle(origine,1);
+ trace ((-1,0.5)--(1,0.5));
+ trace ((-1,-0.5)--(1,-0.5));
+ trace ((0.5,-1)--(0.5,1));
+ trace ((-0.5,-1)--(-0.5,1));
+ trace ((-1,sqrt(3)/2)--(1,sqrt(3)/2));
+ trace ((-1,-sqrt(3)/2)--(1,-sqrt(3)/2));
+ trace ((sqrt(3)/2,-1)--(sqrt(3)/2,1));
+ trace ((-sqrt(3)/2,-1)--(-sqrt(3)/2,1));
+
+ trace Courbe(f,g,0,2*Pi,500) avecCrayon(1.5,Orchid);
+
+ pointe Point(0,0);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp02.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp03-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp03-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp03-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp03-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp03-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp03.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp03.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp03.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,21 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1cm;
+
+vardef f(expr t) = t*t enddef;
+vardef g(expr t) = t*t*t enddef;
+
+beginfig(1);
+
+ Repere(8,12,2,6,1,1);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+ fleche Segment((0,0),(2,0)) avecCrayon(1,Crimson);
+ trace Courbe(f,g,-3,3,300) avecCrayon(1.5,DarkTurquoise);
+ pointe Point(0,0);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp03.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp04-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp04-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp04-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp04-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp04-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp04.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp04.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp04.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,37 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef f(expr t) = t*t+2/t enddef;
+vardef g(expr t) = t+1/t enddef;
+vardef fp(expr t) = t*t enddef;
+vardef gp(expr t) = t enddef;
+
+beginfig(1);
+
+ Repere(12,10,5,4,0.7,0.7);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+
+ drawoptions(withcolor LightSlateGrey);
+ trace Droite(Point(-4,-2),Point(4,2));
+ trace (3,0)--(3,2)--(0,2) dashed evenly;
+ trace (-1,0)--(-1,-2)--(0,-2) dashed evenly;
+ trace Courbe(fp,gp,-4,4,500);
+
+ fleche Segment((3,2),(5,8/3)) avecCrayon(1,DeepPink);
+ fleche Segment((-1,-2),(-2.8,-2)) avecCrayon(1,DeepPink);
+ fleche Segment((-1,-2),(0.8,-2)) avecCrayon(1,DeepPink);
+
+ trace Courbe(f,g,-5,-0.1,100) avecCrayon(1.5,DarkCyan);
+ trace Courbe(f,g,0.1,5,100) avecCrayon(1.5,DarkCyan);
+
+ pointe Point(0,0);
+ pointe Point(3,2);
+ pointe Point(-1,-2);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp04.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp05-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp05-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp05-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp05-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp05-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp05.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp05.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp05.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,37 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef f(expr t) = t*t-2*t enddef;
+vardef g(expr t) = t*t + 1/(t*t) enddef;
+vardef fp(expr t) = 2*t+t*t enddef;
+vardef gp(expr t) = t*t enddef;
+
+beginfig(1);
+
+ Repere(8,10,2,1,1,1);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+
+ drawoptions(withcolor LightSlateGrey);
+ trace (3,0)--(3,2)--(-1,2)--(-1,0) dashed evenly;
+ trace (1,0)--(1,6)--(0,6) dashed evenly;
+ trace Courbe(fp,gp,-5,5,500);
+
+ fleche Segment((-1,2),(-1,2)+(0.5,2)) avecCrayon(1,Crimson);
+ fleche Segment((3,2),(4,2)) avecCrayon(1,Crimson);
+ fleche Segment((3,2),(2,2)) avecCrayon(1,Crimson);
+
+ trace Courbe(f,g,-10,-0.05,300) avecCrayon(1.5,DarkGoldenrod);
+ trace Courbe(f,g,0.05,10,300) avecCrayon(1.5,DarkGoldenrod);
+
+ pointe Point(0,0);
+ pointe Point(-1,2);
+ pointe Point(3,2);
+ pointe Point(1,6);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp05.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp06-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp06-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp06-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp06-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp06-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp06.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp06.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp06.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,31 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef f(expr t) = 1/t + 1/(t+1) enddef;
+vardef g(expr t) = 1/t + 1/(1+2*t+t**2) enddef;
+vardef p(expr x) = x*(x+2)+2 enddef;
+
+beginfig(1);
+
+ Repere(10,10,5,5,1,1);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+
+ drawoptions(withcolor LightSlateGrey);
+ trace Droite(origine,Point(1,1));
+ trace Representation(p,-3,1,20);
+
+ trace Courbe(f,g,-20,-1.1,300) avecCrayon(1.5,Teal);
+ trace Courbe(f,g,-0.9,-0.1,300) avecCrayon(1.5,Teal);
+ trace Courbe(f,g,0.1,20,300) avecCrayon(1.5,Teal);
+
+ pointe Point(0,0);
+ pointe Point(-1,0);
+ pointe Point(-0.526,-0.140);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp06.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp07-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp07-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp07-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp07-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp07-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp07.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp07.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp07.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,26 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef f(expr t) = t/sqrt(1+t*t) enddef;
+vardef g(expr t) = t*(1+f(t)) enddef;
+vardef h(expr t) = -t*(1+f(t)) enddef;
+
+beginfig(1);
+
+ Repere(6,10,3,5,2,2);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+
+ trace Droite((1,-2),(1,2)) withcolor MidnightBlue;
+
+ trace (-1,0)..Courbe(f,g,-18,18,200) avecCrayon(1.5,DarkSalmon);
+ trace (-1,0)..Courbe(f,h,-18,18,200) avecCrayon(1.5,DarkSalmon);
+
+ pointe Point(0,0);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp07.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp08-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp08-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp08-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp08-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp08-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp08.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp08.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp08.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,38 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1cm;
+
+vardef f(expr t) = 2*sin(t) enddef;
+vardef g(expr t) = 2*cos(t)*cos(t)/(2-cos(t)) enddef;
+vardef h(expr t) = -t*(1+f(t)) enddef;
+
+def traceDoubleVecteur(expr o,d)= drawdblarrow ((o-d)--(o+d)) gddEnPlace enddef;
+
+path bicorne;
+bicorne = Courbe(f,g,-Pi,Pi,200)--cycle;
+
+beginfig(1);
+
+ Repere(9,6,4.5,1,2,2);
+ Axes;
+ Debut;
+ Axes;
+ Graduations; Unites(1);
+
+ colorieAvecTransparence(bicorne,CadetBlue,0.2);
+
+ traceDoubleVecteur((0,2),(0.5,0)) avecCrayon(1,Crimson);
+ traceDoubleVecteur((0,2/3),(0.5,0)) avecCrayon(1,Crimson);
+ fleche Segment((2,0),(1.6,0.4)) avecCrayon(1,Crimson);
+ fleche Segment((-2,0),(-1.6,0.4)) avecCrayon(1,Crimson);
+
+ trace bicorne avecCrayon(1.5,CadetBlue);
+
+ pointe Point(0,0);
+ pointe Point(2,0);
+ pointe Point(-2,0);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/courbes/cp08.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001-1.dat
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001-1.dat (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001-1.dat 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,441 @@
+-9.50332 39.03779
+-8.90985 36.92109
+-8.35830 34.94184
+-7.84242 33.07748
+-7.35647 31.30663
+-6.89478 29.60762
+-6.45128 27.95615
+-6.01847 26.32078
+-5.58493 24.65153
+-5.12641 22.83954
+-4.53013 20.37356
+-4.21630 18.99730
+-3.82624 17.15868
+-3.60655 16.02255
+-3.48053 15.31960
+-3.39084 14.78786
+-3.32137 14.35307
+-3.26497 13.98196
+-3.21775 13.65636
+-3.17735 13.36511
+-3.14222 13.10083
+-3.11127 12.85833
+-3.08371 12.63385
+-3.05896 12.42451
+-3.03656 12.22812
+-3.01615 12.04292
+-2.99745 11.86749
+-2.98023 11.70069
+-2.96428 11.54154
+-2.94946 11.38925
+-2.93563 11.24313
+-2.92266 11.10259
+-2.91047 10.96713
+-2.89896 10.83630
+-2.88807 10.70973
+-2.87772 10.58707
+-2.86785 10.46803
+-2.85843 10.35233
+-2.84940 10.23975
+-2.84071 10.13006
+-2.83235 10.02307
+-2.82426 9.91862
+-2.81643 9.81654
+-2.80883 9.71668
+-2.80143 9.61893
+-2.79421 9.52315
+-2.78715 9.42923
+-2.78023 9.33709
+-2.77343 9.24662
+-2.76675 9.15773
+-2.76016 9.07035
+-2.75365 8.98441
+-2.74721 8.89983
+-2.74083 8.81655
+-2.73449 8.73451
+-2.72820 8.65365
+-2.72193 8.57393
+-2.71568 8.49529
+-2.70944 8.41770
+-2.70321 8.34109
+-2.69697 8.26545
+-2.69072 8.19072
+-2.68446 8.11687
+-2.67818 8.04387
+-2.67186 7.97168
+-2.66552 7.90029
+-2.65914 7.82964
+-2.65272 7.75973
+-2.64625 7.69053
+-2.63973 7.62200
+-2.63316 7.55413
+-2.62653 7.48689
+-2.61983 7.42027
+-2.61308 7.35425
+-2.60625 7.28880
+-2.59935 7.22390
+-2.59238 7.15955
+-2.58533 7.09572
+-2.57821 7.03240
+-2.57100 6.96957
+-2.56370 6.90722
+-2.55632 6.84533
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Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001-1.pdf
===================================================================
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Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
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Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001-1.pdf
___________________________________________________________________
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Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001-2.dat
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+4.42384 0.88508
+4.42798 0.87670
+4.43213 0.86832
+4.43631 0.85993
+4.44050 0.85153
+4.44472 0.84313
+4.44896 0.83472
+4.45323 0.82630
+4.45752 0.81788
+4.46183 0.80945
+4.46616 0.80101
+4.47052 0.79257
+4.47490 0.78412
+4.47930 0.77566
+4.48373 0.76719
+4.48819 0.75872
+4.49267 0.75024
+4.49717 0.74175
+4.50171 0.73325
+4.50626 0.72474
+4.51085 0.71623
+4.51546 0.70770
+4.52009 0.69917
+4.52476 0.69063
+4.52945 0.68208
+4.53417 0.67352
+4.53892 0.66495
+4.54370 0.65637
+4.54851 0.64778
+4.55334 0.63918
+4.55821 0.63057
+4.56311 0.62195
+4.56804 0.61332
+4.57300 0.60467
+4.57799 0.59602
+4.58302 0.58735
+4.58807 0.57868
+4.59316 0.56999
+4.59828 0.56129
+4.60344 0.55258
+4.60863 0.54385
+4.61386 0.53512
+4.61912 0.52637
+4.62442 0.51760
+4.62976 0.50883
+4.63513 0.50004
+4.64054 0.49123
+4.64599 0.48242
+4.65148 0.47358
+4.65700 0.46474
+4.66257 0.45588
+4.66818 0.44700
+4.67383 0.43811
+4.67952 0.42921
+4.68525 0.42028
+4.69103 0.41135
+4.69685 0.40239
+4.70271 0.39342
+4.70862 0.38444
+4.71458 0.37543
+4.72058 0.36641
+4.72664 0.35737
+4.73274 0.34831
+4.73889 0.33924
+4.74509 0.33014
+4.75134 0.32103
+4.75764 0.31190
+4.76399 0.30275
+4.77040 0.29358
+4.77687 0.28439
+4.78339 0.27518
+4.78996 0.26594
+4.79660 0.25669
+4.80329 0.24742
+4.81005 0.23812
+4.81686 0.22880
+4.82374 0.21946
+4.83068 0.21009
+4.83768 0.20071
+4.84475 0.19129
+4.85189 0.18186
+4.85910 0.17240
+4.86637 0.16291
+4.87372 0.15340
+4.88114 0.14386
+4.88863 0.13430
+4.89621 0.12470
+4.90385 0.11509
+4.91158 0.10544
+4.91939 0.09576
+4.92728 0.08606
+4.93526 0.07633
+4.94332 0.06656
+4.95147 0.05677
+4.95971 0.04694
+4.96804 0.03708
+4.97647 0.02719
+4.98500 0.01727
+4.99362 0.00731
+5.00235 -0.00268
+5.01118 -0.01271
+5.02012 -0.02277
+5.02916 -0.03287
+5.03832 -0.04301
+5.04760 -0.05318
+5.05699 -0.06340
+5.06650 -0.07365
+5.07614 -0.08395
+5.08591 -0.09428
+5.09581 -0.10466
+5.10584 -0.11508
+5.11602 -0.12555
+5.12634 -0.13606
+5.13680 -0.14662
+5.14742 -0.15723
+5.15820 -0.16789
+5.16914 -0.17859
+5.18024 -0.18935
+5.19152 -0.20016
+5.20298 -0.21102
+5.21462 -0.22194
+5.22645 -0.23292
+5.23848 -0.24395
+5.25071 -0.25505
+5.26316 -0.26620
+5.27582 -0.27742
+5.28872 -0.28871
+5.30185 -0.30006
+5.31523 -0.31149
+5.32886 -0.32298
+5.34276 -0.33455
+5.35694 -0.34620
+5.37141 -0.35792
+5.38619 -0.36973
+5.40128 -0.38162
+5.41670 -0.39360
+5.43248 -0.40567
+5.44862 -0.41783
+5.46514 -0.43009
+5.48207 -0.44246
+5.49943 -0.45493
+5.51724 -0.46752
+5.53553 -0.48022
+5.55433 -0.49305
+5.57367 -0.50600
+5.59359 -0.51909
+5.61412 -0.53232
+5.63530 -0.54570
+5.65720 -0.55925
+5.67986 -0.57296
+5.70334 -0.58685
+5.72773 -0.60094
+5.75309 -0.61524
+5.77952 -0.62976
+5.80714 -0.64452
+5.83607 -0.65955
+5.86648 -0.67488
+5.89854 -0.69052
+5.93249 -0.70652
+5.96862 -0.72294
+6.00730 -0.73982
+6.04901 -0.75724
+6.09440 -0.77530
+6.14442 -0.79416
+6.20046 -0.81401
+6.26480 -0.83521
+6.34164 -0.85836
+6.44070 -0.88489
+6.60174 -0.92047
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,71 @@
+input geom2d;
+gddU := 0.5cm;
+labeloffset := 8pt;
+gddTailleLabel := 1;
+
+beginfig(1);
+ A := Point(3.6,4.8);
+ B := Point(0,0);
+ C := Point(10,0);
+ T := Triangle(A,B,C);
+ X_74 := Point(3.6,-4.8);
+
+ C1 := CourbeDat("K001-1",0);
+ C2 := CourbeDat("K001-2",1);
+
+ CE1 := CercleExinscrit(T,1);
+ CE2 := CercleExinscrit(T,2);
+ CE3 := CercleExinscrit(T,3);
+ I_1 := Centre(CE1);
+ I_2 := Centre(CE2);
+ I_3 := Centre(CE3);
+ CC := CercleCirconscrit(T);
+ O := Centre(CC);
+
+ drawoptions(withcolor LightBlue);
+ trace Droite(A,B);
+ trace Droite(B,C);
+ trace Droite(C,A);
+ trace Droite(I_1,I_2);
+ trace Droite(I_2,I_3);
+ trace Droite(I_3,I_1);
+ trace CE1;
+ trace CE2;
+ trace CE3;
+ trace CC;
+ colorie T withcolor LightGrey;
+ drawoptions(withpen pencircle scaled 1.5);
+ trace T;
+ drawoptions(withcolor DodgerBlue withpen pencircle scaled 1.5);
+ trace Droite(O,A);
+ trace Droite(X_74, Point(2.2,0));
+ drawoptions(withpen pencircle scaled 2);
+ trace C1 withcolor FireBrick;
+ trace C2 withcolor FireBrick;
+ drawoptions(withcolor Olive);
+ trace Droite(A,X_74);
+ trace Droite(B,X_74);
+ trace Droite(C,X_74);
+ drawoptions();
+ pointe A;
+ pointe B;
+ pointe C;
+ pointe I_1;
+ pointe I_2;
+ pointe I_3;
+ pointe O;
+ pointe X_74;
+
+ marque.urt "A";
+ marque.llft "B";
+ marque.lrt "C";
+ marque.rt "I_1";
+ marque.rt "I_2";
+ marque.lft "I_3";
+ marque.bot "O";
+ marque.llft "X_74";
+
+ Fenetre(-4,-13,16,15);
+endfig;
+
+end
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/cubiques/K001.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/brach-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/brach-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/brach-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/brach-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/brach-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/brach.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/brach.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/brach.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,54 @@
+input geom2d;
+
+color darkred,darkblue;
+darkred=(.6,0,0);
+darkblue=(0,0,.6);
+
+labeloffset := 6;
+gddTaillePoint := 3;
+gddCouleurPoint := (1,1,1);
+
+
+% la cycloide
+vardef f(expr t)=
+ t-sin(t)
+enddef;
+vardef g(expr t)=
+ cos(t)-1
+enddef;
+
+
+beginfig(1);
+ Repere(6,4,1,3,1,1);
+ Axes;
+ Debut;
+ Axes;
+ Graduations; Unites(2);
+
+ A = Point(0,0);
+ B = Point(f(3),g(3));
+ C = Point(2.4,-1);
+ M = Point(f(2.4),g(2.4));
+ N = Point(2.4,0);
+ C1 = Cercle(C,1);
+ trace Arc(C,.3,Pi/2,Pi/2+2.4);
+ trace Droite((2.4,0),C) dashed evenly;
+ trace Courbe(f,g,0,3,500) withcolor darkred withpen pencircle scaled 1pt;
+ trace Courbe(f,g,3,4.5,100) dashed evenly;
+ trace Courbe(f,g,-2,0,100) dashed evenly;
+ trace C1;
+ trace Segment(C,M);
+ trace Arc(C,1,Pi/2,Pi/2+2.4) withcolor darkblue withpen pencircle scaled .7pt;
+ trace Segment(A,N) withcolor darkblue withpen pencircle scaled .7pt;
+
+ marque.rt "C";
+ marque.llft "M";
+ pointe(N);
+ label.urt(textext("$N$"),PtR(N));
+ label.ulft(textext("$\theta$"),PtR(C)+.2*gddU*(cos(Pi/2+1.2),sin(Pi/2+1.2)));
+ gddCouleurPoint := Yellow;
+ marque.urt "A";
+ marque.llft "B";
+ Fin;
+endfig;
+end
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/brach.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/divers-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/divers-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/divers-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/divers-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/divers-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/divers.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/divers.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/divers.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,14 @@
+input geom2d;
+
+beginfig(1);
+
+A = Point(2,2);
+B = Rotation(A,Pi/2);
+pointe origine;
+pointe A;
+pointe B;
+C = RotationCentre(B,A,Pi/2);
+pointe C;
+
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/divers.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/epicycloide-const-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/epicycloide-const-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/epicycloide-const-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/epicycloide-const-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/epicycloide-const-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/epicycloide-const.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/epicycloide-const.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/epicycloide-const.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,66 @@
+input geom2d;
+input geom2d-rep;
+input geom2d-lbl;
+input geom2d-tra;
+input geom2d-fct;
+input geom2d-plt;
+input geom2d-arc;
+input svgnames;
+
+lblPreambule := "\usepackage[frenchb]{babel}" &
+ "\usepackage[garamond]{mathdesign}" &
+ "\usepackage{amsmath}";
+
+labeloffset := 4;
+gddU:=1.3cm;
+
+def avecCrayon(expr t,c) = withpen pencircle scaled t withcolor c enddef;
+
+beginfig(1);
+
+ Repere(10,10,5,4,3,3);
+ Axes;
+ Debut;
+ Graduations;
+ Axes;
+ ColorieAvecTransparence(Cercle(origine,1),LightSlateGrey,0.5);
+ trace Cercle(origine,1) avecCrayon(1.5,LightSlateGrey);
+
+ trace Cercle(4/3(cosd(130),sind(130)),1/3);
+
+ drawoptions(withcolor LightSlateGrey);
+ trace Cercle((0,4/3),1/3);
+
+ centre = Point(4/3cosd(130),4/3sind(130));
+ mobile = Point(4/3cosd(130)+1/3cosd(70),4/3sind(130)+1/3sind(70));
+
+ trace (0,0)--Pt(centre)--Pt(mobile) dashed evenly;
+
+ trace Arc(centre,1/3,-5Pi/18,7Pi/18) avecCrayon(1,DodgerBlue);
+ trace Arc(origine,1,Pi/2,13Pi/18) avecCrayon(1,DodgerBlue);
+ fleche Arc(centre,1/6,-5Pi/18,7Pi/18);
+ fleche Arc(origine,1/3,Pi/2,13Pi/18);
+
+ pointe Point(0,4/3);
+ pointe centre;
+ pointe Point(0,0);
+ pointe Point(cosd(130),sind(130));
+
+ gddCouleurPoint := Crimson;
+
+ pointe Point(0,1);
+ pointe mobile;
+
+ drawoptions(withcolor black);
+
+ label.lrt(TEX("\(O\)"),PtR(origine));
+ label.ulft(TEX("\(\Omega(\theta)\)"),PtR(centre));
+ label.urt(TEX("\(M(\theta)\)"),PtR(mobile));
+ label.top(TEX("\(\theta\)"),(1/3cos(11Pi/18),1/3sin(11Pi/18)) gddEnPlace);
+ label.rt(TEX("\(3\theta\)"),PtR(Addition(centre,(1/6,0))));
+ label.bot(TEX("\(N(\theta)\)"),(cos(13Pi/18),sin(13Pi/18)) gddEnPlace);
+ Fin;
+
+endfig;
+
+end
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/epicycloide-const.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/pascalline-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/pascalline-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/pascalline-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/pascalline-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/pascalline-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/pascalline.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/pascalline.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/pascalline.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,28 @@
+input geom2d;
+
+beginfig(1);
+C = Cercle(origine,3);
+for i:=1 upto 6:
+ rd := uniformdeviate(1.0/6)+(i-1)/6;
+ P[i] := PointDe(C,rd);
+endfor;
+D1 = Droite(P1,P3); S1 = Segment(P1,P3);
+D2 = Droite(P3,P5); S2 = Segment(P3,P5);
+D3 = Droite(P6,P2); S3 = Segment(P6,P2);
+D4 = Droite(P4,P6); S4 = Segment(P4,P6);
+D5 = Droite(P5,P2); S5 = Segment(P5,P2);
+D6 = Droite(P1,P4); S6 = Segment(P1,P4);
+I1 = IntersectionDroites(D1,D3);
+I2 = IntersectionDroites(D2,D4);
+I3 = IntersectionDroites(D5,D6);
+PL = Segment(I1,I2);
+trace C;
+drawoptions(withcolor (0.7,0.1,0.1));
+trace S1; trace S2; trace S3; trace S4; trace S5; trace S6;
+drawoptions(withcolor (0.1,0.7,0.1));
+trace PL;
+drawoptions();
+pointe(P1); pointe P2; pointe P3; pointe P4; pointe P5; pointe P6;
+pointe I1; pointe I2; pointe I3;
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/pascalline.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point-0.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point-0.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point-0.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point-0.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point-0.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point.0
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point.0 (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point.0 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,446 @@
+%!PS
+%%BoundingBox: 26 15 144 99
+%%HiResBoundingBox: 26.3517 15.35753 143.727 98.02957
+%%Creator: MetaPost 2.10
+%%CreationDate: 2024.05.27:1529
+%%Pages: 1
+%%BeginProlog
+%%EndProlog
+%%Page: 1 1
+ 0 0 0 setrgbcolor 0 0.5 dtransform truncate idtransform setlinewidth pop
+ [] 0 setdash 1 setlinejoin 10 setmiterlimit
+newpath 141.73225 28.34602 moveto
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+128.39424 16.60536 137.97311 20.82774 141.73225 28.34602 curveto closepath stroke
+ 1 1 1 setrgbcolor
+newpath 143.23225 28.34602 moveto
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+93.46617 70.08463 93.62424 70.46613 93.62424 70.86397 curveto closepath fill
+ 0 0 0 setrgbcolor
+newpath 93.62424 70.86397 moveto
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+90.7823 71.64331 90.62424 71.26181 90.62424 70.86397 curveto
+90.62424 70.46613 90.7823 70.08463 91.0636 69.80333 curveto
+91.3449 69.52203 91.7264 69.36397 92.12424 69.36397 curveto
+92.52208 69.36397 92.90358 69.52203 93.18488 69.80333 curveto
+93.46617 70.08463 93.62424 70.46613 93.62424 70.86397 curveto closepath stroke
+ 1 1 1 setrgbcolor
+newpath 89.37201 62.35951 moveto
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+ 0 0 0 setrgbcolor
+newpath 89.37201 62.35951 moveto
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+89.21394 61.58017 89.37201 61.96167 89.37201 62.35951 curveto closepath stroke
+ 1 1 1 setrgbcolor
+newpath 92.21634 53.85506 moveto
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+92.05827 53.07571 92.21634 53.45721 92.21634 53.85506 curveto closepath fill
+ 0 0 0 setrgbcolor
+newpath 92.21634 53.85506 moveto
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+89.21634 53.45721 89.3744 53.07571 89.6557 52.79442 curveto
+89.937 52.51312 90.3185 52.35506 90.71634 52.35506 curveto
+91.11418 52.35506 91.49568 52.51312 91.77698 52.79442 curveto
+92.05827 53.07571 92.21634 53.45721 92.21634 53.85506 curveto closepath stroke
+ 1 1 1 setrgbcolor
+newpath 109.22482 45.35017 moveto
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+108.12267 43.85017 108.50417 44.00824 108.78546 44.28954 curveto
+109.06676 44.57083 109.22482 44.95233 109.22482 45.35017 curveto closepath fill
+ 0 0 0 setrgbcolor
+newpath 109.22482 45.35017 moveto
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+106.94548 44.00824 107.32698 43.85017 107.72482 43.85017 curveto
+108.12267 43.85017 108.50417 44.00824 108.78546 44.28954 curveto
+109.06676 44.57083 109.22482 44.95233 109.22482 45.35017 curveto closepath stroke
+ 1 1 1 setrgbcolor
+newpath 126.23372 36.84572 moveto
+126.23372 37.24356 126.07565 37.62506 125.79436 37.90636 curveto
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+123.23372 36.44788 123.39178 36.06638 123.67308 35.78508 curveto
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+125.13156 35.34572 125.51306 35.50378 125.79436 35.78508 curveto
+126.07565 36.06638 126.23372 36.44788 126.23372 36.84572 curveto closepath fill
+ 0 0 0 setrgbcolor
+newpath 126.23372 36.84572 moveto
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+124.33588 38.34572 123.95438 38.18765 123.67308 37.90636 curveto
+123.39178 37.62506 123.23372 37.24356 123.23372 36.84572 curveto
+123.23372 36.44788 123.39178 36.06638 123.67308 35.78508 curveto
+123.95438 35.50378 124.33588 35.34572 124.73372 35.34572 curveto
+125.13156 35.34572 125.51306 35.50378 125.79436 35.78508 curveto
+126.07565 36.06638 126.23372 36.44788 126.23372 36.84572 curveto closepath stroke
+ 1 1 1 setrgbcolor
+newpath 100.71259 85.03806 moveto
+100.71259 85.4359 100.55452 85.8174 100.27322 86.0987 curveto
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+98.81474 86.53806 98.43324 86.37999 98.15195 86.0987 curveto
+97.87065 85.8174 97.71259 85.4359 97.71259 85.03806 curveto
+97.71259 84.64021 97.87065 84.25871 98.15195 83.97742 curveto
+98.43324 83.69612 98.81474 83.53806 99.21259 83.53806 curveto
+99.61043 83.53806 99.99193 83.69612 100.27322 83.97742 curveto
+100.55452 84.25871 100.71259 84.64021 100.71259 85.03806 curveto closepath fill
+ 0 0 0 setrgbcolor
+newpath 100.71259 85.03806 moveto
+100.71259 85.4359 100.55452 85.8174 100.27322 86.0987 curveto
+99.99193 86.37999 99.61043 86.53806 99.21259 86.53806 curveto
+98.81474 86.53806 98.43324 86.37999 98.15195 86.0987 curveto
+97.87065 85.8174 97.71259 85.4359 97.71259 85.03806 curveto
+97.71259 84.64021 97.87065 84.25871 98.15195 83.97742 curveto
+98.43324 83.69612 98.81474 83.53806 99.21259 83.53806 curveto
+99.61043 83.53806 99.99193 83.69612 100.27322 83.97742 curveto
+100.55452 84.25871 100.71259 84.64021 100.71259 85.03806 curveto closepath stroke
+showpage
+%%EOF
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point.0
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,25 @@
+input geom2d;
+
+beginfig(0);
+
+ C = Point(3,2);
+ A = Point(5,1);
+ B = Point(3.5,3) ;
+ E = Ellipse(C,A,B);
+ trace E;
+for i=0 step 0.1 until 1:
+pointe PointDe(E,i);
+endfor
+
+T = Triangle(A,B,C);
+trace T;
+
+for i=0 step 0.1 until 1:
+pointe PointDe(T,i);
+endfor
+
+pointe PointDe(0.33333,T);
+
+endfig;
+
+end.
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/point.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/polygone-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/polygone-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/polygone-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/polygone-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/polygone-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/polygone.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/polygone.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/polygone.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,20 @@
+input geom2d;
+
+beginfig(1);
+
+
+ A = Point(0,0);
+ B = Point(3,3);
+ C = Point(3,4);
+ D = Point(2,2.4);
+ F = Point(0,5);
+ G = Barycentre(A,B,C,D,F);
+ P = Polygone(A,B,C,D,F);
+ Q1 = PolygoneRegulier(10,2,0,(2,2));
+ trace(P);
+ pointe(G);
+ trace(Q1);
+ pointe(PointPolygone(Q1,1));
+ pointe(CentrePolygone(Q1));
+endfig;
+end
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/polygone.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/vecteurs-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/vecteurs-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/vecteurs-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/vecteurs-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/vecteurs-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/vecteurs.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/vecteurs.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/vecteurs.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,14 @@
+input geom2d;
+
+beginfig(1);
+ A = Point(2,0);
+ B = Point(3,3);
+ C = Vecteur(2,2);
+ D = Segment(A,B);
+ fleche C;
+ fleche D;
+ E = SegmentToVecteur(D);
+ fleche E;
+ show ProduitScalaire(C,E);
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/divers/vecteurs.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/cos-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/cos-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/cos-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/cos-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/cos-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/cos.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/cos.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/cos.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,10 @@
+input geom2d;
+beginfig(1);
+RepereMinMax(-2Pi,2Pi,-1.1,1.1,0.5,1);
+Axes;
+Graduations;
+Debut;
+trace Representation(cos,-2Pi,2Pi,100);
+Fin;
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/cos.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction1-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction1-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction1-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction1-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction1-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction1.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction1.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction1.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,25 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef f(expr x) = sqrt(x+3-4*sqrt(x-1))+sqrt(x+8-6*sqrt(x-1)) enddef;
+
+
+beginfig(1);
+
+Repere(10,6,1,2,.8,0.8);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+
+ trace Representation(f,1,12,100) avecCrayon(1.5,Indigo);
+
+ pointe Point(5,1);
+ pointe Point(10,1);
+
+ label.top(textext("\(y=\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}\)"),
+ (7,2.5) gddEnPlace) withcolor Olive;
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction1.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction2-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction2-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction2-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction2-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction2-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction2.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction2.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction2.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,53 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1cm;
+
+vardef f(expr x) = x*(Pi-x) enddef; % f
+vardef g(expr x) = Pi-2*x enddef; % f'
+vardef h(expr x) = -2 enddef; % f''
+
+beginfig(1);
+
+Repere(9,6,5,3,.8,0.8);
+Axes;
+ Debut;
+ Graduations;
+
+ trace (Pi,-2)--(Pi,2) dashed evenly;
+ trace (-Pi,-2)--(-Pi,2) dashed evenly;
+
+ trace Representation(f,0,Pi,100) avecCrayon(1.5,Indigo);
+ trace (Representation(f,0,Pi,100) scaled -1) avecCrayon(1.5,Indigo);
+ trace (Representation(f,0,Pi,100) shifted (-2*Pi,0)) avecCrayon(1.5,Indigo);
+ trace (Representation(f,0,Pi,100) scaled -1 shifted (2*Pi,0)) avecCrayon(1.5,Indigo);
+
+ trace Representation(g,0,Pi,100) avecCrayon(1.5,Olive);
+ trace (Representation(g,0,Pi,100) xscaled -1) avecCrayon(1.5,Olive);
+ trace (Representation(g,0,Pi,100) shifted (-2*Pi,0)) avecCrayon(1.5,Olive);
+ trace (Representation(g,0,Pi,100) xscaled -1 shifted (2*Pi,0)) avecCrayon(1.5,Olive);
+
+ trace Representation(h,0,Pi,100) avecCrayon(1.5,Orange);
+ trace (Representation(h,0,Pi,100) scaled -1) avecCrayon(1.5,Orange);
+ trace (Representation(h,0,Pi,100) shifted (-2*Pi,0)) avecCrayon(1.5,Orange);
+ trace (Representation(h,0,Pi,100) scaled -1 shifted (2*Pi,0)) avecCrayon(1.5,Orange);
+
+ pointe Point(Pi,2);
+ pointe Point(Pi,-2);
+ pointe Point(-Pi,2);
+ pointe Point(-Pi,-2);
+
+ label.urt(textext("\(-\pi\)"), (-Pi,0) gddEnPlace) withcolor Peru;
+ label.ulft(textext("\(\pi\)"), (Pi,0) gddEnPlace) withcolor Peru;
+Fin;
+
+trace (0,-0.5)--(1,-0.5) avecCrayon(1.5,Indigo);
+label.rt(textext("\(f\)"), (1,-0.5) gddEnPlace);
+trace (2,-0.5)--(3,-0.5) avecCrayon(1.5,Olive);
+label.rt(textext("\(f'\)"), (3,-0.5) gddEnPlace);
+trace (4,-0.5)--(5,-0.5) avecCrayon(1.5,Orange);
+label.rt(textext("\(f''\)"), (5,-0.5) gddEnPlace);
+
+endfig;
+
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/fonctions/fonction2.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol01-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol01-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol01-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol01-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol01-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol01.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol01.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol01.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,40 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef r(expr t) = 1/(cos(t)-cos(2*t)) enddef;
+vardef rp(expr t) = (r(t)*cos(t),r(t)*sin(t)) enddef;
+vardef f(expr t) = 3/2*t*t-7/18 enddef;
+
+def DroiteN(expr r, t) = Droite((r*cos(t),r*sin(t)), (r*cos(t)-2*sin(t),r*sin(t)+2*cos(t))) enddef;
+def traceDoubleVecteur(expr o,d)= drawdblarrow ((o-d)--(o+d)) gddEnPlace enddef;
+
+def Crayon(expr t,c) = drawoptions(withpen pencircle scaled t withcolor c) enddef;
+
+beginfig(1);
+Repere(10,10,2,5,3.5,3.5);
+Axes;
+ Debut;
+ Graduations; Unites(1);
+ trace Cercle(origine,1);
+ Crayon(0.75,1.1*LightSlateGrey);
+ trace rp(-arccos(1/4))--(0,0)--rp(arccos(1/4)) dashed evenly;
+ Crayon(0.75,1.1*FireBrick);
+ trace DroiteN(-2/3/sqrt(3),7*Pi/6);
+ trace DroiteN(-2/3/sqrt(3),5*Pi/6);
+ trace Representation(f,-3,3,100) rotated -90;
+ Crayon(1.5,0.8*LightSlateGrey);
+ trace CourbeEnPolaires(r,0.1,2*Pi/3-0.1,100);
+ trace CourbeEnPolaires(r,-0.1,-2*Pi/3+0.1,100);
+ trace CourbeEnPolaires(r,2*Pi/3+0.1,4*Pi/3-0.1,100);
+ Crayon(1,DodgerBlue);
+ traceDoubleVecteur(rp(Pi),(0,0.2));
+ traceDoubleVecteur(rp(arccos(1/4)),0.05*(-sqrt(15),1));
+ traceDoubleVecteur(rp(-arccos(1/4)),0.05*(sqrt(15),1));
+ pointe rp(Pi);
+ pointe rp(arccos(1/4));
+ pointe rp(-arccos(1/4));
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol01.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol02-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol02-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol02-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol02-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol02-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol02.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol02.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol02.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,52 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=0.9cm;
+
+vardef r(expr t) = 1+cos(t) enddef;
+vardef rp(expr t) = (r(t)*cos(t),r(t)*sin(t)) enddef;
+
+def traceDoubleVecteur(expr o,d)= drawdblarrow ((o-d)--(o+d)) gddEnPlace enddef;
+
+beginfig(1);
+ Repere(10,10,2,5,3.5,3.5);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+
+ drawoptions(withcolor LightSlateGrey);
+ draw fullcircle shifted (0.5,0) gddEnPlace avecCrayon(1,Gold);
+
+ nb = 80;
+ pas = 2Pi / nb;
+ for i=0 upto nb:
+ theta := i * pas;
+ draw (fullcircle scaled 2cos(theta)
+ shifted (cos(theta)*cos(theta),cos(theta)*sin(theta))) gddEnPlace;
+ endfor;
+
+
+ traceDoubleVecteur(rp(0),(0,0.3)) avecCrayon(1,LightPink);
+ traceDoubleVecteur(rp(Pi/3),(0.3,0)) avecCrayon(1,LightPink);
+ traceDoubleVecteur(rp(Pi/2),(0.2,0.2)) avecCrayon(1,LightPink);
+ traceDoubleVecteur(rp(2Pi/3),(0,0.3)) avecCrayon(1,LightPink);
+ traceDoubleVecteur(rp(-Pi/3),(0.3,0)) avecCrayon(1,LightPink);
+ traceDoubleVecteur(rp(-Pi/2),(0.2,-0.2)) avecCrayon(1,LightPink);
+ traceDoubleVecteur(rp(-2Pi/3),(0,0.3)) avecCrayon(1,LightPink);
+
+ fleche Segment(origine,(-0.3,0)) avecCrayon(1,LightPink);
+ trace CourbeEnPolaires(r,-Pi,Pi,100) avecCrayon(1.5,Indigo);
+
+ pointe Point(0,0);
+ pointe Point(2,0);
+ pointe PairTOPoint(rp(Pi/3));
+ pointe PairTOPoint(rp(-Pi/3));
+ pointe PairTOPoint(rp(2Pi/3));
+ pointe PairTOPoint(rp(-2Pi/3));
+ pointe Point(0,1);
+ pointe Point(0,-1);
+
+ label.urt(textext("\(\mathcal{C}\)"),PtR(Point(1,0))) withcolor Magenta;
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol02.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol03-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol03-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol03-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol03-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol03-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol03.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol03.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol03.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,33 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef r(expr t) = 1+2*cos(t) enddef;
+vardef rp(expr t) = (r(t)*cos(t),r(t)*sin(t)) enddef;
+
+def traceDoubleVecteur(expr o,d)= drawdblarrow ((o-d)--(o+d)) gddEnPlace enddef;
+
+beginfig(1);
+ Repere(10,10,2.2,5,2,2);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+ drawoptions(withcolor LightSlateGrey);
+
+ nb = 50;
+ pas = 4 / nb;
+ for i=1 upto nb:
+ vardef rt(expr t) = 1 + (-1+i*pas)*cos(t) enddef;
+ trace CourbeEnPolaires(rt,-Pi,Pi,100) withcolor ((i/nb)[Gainsboro,Chartreuse]);
+ endfor;
+
+ trace CourbeEnPolaires(r,-Pi,Pi,100) avecCrayon(1.5,LightSeaGreen);
+
+ pointe Point(0,0);
+ pointe Point(0,1);
+ pointe Point(0,-1);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol03.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol04-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol04-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol04-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol04-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol04-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol04.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol04.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol04.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,44 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef r(expr t) = cos(2t)+cos(t)*cos(t) enddef;
+vardef rp(expr t) = (r(t)*cos(t),r(t)*sin(t)) enddef;
+
+def traceDoubleVecteur(expr o,d)= drawdblarrow ((o-d)--(o+d)) gddEnPlace enddef;
+
+a = arccos(1/sqrt(3));
+
+beginfig(1);
+ Repere(10,8,5,4,2,2);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+ drawoptions(withcolor LightBlue);
+
+ nb = 60;
+ pas = 2Pi/ nb;
+ for i:=0 upto nb:
+ trace (0,0) -- rp(i*pas);
+ endfor;
+
+ traceDoubleVecteur((0,0),0.5(cos(a),sin(a))) avecCrayon(1,MediumVioletRed);
+ traceDoubleVecteur((0,0),0.5(-cos(a),sin(a))) avecCrayon(1,MediumVioletRed);
+ traceDoubleVecteur((2,0),(0,0.5)) avecCrayon(1,MediumVioletRed);
+ traceDoubleVecteur((-2,0),(0,0.5)) avecCrayon(1,MediumVioletRed);
+ traceDoubleVecteur((0,1),(0.5,0)) avecCrayon(1,MediumVioletRed);
+ traceDoubleVecteur((0,-1),(-0.5,0)) avecCrayon(1,MediumVioletRed);
+
+ trace CourbeEnPolaires(r,-Pi,Pi,150) avecCrayon(1.5,DarkOliveGreen);
+
+ pointe Point(0,0);
+ pointe Point(0,1);
+ pointe Point(0,-1);
+ pointe Point(2,0);
+ pointe Point(-2,0);
+
+ Fin;
+endfig;
+
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol04.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol05-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol05-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol05-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol05-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol05-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol05.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol05.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol05.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,57 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef r(expr t) = sqrt(cos(2*t)) enddef;
+vardef ri(expr t) = -sqrt(cos(2*t)) enddef;
+vardef rh(expr t) = 1 / r(t) enddef;
+vardef rhi(expr t) = 1 / ri(t) enddef;
+
+vardef u(expr v) = sqrt(v*v+4) enddef;
+vardef rp(expr t) = (r(t)*cos(t),r(t)*sin(t)) enddef;
+
+def traceDoubleVecteur(expr o,d)= drawdblarrow ((o-d)--(o+d)) gddEnPlace enddef;
+
+a = arccos(1/sqrt(3));
+
+beginfig(1);
+ Repere(10,6,5,3,3,3);
+ Axes;
+ Debut;
+ Graduations;
+ drawoptions(withcolor Gainsboro);
+
+ nb = 40;
+ pas = Pi / (2*nb);
+ for i:=0 upto nb:
+ trace Droite((0,0),(cos(-Pi/4+i*pas),sin(-Pi/4+i*pas)));
+ endfor;
+
+ trace Droite((0,0),(1,1));
+ trace Droite((0,0),(-1,1));
+
+ trace CourbeEnPolaires(rh,-Pi/4+0.01,Pi/4-0.01,150)
+ avecCrayon(0.75,Crimson);
+ trace CourbeEnPolaires(rhi,-Pi/4+0.01,Pi/4-0.01,150)
+ avecCrayon(0.75,Crimson);
+
+ traceDoubleVecteur((0,0),0.25(1,1)) avecCrayon(1,LightSalmon);
+ traceDoubleVecteur((0,0),0.25(-1,1)) avecCrayon(1,LightSalmon);
+ traceDoubleVecteur((1,0),(0,0.2)) avecCrayon(1,LightSalmon);
+ traceDoubleVecteur((-1,0),(0,0.2)) avecCrayon(1,LightSalmon);
+ traceDoubleVecteur(rp(Pi/6),(0.2,0)) avecCrayon(1,LightSalmon);
+ traceDoubleVecteur(rp(-Pi/6),(0.2,0)) avecCrayon(1,LightSalmon);
+ traceDoubleVecteur(rp(5Pi/6),(0.2,0)) avecCrayon(1,LightSalmon);
+ traceDoubleVecteur(rp(-5Pi/6),(0.2,0)) avecCrayon(1,LightSalmon);
+
+ trace (0,0)--CourbeEnPolaires(r,-Pi/4+0.0001,Pi/4-0.0001,150)--cycle
+ avecCrayon(1.5,LightSlateGrey);
+ trace (0,0)--CourbeEnPolaires(ri,-Pi/4+0.0001,Pi/4-0.0001,150)--cycle
+ avecCrayon(1.5,LightSlateGrey);
+
+ pointe Point(0,0);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol05.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol06-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol06-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol06-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol06-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol06-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol06.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol06.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol06.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,42 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.5cm;
+
+vardef r(expr t) = cos(t)*cos(t)*cos(t)-sin(t)*sin(t)*sin(t) enddef;
+vardef rp(expr t) = (r(t)*cos(t),r(t)*sin(t)) enddef;
+
+def traceDoubleVecteur(expr o,d)= drawdblarrow ((o-d)--(o+d)) gddEnPlace enddef;
+
+a = arccos(1/sqrt(3));
+
+beginfig(1);
+
+ Repere(6,6,2,4,3,3);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+
+ drawoptions(withcolor Gainsboro);
+
+ trace (0,0)--rp(-Pi/12);
+ trace (0,0)--rp(-Pi/4);
+ trace (0,0)--rp(-5Pi/12);
+
+ traceDoubleVecteur(rp(Pi/4),(0.18,0.18)) avecCrayon(1,DarkOrchid);
+ traceDoubleVecteur(rp(-Pi/4),(0.18,0.18)) avecCrayon(1,DarkOrchid);
+ traceDoubleVecteur(rp(-Pi/12),(0.18,0.18)) avecCrayon(1,DarkOrchid);
+ traceDoubleVecteur(rp(-5Pi/12),(0.18,0.18)) avecCrayon(1,DarkOrchid);
+
+ trace CourbeEnPolaires(r,-Pi/2,Pi/2,150) avecCrayon(1.5,Crimson);
+
+ drawoptions(withcolor LightGoldenrod);
+
+ pointe Point(0,0);
+ pointe rp(-Pi/12);
+ pointe rp(-Pi/4);
+ pointe rp(-5Pi/12);
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol06.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol07-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol07-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol07-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol07-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol07-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol07.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol07.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol07.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,29 @@
+input geom2d;
+
+labeloffset := 6;
+gddU:=1.5cm;
+
+vardef r(expr t) = 4*cos(t/3)*cos(t/3)*cos(t/3) enddef;
+vardef rp(expr t) = (r(t)*cos(t),r(t)*sin(t)) enddef;
+
+def traceDoubleVecteur(expr o,d)= drawdblarrow ((o-d)--(o+d)) gddEnPlace enddef;
+
+
+
+beginfig(1);
+ Repere(8,8,2,4,1,1);
+ Axes;
+ Debut;
+ Graduations; Unites(1);
+
+ drawoptions(withcolor Gainsboro);
+
+ trace CourbeEnPolaires(r,0,3Pi,450)
+ avecCrayon(1.5,Crimson);
+
+ drawoptions(withcolor LightGoldenrod);
+
+ pointe Point(0,0);
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/polaires/pol07.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/mptextmp.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/mptextmp.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/mptextmp.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1 @@
+btex $\vec\jmath$ etex
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/mptextmp.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/mpxerr.tex
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/mpxerr.tex (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/mpxerr.tex 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,14 @@
+\gdef\mpxshipout{\shipout\hbox\bgroup%
+ \setbox0=\hbox\bgroup}%
+\gdef\stopmpxshipout{\egroup \dimen0=\ht0 \advance\dimen0\dp0
+ \dimen1=\ht0 \dimen2=\dp0
+ \setbox0=\hbox\bgroup
+ \box0
+ \ifnum\dimen0>0 \vrule width1sp height\dimen1 depth\dimen2
+ \else \vrule width1sp height1sp depth0sp\relax
+ \fi\egroup
+ \ht0=0pt \dp0=0pt \box0 \egroup}
+\mpxshipout% line 1 ./mptextmp.mp
+\(y\vec\jmath\)%
+\stopmpxshipout
+\end{document}
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/mpxerr.tex
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes1-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes1-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes1-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes1-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes1-1.pdf
___________________________________________________________________
Added: svn:mime-type
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+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes1.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes1.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes1.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,49 @@
+input geom2d;
+
+labeloffset := 4;
+gddU:=1.3cm;
+
+beginfig(1);
+
+
+ O = Point(0,0);
+ I = Point(1,0);
+ J = Point(0.3,0.8);
+ M = PointDansRepere(5,3,O,I,J);
+ H = PointDansRepere(5,0,O,I,J);
+ K = PointDansRepere(0,3,O,I,J);
+
+ Repere(8,6,1.5,1.5,1,1);
+ Debut;
+
+ trace Droite(O,I);
+ trace Droite(O,J);
+ trace Pt(K)--Pt(M)--Pt(H) dashed evenly;
+
+ marque.urt "M";
+
+ drawoptions(withpen pencircle scaled 1pt withcolor DodgerBlue);
+ trace Vecteur(O,K);
+ trace Vecteur(O,H);
+ trace Vecteur(O,M);
+ label.top(textext("$x\vec\imath$"),PtR(Milieu(O,H)));
+ label.rt(textext("$y\vec\jmath$"),PtR(Milieu(O,K)));
+
+ drawoptions(withpen pencircle scaled 1.5pt withcolor Crimson);
+ trace Vecteur(O,I);
+ trace Vecteur(O,J);
+
+ drawoptions();
+ marque.llft "O";
+
+ label.bot(textext("$x$"), PtR(H));
+ label.lft(textext("$y$"), PtR(K));
+ label.bot(textext("$\vec\imath$"), PtR(I));
+ label.lft(textext("$\vec\jmath$"), PtR(J));
+
+ Fin;
+
+
+endfig;
+
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes1.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes2-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes2-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes2-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes2-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes2-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes2.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes2.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes2.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,69 @@
+input geom2d;
+
+labeloffset := 4;
+gddU:=1.cm;
+
+beginfig(1);
+ O = Point(0,0);
+ I = Point(1,0);
+ J = Point(0.3,0.8);
+ M = PointDansRepere(5,3,O,I,J);
+ H = PointDansRepere(5,0,O,I,J);
+ K = PointDansRepere(0,3,O,I,J);
+ O' = Point(3,2);
+ I' = Point(3.7,1.8);
+ J' = Point(2.8,3);
+
+ pair Mt;
+ Mt = CoordonneesRepere(M,O',I',J');
+ H' = PointDansRepere(xpart Mt,0,O',I',J');
+ K' = PointDansRepere(0,ypart Mt,O',I',J');
+
+ Repere(8,6,1.5,1.5,1,1);
+ Debut;
+ trace Droite(O,I);
+ trace Droite(O,J);
+ trace Droite(O',I');
+ trace Droite(O',J');
+
+ trace Pt(K)--Pt(M)--Pt(H) dashed evenly;
+ trace Pt(K')--Pt(M)--Pt(H') dashed evenly;
+
+ marque.urt "M";
+
+ drawoptions(withpen pencircle scaled 1pt withcolor DodgerBlue);
+ fleche Segment(O,K);
+ fleche Segment(O,H);
+ fleche Segment(O,M);
+
+ drawoptions(withpen pencircle scaled 1pt withcolor LimeGreen);
+ fleche Segment(O',M);
+ fleche Segment(O',H');
+ fleche Segment(O',K');
+
+ drawoptions(withpen pencircle scaled 1.5pt withcolor Crimson);
+ fleche Segment(O,I);
+ fleche Segment(O,J);
+ fleche Segment(O',I');
+ fleche Segment(O',J');
+
+ drawoptions(withpen pencircle scaled 1pt withcolor LightCoral);
+ fleche Segment(O,O');
+
+ drawoptions();
+ marque.llft "O";
+ marque.llft "O'";
+
+ label.bot(textext("\(x\)"), PtR(H));
+ label.lft(textext("\(y\)"), PtR(K));
+ label.bot(textext("\(\vec\imath\)"), PtR(I));
+ label.lft(textext("\(\vec\jmath\)"), PtR(J));
+
+ label.bot(textext("\(x'\)"), PtR(H'));
+ label.urt(textext("\(y'\)"), PtR(K'));
+ label.bot(textext("\(\vec\imath'\)"), PtR(I'));
+ label.lft(textext("\(\vec\jmath'\)"), PtR(J'));
+
+ Fin;
+endfig;
+end
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/reperes/reperes2.mp
___________________________________________________________________
Added: svn:eol-style
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\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
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Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette.1
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette.1 (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette.1 2024-10-14 19:15:06 UTC (rev 72550)
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+(T) cmr9 8.96637 fshow
+353.58847 -410.39111 moveto
+(urquoise) cmr9 8.96637 fshow
+ 0.932 0.51 0.932 setrgbcolor
+newpath 0 -424.52733 moveto
+18.14215 -424.52733 lineto
+18.14215 -415.45625 lineto
+0 -415.45625 lineto
+ closepath fill
+ 0 0 0 setrgbcolor
+newpath 0 -424.52733 moveto
+18.14215 -424.52733 lineto
+18.14215 -415.45625 lineto
+0 -415.45625 lineto
+ closepath stroke
+21.14215 -423.10515 moveto
+(Violet) cmr9 8.96637 fshow
+ 0.816 0.125 0.565 setrgbcolor
+newpath 108.8529 -424.52733 moveto
+126.99506 -424.52733 lineto
+126.99506 -415.45625 lineto
+108.8529 -415.45625 lineto
+ closepath fill
+ 0 0 0 setrgbcolor
+newpath 108.8529 -424.52733 moveto
+126.99506 -424.52733 lineto
+126.99506 -415.45625 lineto
+108.8529 -415.45625 lineto
+ closepath stroke
+129.99506 -423.10515 moveto
+(VioletRed) cmr9 8.96637 fshow
+ 0.96 0.87 0.7 setrgbcolor
+newpath 217.70581 -424.52733 moveto
+235.84796 -424.52733 lineto
+235.84796 -415.45625 lineto
+217.70581 -415.45625 lineto
+ closepath fill
+ 0 0 0 setrgbcolor
+newpath 217.70581 -424.52733 moveto
+235.84796 -424.52733 lineto
+235.84796 -415.45625 lineto
+217.70581 -415.45625 lineto
+ closepath stroke
+238.84796 -423.10515 moveto
+(Wheat) cmr9 8.96637 fshow
+ 1 1 1 setrgbcolor
+newpath 326.55872 -424.52733 moveto
+344.70087 -424.52733 lineto
+344.70087 -415.45625 lineto
+326.55872 -415.45625 lineto
+ closepath fill
+ 0 0 0 setrgbcolor
+newpath 326.55872 -424.52733 moveto
+344.70087 -424.52733 lineto
+344.70087 -415.45625 lineto
+326.55872 -415.45625 lineto
+ closepath stroke
+347.70087 -423.10515 moveto
+(White) cmr9 8.96637 fshow
+ 0.96 0.96 0.96 setrgbcolor
+newpath 0 -436.31975 moveto
+18.14215 -436.31975 lineto
+18.14215 -427.24867 lineto
+0 -427.24867 lineto
+ closepath fill
+ 0 0 0 setrgbcolor
+newpath 0 -436.31975 moveto
+18.14215 -436.31975 lineto
+18.14215 -427.24867 lineto
+0 -427.24867 lineto
+ closepath stroke
+21.14215 -434.89757 moveto
+(WhiteSmok) cmr9 8.96637 fshow
+67.98904 -434.89757 moveto
+(e) cmr9 8.96637 fshow
+ 1 1 0 setrgbcolor
+newpath 108.8529 -436.31975 moveto
+126.99506 -436.31975 lineto
+126.99506 -427.24867 lineto
+108.8529 -427.24867 lineto
+ closepath fill
+ 0 0 0 setrgbcolor
+newpath 108.8529 -436.31975 moveto
+126.99506 -436.31975 lineto
+126.99506 -427.24867 lineto
+108.8529 -427.24867 lineto
+ closepath stroke
+129.99506 -434.89757 moveto
+(Y) cmr9 8.96637 fshow
+136.13725 -434.89757 moveto
+(ello) cmr9 8.96637 fshow
+149.70776 -434.89757 moveto
+(w) cmr9 8.96637 fshow
+ 0.604 0.804 0.196 setrgbcolor
+newpath 217.70581 -436.31975 moveto
+235.84796 -436.31975 lineto
+235.84796 -427.24867 lineto
+217.70581 -427.24867 lineto
+ closepath fill
+ 0 0 0 setrgbcolor
+newpath 217.70581 -436.31975 moveto
+235.84796 -436.31975 lineto
+235.84796 -427.24867 lineto
+217.70581 -427.24867 lineto
+ closepath stroke
+238.84796 -434.89757 moveto
+(Y) cmr9 8.96637 fshow
+244.99016 -434.89757 moveto
+(ello) cmr9 8.96637 fshow
+258.56067 -434.89757 moveto
+(wGreen) cmr9 8.96637 fshow
+showpage
+%%EOF
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette.1
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,168 @@
+input geom2d;
+
+gddU:=0.32cm;
+beginfig(1);
+i:=0;
+N:=4;
+for t=
+"AliceBlue",
+"AntiqueWhite",
+"Aqua",
+"Aquamarine",
+"Azure",
+"Beige",
+"Bisque",
+"Black",
+"BlanchedAlmond",
+"Blue",
+"BlueViolet",
+"Brown",
+"BurlyWood",
+"CadetBlue",
+"Chartreuse",
+"Chocolate",
+"Coral",
+"CornflowerBlue",
+"Cornsilk",
+"Crimson",
+"Cyan",
+"DarkBlue",
+"DarkCyan",
+"DarkGoldenrod",
+"DarkGray",
+"DarkGreen",
+"DarkGrey",
+"DarkKhaki",
+"DarkMagenta",
+"DarkOliveGreen",
+"DarkOrange",
+"DarkOrchid",
+"DarkRed",
+"DarkSalmon",
+"DarkSeaGreen",
+"DarkSlateBlue",
+"DarkSlateGray",
+"DarkSlateGrey",
+"DarkTurquoise",
+"DarkViolet",
+"DeepPink",
+"DeepSkyBlue",
+"DimGray",
+"DimGrey",
+"DodgerBlue",
+"FireBrick",
+"FloralWhite",
+"ForestGreen",
+"Fuchsia",
+"Gainsboro",
+"GhostWhite",
+"Gold",
+"Goldenrod",
+"Gray",
+"Green",
+"GreenYellow",
+"Grey",
+"Honeydew",
+"HotPink",
+"IndianRed",
+"Indigo",
+"Ivory",
+"Khaki",
+"Lavender",
+"LavenderBlush",
+"LawnGreen",
+"LemonChiffon",
+"LightBlue",
+"LightCoral",
+"LightCyan",
+"LightGoldenrod",
+"LightGoldenrodYellow",
+"LightGray",
+"LightGreen",
+"LightGrey",
+"LightPink",
+"LightSalmon",
+"LightSeaGreen",
+"LightSkyBlue",
+"LightSlateBlue",
+"LightSlateGray",
+"LightSlateGrey",
+"LightSteelBlue",
+"LightYellow",
+"Lime",
+"LimeGreen",
+"Linen",
+"Magenta",
+"Maroon",
+"MediumAquamarine",
+"MediumBlue",
+"MediumOrchid",
+"MediumPurple",
+"MediumSeaGreen",
+"MediumSlateBlue",
+"MediumSpringGreen",
+"MediumTurquoise",
+"MediumVioletRed",
+"MidnightBlue",
+"MintCream",
+"MistyRose",
+"Moccasin",
+"NavajoWhite",
+"Navy",
+"NavyBlue",
+"OldLace",
+"Olive",
+"OliveDrab",
+"Orange",
+"OrangeRed",
+"Orchid",
+"PaleGoldenrod",
+"PaleGreen",
+"PaleTurquoise",
+"PaleVioletRed",
+"PapayaWhip",
+"PeachPuff",
+"Peru",
+"Pink",
+"Plum",
+"PowderBlue",
+"Purple",
+"Red",
+"RosyBrown",
+"RoyalBlue",
+"SaddleBrown",
+"Salmon",
+"SandyBrown",
+"SeaGreen",
+"Seashell",
+"Sienna",
+"Silver",
+"SkyBlue",
+"SlateBlue",
+"SlateGray",
+"SlateGrey",
+"Snow",
+"SpringGreen",
+"SteelBlue",
+"Tan",
+"Teal",
+"Thistle",
+"Tomato",
+"Turquoise",
+"Violet",
+"VioletRed",
+"Wheat",
+"White",
+"WhiteSmoke",
+"Yellow",
+"YellowGreen":
+fill ((0,0)--(2,0)--(2,1)--(0,1)--cycle) scaled gddU shifted (((i mod N)
+)*(gddU+11*gddU),-(i div N)*1.3*gddU) withcolor scantokens t;
+draw ((0,0)--(2,0)--(2,1)--(0,1)--cycle) scaled gddU shifted ((i mod
+N )*(gddU+11*gddU),-(i div N)*1.3*gddU);
+label.rt(textext("\small "&t),(((i mod N)
+)*(gddU+11*gddU)+2*gddU,-(i div N)*1.3*gddU+0.5*gddU));
+i:=i+1;
+endfor;
+endfig;
+end.
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/svgnames/palette.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/homothetie-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/homothetie-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/homothetie-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/homothetie-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/homothetie-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/homothetie.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/homothetie.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/homothetie.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,36 @@
+input geom2d;
+
+beginfig(1);
+ O = Point(0,0);
+ P = Point(2,1);
+ A = Point(3,2);
+ Q = Point(-1,2);
+ R = Point(0,4);
+ B = Homothetie(A,P,3);
+ fleche Segment(O,P);
+ fleche Segment(P,A);
+ fleche Segment(A,B);
+
+ T = Triangle(A,Q,R);
+ T'= Homothetie(T,P,3);
+ trace T;
+ trace T';
+
+ C = Cercle(A,1.5);
+ trace C;
+ CC = Homothetie(C,P,3);
+ trace CC;
+
+ path p;
+ p:=Pt(A)..Pt(Q)..Pt(R);
+ W = Chemin(p);
+ trace W;
+ X = Homothetie(W,P,3);
+ trace X;
+
+ Q1 = PolygoneRegulier(10,2,0,(2,2));
+ trace Q1;
+ Q2 = Homothetie(Q1,P,3);
+ trace Q2;
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/homothetie.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/inversion-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/inversion-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/inversion-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/inversion-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/inversion-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/inversion.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/inversion.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/inversion.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,40 @@
+input geom2d;
+
+beginfig(1);
+A = Point(2,2);
+C = Cercle(A,2);
+trace C;
+marque.rt "A";
+B = Point(0,1);
+D = Inversion(B,C);
+drawoptions(withcolor DarkRed);
+CB = Cercle(B,1);
+trace CB;
+CD = Inversion(CB,C);
+trace CB;
+trace CD;
+ marque.rt "B"; marque.rt "D";
+
+drawoptions(withcolor DarkBlue);
+E = Point(3,1);
+CE = Cercle(E,0.5);
+trace CE;
+marque.rt "E";
+iCE = Inversion(CE,C);
+trace iCE;
+
+
+drawoptions(withcolor DarkGreen);
+d = Droite((3,3),(4,2));
+trace d;
+Cd = Inversion(d,C);
+trace Cd;
+
+drawoptions(withcolor Salmon);
+S = Point(1,3);
+CS = CercleCP(S,A);
+trace CS;
+dS = Inversion(CS,C);
+trace dS;
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/inversion.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrie-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrie-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrie-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrie-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrie-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrie.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrie.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrie.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,26 @@
+input geom2d;
+
+beginfig(1);
+
+A = Point(2,2);
+a = Point(-1,-1);
+b = Point(2,0);
+c = Point(3,-2);
+aa = Point(-1,-1.5);
+DD = Droite(aa,c);
+D = Droite(a,b);
+B = SymetrieAxialePoint(A,D);
+pointe A;
+pointe B;
+trace D;
+C = Cercle(A,2);
+P = ParaboleFD(A,DD);
+trace C;
+CC = SymetrieAxiale(C,D);
+PP = SymetrieAxiale(P,D);
+trace CC;
+trace P;
+trace PP;
+
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrie.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrieCentrale-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrieCentrale-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrieCentrale-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrieCentrale-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrieCentrale-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrieCentrale.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrieCentrale.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrieCentrale.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,27 @@
+input geom2d;
+
+beginfig(1);
+
+A = Point(2,2);
+a = Point(-1,-1);
+b = Point(2,0);
+c = Point(3,-2);
+aa = Point(-1,-1.5);
+DD = Droite(aa,c);
+D = Droite(a,b);
+B = SymetrieCentralePoint(A,a);
+pointe a avecCrayon(1,red);
+pointe A;
+pointe B;
+%trace D;
+C = Cercle(A,2);
+P = ParaboleFD(A,DD);
+trace C;
+CC = SymetrieCentrale(C,a);
+PP = SymetrieCentrale(P,a);
+trace CC;
+trace P;
+trace PP;
+
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/transformations/symetrieCentrale.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/apollonius-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/apollonius-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/apollonius-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/apollonius-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/apollonius-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/apollonius.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/apollonius.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/apollonius.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,90 @@
+input geom2d;
+gddU:=0.35cm;
+beginfig(1);
+% nos trois points
+A = Point(0,0);
+B = Point(6,0);
+C = Point(0.8,4);
+T_ABC = Triangle(A,B,C);
+
+C_I = CercleInscrit(T_ABC);
+C_A = CercleExinscrit(T_ABC,2);
+C_B = CercleExinscrit(T_ABC,3);
+C_C = CercleExinscrit(T_ABC,1);
+
+d_AB = Droite(A,B);
+d_BC = Droite(B,C);
+d_CA = Droite(C,A);
+
+I = Centre(C_I);
+I_C_A = Centre(C_A);
+I_C_B = Centre(C_B);
+I_C_C = Centre(C_C);
+d_CAA = Droite(A,I_C_A);
+d_CAB = Droite(B,I_C_B);
+d_CAC = Droite(C,I_C_C);
+
+A_S = AxeDeSimilitude(C_A,C_B,C_C);
+P_CA = ProjectionPointSurDroite(I_C_A,A_S);
+P_CB = ProjectionPointSurDroite(I_C_B,A_S);
+P_CC = ProjectionPointSurDroite(I_C_C,A_S);
+
+P_A = Inversion(P_CA,C_A);
+P_B = Inversion(P_CB,C_B);
+P_C = Inversion(P_CC,C_C);
+
+C_R = CentreRadical(C_A,C_B,C_C);
+% les neuf points pour les cercles d’euler (tangent intérieur)
+% et d’apollonius (tangent extérieur)
+D1 = Droite(C_R,P_A);
+P1 = IntersectionDroiteCercle(D1,C_A,1);
+Q1 = IntersectionDroiteCercle(D1,C_A,2);
+
+D2 = Droite(C_R,P_B);
+P2 = IntersectionDroiteCercle(D2,C_B,1);
+Q2 = IntersectionDroiteCercle(D2,C_B,2);
+
+D3 = Droite(C_R,P_C);
+P3 = IntersectionDroiteCercle(D3,C_C,2);
+Q3 = IntersectionDroiteCercle(D3,C_C,1);
+
+% le cercle d’apollonius
+Apol = CercleTroisPoints(P1,P2,P3);
+colorie Apol withcolor 1.05*Lavender;
+trace Apol withcolor CadetBlue;
+
+% cercle inscrit
+colorie C_I withcolor LightBlue;
+% cercles exinscrits
+colorie C_A withcolor PapayaWhip;
+colorie C_B withcolor PapayaWhip;
+colorie C_C withcolor PapayaWhip;
+
+trace d_AB;
+trace d_BC;
+trace d_CA;
+
+trace d_CAA dashed evenly;
+trace d_CAB dashed evenly;
+trace d_CAC dashed evenly;
+
+trace T_ABC withpen pencircle scaled 2 withcolor Chocolate;
+
+C_E = CercleEuler(T_ABC);
+trace C_E withcolor Goldenrod;
+
+pointe P1;
+pointe P2;
+pointe P3;
+
+pointe Q1;
+pointe Q2;
+pointe Q3;
+
+
+marque.llft "A";
+marque.urt "B";
+marque.urt "C";
+Fenetre(-7,-12,20,15)
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/apollonius.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/pedale-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/pedale-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/pedale-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/pedale-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/pedale-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/pedale.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/pedale.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/pedale.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,106 @@
+input geom2d;
+gddU:=1.5cm;
+beginfig(1);
+numeric A[],B[],C[],E[],F[],G[],U[],W[],V[],T[],R[],P[];
+A[1] = Point(0,0);
+B1 = Point(1,2);
+C1 = Point(2.5,0.2);
+W1 = PointDe(Segment(A1,B1),0.2);
+U1 = PointDe(Segment(B1,C1),0.23);
+V1 = PointDe(Segment(C1,A1),0.3);
+G1 = ProjectionPointSurDroite(B1,Droite(A1,C1));
+F1 = ProjectionPointSurDroite(C1,Droite(A1,B1));
+E1 = ProjectionPointSurDroite(A1,Droite(B1,C1));
+
+
+
+for i:=0 step 3 until 3:
+
+D[1+i] = Droite(B[1+i],C[1+i]);
+A[2+i] = SymetrieAxiale(A[1+i],D[1+i]);
+
+B[2+i] = B[1+i];
+C[2+i] = C[1+i];
+
+W[2+i] = SymetrieAxiale(W[1+i],D[1+i]);
+V[2+i] = SymetrieAxiale(V[1+i],D[1+i]);
+U[2+i] = U[1+i];
+
+G[2+i] = SymetrieAxiale(G[1+i],D[1+i]);
+F[2+i] = SymetrieAxiale(F[1+i],D[1+i]);
+E[2+i] = E[1+i];
+
+D[2+i] = Droite(A[2+i],C[2+i]);
+B[3+i] = SymetrieAxiale(B[2+i],D[2+i]);
+A[3+i] = A[2+i];
+C[3+i] = C[2+i];
+W[3+i] = SymetrieAxiale(W[2+i],D[2+i]);
+U[3+i] = SymetrieAxiale(U[2+i],D[2+i]);
+V[3+i] = V[2+i];
+E[3+i] = SymetrieAxiale(E[2+i],D[2+i]);
+F[3+i] = SymetrieAxiale(F[2+i],D[2+i]);
+G[3+i] = G[2+i];
+
+D[3+i] = Droite(A[3+i],B[3+i]);
+C[4+i] = SymetrieAxiale(C[3+i],D[3+i]);
+A[4+i] = A[3+i];
+B[4+i] = B[3+i];
+U[4+i] = SymetrieAxiale(U[3+i],D[3+i]);
+V[4+i] = SymetrieAxiale(V[3+i],D[3+i]);
+W[4+i] = W[3+i];
+E[4+i] = SymetrieAxiale(E[3+i],D[3+i]);
+G[4+i] = SymetrieAxiale(G[3+i],D[3+i]);
+F[4+i] = F[3+i];
+endfor;
+
+for i:=1 upto 7:
+ T[i] = Triangle(A[i],B[i],C[i]);
+ Q[i] = Triangle(U[i],V[i],W[i]);
+ P[i] = Triangle(E[i],F[i],G[i]);
+ colorie Q[i] avecCrayon(0.5,LightGray);
+ trace P[i] avecCrayon(0.8,MediumSlateBlue);
+endfor;
+for i:=1 upto 7:
+ trace T[i] avecCrayon(1,black);
+endfor;
+
+trace LigneBrisee(U1,V2,W3,U4,V5,W6,U7) avecCrayon(1,Peru) ;
+trace Segment(U1,U7) dashed evenly;
+trace Segment(E1,E7) dashed evenly;
+pointe A1; pointe B1; pointe C1;
+pointe A2; pointe B3; pointe C4;
+pointe A5; pointe B6; pointe C7;
+gddLabel.lft(textext("$A$"),A1);
+gddLabel.lft(textext("$B$"),B1);
+gddLabel.bot(textext("$C$"),C1);
+gddLabel.top(textext("$A'$"),A2);
+gddLabel.bot(textext("$B'$"),B3);
+gddLabel.top(textext("$C'$"),C4);
+gddLabel.bot(textext("$A''$"),A5);
+gddLabel.top(textext("$B''$"),B7);
+gddLabel.bot(textext("$C''$"),C7);
+
+pointe U1; pointe V1; pointe W1;
+label.lft(textext("$U$"),PtR(U1)) withcolor Gray;
+label.bot(textext("$V$"),PtR(V1)) withcolor Gray;
+label.lft(textext("$W$"),PtR(W1)) withcolor Gray;
+
+label.lft(textext("$U'$"),PtR(U4)) withcolor Gray;
+label.lrt(textext("$V'$"),PtR(V2)) withcolor Gray;
+label.urt(textext("$W'$"),PtR(W3)) withcolor Gray;
+label.urt(textext("$U''$"),PtR(U7)) withcolor Gray;
+label.urt(textext("$V''$"),PtR(V5)) withcolor Gray;
+label.lrt(textext("$W''$"),PtR(W7)) withcolor Gray;
+pointe U4; pointe V2; pointe W3;
+pointe U7; pointe V5; pointe W7;
+pointe E1; pointe F1; pointe G1;
+label.lrt(textext("$E$"),PtR(E1)) withcolor MediumSlateBlue;
+label.lft(textext("$F$"),PtR(F1)) withcolor MediumSlateBlue;
+label.bot(textext("$G$"),PtR(G1)) withcolor MediumSlateBlue;
+
+label.ulft(textext("$F''$"),PtR(F7)) withcolor MediumSlateBlue;
+pointe F7;
+label.rt(textext("$E''$"),PtR(E7)) withcolor MediumSlateBlue;
+pointe E7;
+endfig;
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/pedale.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/triangles-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/triangles-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/triangles-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/triangles-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/triangles-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/triangles.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/triangles.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/triangles.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,27 @@
+input geom2d;
+
+beginfig(1);
+
+ A = Point(0,0);
+ B = Point(7,0.3);
+ C = Point(1,3);
+ TABC = Triangle(A,B,C);
+ D = Orthocentre(TABC);
+ C_C = CercleCirconscrit(TABC);
+ C_E = CercleEuler(TABC);
+ trace TABC;
+ trace C_C withcolor DarkBlue;
+ trace C_E withcolor DarkRed;
+ pointe A;
+ pointe B;
+ pointe C;
+ pointe D;
+ pointe Centre(C_C);
+ pointe Centre(C_E);
+ marque.lft "A";
+ marque.rt "B";
+ marque.lft "C";
+ marque.rt "D";
+endfig;
+
+end.
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/triangles/triangles.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/vecteur/vecteur-1.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/vecteur/vecteur-1.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/vecteur/vecteur-1.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/vecteur/vecteur-1.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/vecteur/vecteur-1.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/vecteur/vecteur.mp
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/vecteur/vecteur.mp (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/vecteur/vecteur.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,10 @@
+input geom2d;
+beginfig(1);
+AB = Vecteur(2,3);
+pair a;
+a := (3,2);
+A = VecteurP(a);
+trace AB;
+trace A;
+endfig;
+end.
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/exemples/vecteur/vecteur.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/figure.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/figure.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/figure.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/figure.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/figure.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/fond.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/fond.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/fond.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/fond.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/fond.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/locctan.bib
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/locctan.bib (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/locctan.bib 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,67 @@
+ at manual{ctan-metapost,
+ title = {The \texttt{metapost} package},
+ subtitle = {A development of Metafont for creating graphics},
+ author = {{The MetaPost Team} and John Hobby},
+ date = {2021-08-26},
+ license = {lgpl},
+ url = {https://ctan.org/pkg/metapost},
+ annotation = {MetaPost uses a language based on that of
+ to produce precise
+ technical illustrations. Its output is scalable PostScript or
+ SVG, rather than the bitmaps Metafont creates.},
+}
+
+ at manual{ctan-luamplib,
+ title = {The \texttt{luamplib} package},
+ subtitle = {Use LuaTeX’s built-in MetaPost interpreter},
+ author = {Hans Hagen and Taco Hoekwater and Élie Roux and Manuel Pégourié-Gonnard and Philipp Gesang and Dohyun Kim},
+ date = {2024-08-03},
+ version = {2.34.5},
+ license = {gpl2},
+ mirror = {https://mirror.ctan.org/macros/luatex/generic/luamplib},
+ url = {https://ctan.org/pkg/luamplib},
+}
+
+ at manual{ctan-minim-mp,
+ title = {The \texttt{minim-mp} package},
+ subtitle = {Low-level mplib integration for LuaTeX},
+ author = {Esger Renkema},
+ date = {2024-04-06},
+ version = {2024/1.6},
+ license = {eupl},
+ mirror = {https://mirror.ctan.org/macros/luatex/generic/minim-mp},
+ url = {https://ctan.org/pkg/minim-mp},
+}
+
+ at manual{ctan-latexmp,
+ title = {The \texttt{latexMP} package},
+ subtitle = {Interface for \LaTeX{}-based typesetting in MetaPost},
+ author = {Jens-Uwe Morawski},
+ date = {2020-06-21},
+ version = {1.2.1},
+ license = {pd},
+ mirror = {https://mirror.ctan.org/graphics/metapost/contrib/macros/latexmp},
+ url = {https://ctan.org/pkg/latexmp},
+ annotation = {The MetaPost package latexMP implements a user-friendly
+ interface to access \LaTeX{}-based typesetting capabilities in
+ MetaPost. The text to be typeset is given as string. This
+ allows even dynamic text elements, for example counters, to be
+ used in labels. Compared to other implementations it is much
+ more flexible, since it can be used as direct replacement for
+ , and much faster, compared for example to the
+ solution provided by .},
+}
+
+ at book{toeplitz,
+ Author = {Rademacher, Hans and Toeplitz, Otto},
+ Title = {The enjoyment of math. {Translated} from the {German}. {With} a new foreword by {Alex} {Kontorovich}},
+ Edition = {Reprint},
+ FSeries = {Princeton Science Library},
+ Series = {Princeton Sci. Libr.},
+ ISBN = {978-0-691-24154-8; 978-0-691-24153-1},
+ Year = {2023},
+ Publisher = {Princeton, NJ: Princeton University Press},
+ Language = {English},
+ DOI = {10.1515/9780691241531},
+ Keywords = {00A08,01A75},
+}
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/locctan.bib
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/mp-geom2d-doc.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/mp-geom2d-doc.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/mp-geom2d-doc.pdf 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/mp-geom2d-doc.pdf 2024-10-14 19:15:06 UTC (rev 72550)
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/mp-geom2d-doc.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/mp-geom2d-doc.tex
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/mp-geom2d-doc.tex (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/mp-geom2d-doc.tex 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,3456 @@
+
+%! TEX root
+\documentclass[a4paper,french]{article}
+
+\usepackage{xcharter-otf}
+\usepackage[left=4cm]{geometry}
+\usepackage{xspace}
+\usepackage[svgnames]{xcolor}
+\usepackage{multicol}
+\usepackage{hologo}
+\usepackage{listings}
+\usepackage{showexpl} % examples
+\usepackage{mflogo}
+\usepackage{babel}
+\usepackage{tikz}
+\usepackage{url}
+\usepackage{tikz}
+\usepackage{luamplib}
+\usepackage{siunitx}
+\usepackage{pdflscape}
+\usepackage{fancyvrb,xparse,xargs}
+\usepackage{imakeidx}
+\usepackage[colorlinks]{hyperref}
+\setmonofont{FiraCode-Regular}[
+BoldFont=FiraCode-Bold,
+Contextuals=Alternate, % Activate the calt feature
+Scale=MatchLowercase
+]
+\usepackage{biblatex}
+
+\makeindex[title=Index, columns=2]
+\usepackage[verbatim]{lstfiracode} % Activate ligatures in verbatim
+\usepackage[most]{tcolorbox}
+\tcbuselibrary{listings,breakable}
+\addbibresource{locctan.bib}
+\newcommand\package[1]{\href{https://ctan.org/pkg/#1}{#1}}
+
+\newtcolorbox{colourband}[1][]{%
+arc=0pt,outer arc=0pt,enhanced, breakable, spread sidewards, left*=0pt, right*=0pt, boxrule=0pt, colback=LightSteelBlue!10, #1}
+
+
+\definecolor{hellgelb}{rgb}{1,1,0.85}
+\definecolor{colKeys}{rgb}{0,0,1}
+\definecolor{colIdentifier}{rgb}{0,0,0}
+\definecolor{colComments}{rgb}{0.3,0.7,0.3}
+\definecolor{colString}{rgb}{0,0.5,0}
+\definecolor{mpcode}{rgb}{0.5,0.1,0.1}
+
+\lstset{%
+ language=metapost,%
+ float=hbp,%
+ basicstyle=\ttfamily, %
+ identifierstyle=\color{DarkSlateGrey}, %
+ keywordstyle=\color{DarkBlue}\itshape, %
+ stringstyle=\color{Green}, %
+ commentstyle=\color{LightSlateGrey}\itshape, %
+ columns=flexible, %
+ tabsize=4, %
+ extendedchars=true, %
+ showspaces=false, %
+ showstringspaces=false, %
+ numbers=left,
+ numbersep=1em,
+ numberstyle=\tiny\color{gray}, %
+ breaklines=true, %
+ breakautoindent=true,
+ captionpos=b,
+ xleftmargin=0em,
+ sensitive=true,
+ morekeywords=[10]{colorie, trace,fermeture,fleche,pointe,marque,gddLabel,avecCrayon,ChampVecteurs,ChampVecteursDD,EtiquetteChemin},
+ keywordstyle=[10]\color{Salmon},
+ morekeywords=[7]{Abscisse,Addition,AdditionAbscisses,AdditionOrdonnee,AdditionVecteur,AireTriangle,Arc,arccos,arctan,arcsin,AsymptoteHyperbole,AxeDeSimilitude,AxeRadical,Axes,AxesBords,
+ Barycentre,Bissectrice,
+ CadreRepere,Centre,CentreRadical,Cercle,CercleCirconscrit,CercleCP,CercleD,CercleEuler,CercleExinscrit,CercleInscrit,CerclePrincipale,CercleTroisPoints,ch,Chemin,cos,Courbe,CourbeDat,CourbeEnPolaires,
+ CoVertex,
+ Debut,DemieHyperbole,DemiGrandAxe,DemiPetitAxe,Directrice,DistancePointDroite,Droite,DroitePerpendiculaire,
+ Ellipse,EllipseF, EquationDroite,Excentricite,exp,
+ Fenetre, Fin,Foyer,
+ gddEnPlace,gddTraceArcDeCercle,gddTraceObjet,Graduations,GraduationsBords,GrilleRepere,
+ Homothetie,HyperboleFD,
+ Inclinaison,IntersectionCercles,IntersectionDroiteCercle,IntersectionDroites,Inversion,IsoBarycentre,
+ LigneBrisee,ln,Longueur,LongueurSegment,
+ Marque,MarqueTrait,Milieu,
+ NombreCotesPolygone,
+ Norme,
+ Ordonnee,OrdonneeRelativePointDroite,Orthocentre,
+ PairImp,PairTOPoint,ParaboleFD,Point,PointDansRepere,PointDe,
+ PointImp,PointPolygone,PointTOPair,Polygone,PolygoneRegulier,ProduitScalaire,ProjectionPointSurDroite,ProjectionPointSurDroite,
+ Rayon,Repere,RepereMinMax,ReportSurDroite,Representation,Rotation,RotationCentre,
+ ScalaireVecteur,Segment,SegmentTOVecteur,sh,SigneOrtho,sin,Sommet,SoustractionVecteur,SymetrieAxiale,SymetrieCentrale,
+ tan,TangenteCommuneExterieure,TangenteCommuneInterieure,TangenteExterieureEllipse,TangenteEllipse,th,Triangle,
+ Unites,
+ Vecteur,VecteurP,Vertex},
+ keywordstyle=[7]\color{FireBrick},
+ morekeywords=[8]{gddO,gddA,gddB,gddC,gddD,gddE,gddF,gddT,gddP,gddS,gddX,gddPX,gddU,gddW,gddCouleurPoint,gddExtensionDroite,gddTaillePoint,
+ gddXlabel,gddYlabel, _E, Pi,
+ AliceBlue,
+AntiqueWhite,
+Aqua,
+Aquamarine,
+Azure,
+Beige,
+Bisque,
+Black,
+BlanchedAlmond,
+Blue,
+BlueViolet,
+Brown,
+BurlyWood,
+CadetBlue,
+Chartreuse,
+Chocolate,
+Coral,
+CornflowerBlue,
+Cornsilk,
+Crimson,
+Cyan,
+DarkBlue,
+DarkCyan,
+DarkGoldenrod,
+DarkGray,
+DarkGreen,
+DarkGrey,
+DarkKhaki,
+DarkMagenta,
+DarkOliveGreen,
+DarkOrange,
+DarkOrchid,
+DarkRed,
+DarkSalmon,
+DarkSeaGreen,
+DarkSlateBlue,
+DarkSlateGray,
+DarkSlateGrey,
+DarkTurquoise,
+DarkViolet,
+DeepPink,
+DeepSkyBlue,
+DimGray,
+DimGrey,
+DodgerBlue,
+FireBrick,
+FloralWhite,
+ForestGreen,
+Fuchsia,
+Gainsboro,
+GhostWhite,
+Gold,
+Goldenrod,
+Gray,
+Green,
+GreenYellow,
+Grey,
+Honeydew,
+HotPink,
+IndianRed,
+Indigo,
+Ivory,
+Khaki,
+Lavender,
+LavenderBlush,
+LawnGreen,
+LemonChiffon,
+LightBlue,
+LightCoral,
+LightCyan,
+LightGoldenrod,
+LightGoldenrodYellow,
+LightGray,
+LightGreen,
+LightGrey,
+LightPink,
+LightSalmon,
+LightSeaGreen,
+LightSkyBlue,
+LightSlateBlue,
+LightSlateGray,
+LightSlateGrey,
+LightSteelBlue,
+LightYellow,
+Lime,
+LimeGreen,
+Linen,
+Magenta,
+Maroon,
+MediumAquamarine,
+MediumBlue,
+MediumOrchid,
+MediumPurple,
+MediumSeaGreen,
+MediumSlateBlue,
+MediumSpringGreen,
+MediumTurquoise,
+MediumVioletRed,
+MidnightBlue,
+MintCream,
+MistyRose,
+Moccasin,
+NavajoWhite,
+Navy,
+NavyBlue,
+OldLace,
+Olive,
+OliveDrab,
+Orange,
+OrangeRed,
+Orchid,
+PaleGoldenrod,
+PaleGreen,
+PaleTurquoise,
+PaleVioletRed,
+PapayaWhip,
+PeachPuff,
+Peru,
+Pink,
+Plum,
+PowderBlue,
+Purple,
+Red,
+RosyBrown,
+RoyalBlue,
+SaddleBrown,
+Salmon,
+SandyBrown,
+SeaGreen,
+Seashell,
+Sienna,
+Silver,
+SkyBlue,
+SlateBlue,
+SlateGray,
+SlateGrey,
+Snow,
+SpringGreen,
+SteelBlue,
+Tan,
+Teal,
+Thistle,
+Tomato,
+Turquoise,
+Violet,
+VioletRed,
+Wheat,
+White,
+WhiteSmoke,
+Yellow,
+YellowGreen},
+ keywordstyle=[8]\color{Sienna},
+ morekeywords=[9]{},
+ keywordstyle=[9]\color{Olive}
+}
+\lstset{explpreset={pos=t,wide=false,rframe={},preset=\centering}}
+\lstdefinestyle{syntax}{backgroundcolor=\color{blue!15},numbers=none,xleftmargin=0pt,xrightmargin=0pt,
+ frame=single}
+\lstdefinestyle{code}{backgroundcolor=\color{red!15},%numbers=left,
+ xleftmargin=0pt,xrightmargin=0pt,
+ frame=single}
+
+\newtcblisting{mpcode}{
+ arc=0pt,outer arc=0pt,
+ colback=mpcode!3,
+ breakable,
+ boxsep=0pt,left=2pt,right=2pt,top=0pt,bottom=0pt, bottomtitle =
+ 3pt, toptitle=3pt,
+ boxrule=0pt,bottomrule=0.pt,toprule=0.pt, toprule at break =
+ 0pt, bottomrule at break = 0pt,
+ listing only,boxsep=0pt,listing
+ options={breaklines}
+}
+
+\makeatletter
+\tcbset{%
+ listing metapost/.code={%
+ \def\tcbuselistingtext at input{\begin{mplibcode}
+ background:=(.988,.976,.976); input \jobname.listing;
+ \end{mplibcode}}%
+ }
+}
+\makeatother
+\newtcblisting[auto counter,]{ExempleMP}[1][]{%
+ arc=0pt,outer arc=0pt,
+ colback=FireBrick!3,
+ colframe=FireBrick,
+ breakable,fontupper=\small,
+ boxsep=0pt,left=2pt,right=2pt,top=0pt,bottom=2pt, bottomtitle =
+ 3pt, toptitle=3pt, lefttitle=5pt,
+ boxrule=0pt,bottomrule=0.5pt,toprule=0.5pt, toprule at break =
+ 0pt, bottomrule at break = 0pt,
+ listing side text,
+ listing metapost,
+ title={\bfseries\sffamily Exemple~\thetcbcounter},
+ listing options={breaklines},#1
+}
+
+
+\newcommand\mpgeomdd{\texttt{mp-geom2d}\xspace}
+\newcommand\fichier[1]{\texttt{#1}}
+\newcommand\variableGDD[1]{\texttt{\color{Sienna}#1}}
+\newcommand\typeMP[1]{\texorpdfstring{\texttt{\color{Tomato}#1}}{#1}}
+\newcommand\typeGDD[1]{\texorpdfstring{\texttt{\color{Sienna}#1}}{#1}}
+\newcommand\foncGDD[1]{\texorpdfstring{\texttt{\color{Sienna}#1}}{#1}}
+
+\newenvironment{Note}{
+ \noindent\textbf{Note~---~}}
+ {}
+
+
+
+%
+\colorlet{code}{blue!80!black}
+\newcommand\cmd{\texttt}
+\newcommand\code[1]{\texorpdfstring{\texttt{\color{code}#1}}{#1}}
+\newcommand*\cs[1]{\code{\textbackslash #1}}
+\newcommand*\macro{\par\bigskip\noindent\hspace{-30pt}%
+ \SaveVerb[aftersave={%
+ \UseVerb{Vitem}%
+ }%
+ ]{Vitem}%
+ % \bigskip
+}
+\newcommand\vitem[1][]{\SaveVerb[%
+ aftersave={\item[\textnormal{\UseVerb[#1]{vsave}}]}]{vsave}}
+\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{\|}
+\setlength{\fboxsep}{2pt}
+\fvset{%
+ codes={\catcode`\«\active \catcode`\×\active },
+ defineactive={\makefancyog\makefancytimes},
+ formatcom=\color{FireBrick},
+ 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{}}}}
+
+\NewDocumentEnvironment{Macro}{ov}{%
+\Verb+#2+
+}{%
+}
+\newcommand{\return}[1]{~$\rightarrow$~#1}
+\newcommand{\indication}[1]{\hfill(\itshape #1)}
+
+\newcommand{\R}{\mathbf{R}}
+
+\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
+{\scalebox{1.5}{\Huge \mpgeomdd}}\\
+{\Large Paquet \MP{} pour des figures de géométrie plane}\\[1cm]
+\parbox{0.6\textwidth}{
+\includegraphics[scale=0.86]{figure.pdf}
+}\hfill
+\parbox{0.4\textwidth}{\Large\raggedleft
+ \textbf{Contributeurs}\\
+ Maxime \textsc{Chupin}\\
+ Jean-Michel \textsc{Sarlat}
+}
+\vfill
+\begin{center}
+Version 1.0 du 13 octobre 2024\\
+\url{https://gitlab.gutenberg-asso.fr/mchupin/mp-geom2d}\\
+\url{https://ctan.org/pkg/mp-geom2d}
+\end{center}
+%% == Page de garde ====================================================
+\newpage
+
+
+
+\section{Objectif}
+
+\mpgeomdd a été écrit avec le but de proposer des macros \MP{} permettant
+de réaliser une figure de géométrie \emph{en collant} d'assez près
+à une description impérative:
+\begin{quote}\itshape
+Soit \(A\) le point de coordonnées (2,3).\\
+Soit \(B\) le point de coordonnées (4,5).\\
+Trace la droite \((A,B)\).\\
+....
+\end{quote}
+Dans ce cadre, les objets géométriques sont le plus souvent nommés
+(\(A\), \(B\), etc.) ou désignés par leur nature et leurs attributs
+(droite \((A,B)\), etc.). Pour ne pas avoir à dépasser ce mode de
+description, en particulier pour éviter d'avoir à déclarer le
+\emph{type} de ces objets, le choix a été fait de les identifier par
+un \emph{index}\footnote{Le type \typeMP{numeric}, qui est le type par
+défaut dans \MP, ne demande pas de déclaration préalable.} dans des
+tables qui en précisent les caractéristiques.
+
+\begin{Note} À ce jour, l'objectif n'est pas atteint, le
+développement est loin d'être achevé; il est encore nécessaire de
+faire appel à des commandes \MP{} ou à des \emph{macros
+intermédiaires} pour décrire une figure. Cela évoluera sans doute
+avec le temps, le temps de trouver une syntaxe satisfaisante...
+\end{Note}
+
+
+\section{Les fichiers}
+
+\mpgeomdd est un ensemble d'outils pour la géométrie plane avec
+\MP~\cite{ctan-metapost}. Cet
+ensemble est organisé en plusieurs fichiers :
+
+\begin{enumerate}
+\item \fichier{geom2d.mp} : c’est le fichier principal, qui charge tous les
+autres.
+\item \fichier{geom2d-main.mp} : il contient
+ les structures et fonctions générales.
+\item \fichier{geom2d.mp} :
+ contient tout ce qui concerne les arcs de cercles.
+\item \fichier{geom2d-c2d.mp} :
+ contient tout ce qui concerne les courbes du second degré.
+\item \fichier{geom2d-fct.mp} :
+ contient quelques fonctions mathématiques usuelles.
+\item \fichier{geom2d-lbl.mp} :
+ contient les fonctions relatives aux labels.
+\item \fichier{geom2d-plt.mp} :
+ contient des fonctions facilitant la représentation de fonctions
+ mathématiques.
+\item \fichier{geom2d-rep.mp}
+ contient différents outils pour le tracé de figure dans un repère.
+\item \fichier{geom2d-tra.mp}
+ contient les fonctions permettant de gérer la transparence (code
+ emprunté à Anthony \bsc{Phan}).
+\item \fichier{geom2d-svgnames.mp} fournit les 150 couleurs de la spécification
+SVG.
+\end{enumerate}
+
+Nous allons, dans la suite, décrire plus en détails chacune de ces
+fonctions. Certaines fonctions s'appuient sur
+l'extension \fichier{graph.mp} présente dans toutes les bonnes
+distributions \TeX.
+
+\section{Principe général de fonctionnement}
+
+\mpgeomdd utilise des tables comme structure principale. Chaque objet est
+numéroté \emph{via} le compteur \variableGDD{gddO}, son type\footnote{Les types
+sont propres à \mpgeomdd et seront décrits plus tard.} est stocké dans
+la table \variableGDD{gddT[]} à la place \variableGDD{gddT[gddO]}. Les
+propriétés des objets sont définies dans, là encore, des tables de
+type \typeMP{numeric} qui sont \variableGDD{gddA[]}, \variableGDD{gddB[]},
+\dots, \variableGDD{gddF[]}.
+
+Par exemple, pour un \typeGDD{Point} (type \mpgeomdd), la première coordonnée
+se trouve dans \variableGDD{gddA[]} et la seconde dans \variableGDD{gddB[]}
+(les autres table ne sont pas utilisées pour un tel objet).
+
+Il y a trois tables particulières \variableGDD{gddP[]} qui est du type
+\typeMP{path}, \variableGDD{gddPX[][]} qui est saversion étendue, et \variableGDD{gddS[]} qui est du type
+\typeMP{string}. Nous verrons plus tard quelle est leur utilité.
+
+Bien entendu, lors d'une utilisation classique de \mpgeomdd, l'appel à
+toutes ces tables n'est pas chose courante. Les fonctions que nous
+allons décrire dans la suite de ce document permettent de ne pas
+avoir recours trop précisément à cette machinerie.
+
+
+\section{Tracés}
+
+\mpgeomdd fournit des macros pour tracer des objets. Une commande permet de tracer
+la plupart des objets de \mpgeomdd (qui sont décrits dans la
+section~\ref{sec:types}), ainsi que certains type \MP. Les exemples tout au long
+de la documentation permettrons d’illustrer les commandes de tracé.
+
+Pour comprendre comment fonctionne les représentations avec \mpgeomdd, il nous faut
+tout d’abord décrire le mécanisme de gestion des unités.
+
+\subsection{Unité}
+
+\mpgeomdd définit une unité générale avec la variable globale
+\lstinline+gddU+. Ce \typeMP{numeric} vaut par
+défaut \SI{1}{cm}.
+\begin{colourband}
+ \macro|gddU|
+ \index{gddU@\lstinline+gddU+}
+ \end{colourband}
+\subsection{En place}
+
+Lors de l’utilisation des commandes de tracé, \mpgeomdd utilise la macro\label{gddEnPlace}
+\begin{colourband}
+\macro|gddEnPlace|
+\index{gddEnPlace@\lstinline+gddEnPlace+}
+\end{colourband}
+Cette macro permet de spécifier les transformations géomtriques nécessaires au
+placement de l’objet, notamment le facteur d’échelle relatif à l’unité
+\lstinline+gddU+.
+
+En interne, cette macro est un \lstinline+scantoken+ de la variable globale
+\variableGDD{gddW}\index{gddW@\lstinline+gddW+} (\typeMP{string}) qui contient les transformations.
+
+\subsection{Commandes de tracés}\label{sec:trace}
+
+La macro de tracé la plus courante est la macro \lstinline+trace+.
+\begin{colourband}
+\macro|trace(«objet»)|
+\begin{description}
+ \item[\meta{objet}:] peut être:
+ \begin{itemize}
+ \item pour le côté \MP, un \typeMP{path}, une
+ \typeMP{picture} ou un \typeMP{pair}, et dans ce cas \lstinline+trace+ sera
+ équivalent à \lstinline+draw+;
+ \item du côté de \mpgeomdd,
+ n’importe quel des 6 objets définis jusque là : \typeGDD{triangle},
+ \typeGDD{segment}, \typeGDD{droite}, \typeGDD{cercle}, \typeGDD{ellipse},
+ \typeGDD{parabole}, \typeGDD{hyperbole},
+ \typeGDD{polygone}, \typeGDD{chemin},
+ \typeGDD{courbe} ou \typeGDD{vecteur} (pour ce dernier, une flêche sera
+ ajoutée à l’extrếmité du vecteur).
+ \end{itemize}
+\end{description}\index{trace@\lstinline+trace+}
+\end{colourband}
+
+Lorsque \lstinline+trace+ est utilisée sur un objet de \mpgeomdd, la macro fait
+appel à la commande \MP\ \lstinline+draw+ avec le mécanisme de mise en place
+décrit plus haut.
+
+\mpgeomdd fournit un tracé avec flêche faisant non plus appel à \lstinline+draw+
+mais à \lstinline+drawarrow+.
+
+\begin{colourband}
+\macro|fleche(«objet»)|
+\begin{description}
+ \item[\meta{objet}:] peut être:
+ \begin{itemize}
+ \item pour le côté \MP, un \typeMP{path}, une
+ \typeMP{picture} ou un \typeMP{pair}, et dans ce cas \lstinline+trace+ sera
+ équivalent à \lstinline+drawarrow+;
+ \item du côté de \mpgeomdd,
+ n’importe quel des 6 objets définis jusque là : \typeGDD{triangle},
+ \typeGDD{segment}, \typeGDD{droite}, \typeGDD{cercle}, \typeGDD{ellipse},
+ \typeGDD{polygone}, \typeGDD{chemin},
+ \typeGDD{courbe} ou \typeGDD{vecteur} (pour ce dernier, une flêche sera
+ ajoutée à l’extrếmité du vecteur).
+ \end{itemize}
+\end{description}\index{fleche@\lstinline+fleche+}
+\end{colourband}
+
+On peut aussi colorier un objet grâce à la macro suivante.
+\begin{colourband}
+\macro|colorie(«objet»)|
+\begin{description}
+ \item[\meta{objet}:] peut être:
+ \begin{itemize}
+ \item pour le côté \MP, uniquement un \typeMP{path} et dans ce cas \lstinline+trace+ sera équivalent à \lstinline+fill+;
+ \item du côté de \mpgeomdd,
+ n’importe quel objets coloriable : \typeGDD{triangle},
+ \typeGDD{cercle}, \typeGDD{ellipse}, \typeGDD{polygone}, \typeGDD{chemin}, ou
+ \typeGDD{courbe}.
+ \end{itemize}
+\end{description}\index{colorie@\lstinline+colorie+}
+\end{colourband}
+
+
+Les commandes de tracés de \mpgeomdd font appel aux macros de
+base de \MP : \lstinline+draw+ et \lstinline+fill+. Ainsi, pour spécifier la
+couleur, on pourra
+utiliser la commande \lstinline+withcolor+ ou bien la macro
+\lstinline+drawoptions+.
+
+
+On peut aussi colorier avec de la transparence\footnote{En réalité, on simule de
+la transparence avec le code emprunté à Anthony Phan :
+\url{http://www-math.univ-poitiers.fr/~phan/metalpha.html}} avec la commande
+suivante.
+\begin{colourband}
+\macro|colorieAvecTransparence(«objet»,«couleur»,«coefficient de transparence»)|
+\begin{description}
+ \item[\meta{objet}:] peut être:
+ \begin{itemize}
+ \item pour le côté \MP, uniquement un \typeMP{path} et dans ce cas \lstinline+trace+ sera équivalent à \lstinline+fill+;
+ \item du côté de \mpgeomdd,
+ n’importe quel objets coloriable : \typeGDD{triangle},
+ \typeGDD{cercle}, \typeGDD{ellipse}, \typeGDD{polygone}, \typeGDD{chemin}, ou
+ \typeGDD{courbe}.
+ \end{itemize}
+ \item[\meta{couleur}:] est une \typeMP{color}.
+ \item[\meta{coefficient de transparence}:] est un \typeMP{numeric} compris
+ entre 0 et 1, 0 pour un coloriage opaque et 1 pour un coloriage invisible.
+\end{description}\index{colorie@\lstinline+colorie+}
+\end{colourband}
+
+
+
+
+Les macros ci-dessus, font appel à une macro plus bas niveau qui permet de
+retourner le \typeMP{path} à tracer ou colorier pour tous les objets \mpgeomdd.
+
+\begin{colourband}
+\macro|gddTraceObjet(«objet»)|\return{\typeMP{path}}
+\begin{description}
+ \item[\meta{objet}:]
+ \typeGDD{triangle}, \typeGDD{segment}, \typeGDD{vecteur},
+ \typeGDD{cercle}, \typeGDD{ellipse}, \typeGDD{parabole}, \typeGDD{hyperbole},\typeGDD{polygone}, \typeGDD{chemin}, ou
+ \typeGDD{courbe}.
+\end{description}\index{gddTraceObjet@\lstinline+gddTraceObjet+}
+\end{colourband}
+
+Si l’objet n’est pas fermé, \mpgeomdd fournit la macro suivante qui ajoute un
+\lstinline+--cycle+ à la suite du chemin :
+\begin{colourband}
+\macro|fermeture(«objet»)|\return{\typeMP{path}}\indication{fermé \lstinline+--cycle+}
+\begin{description}
+ \item[\meta{objet}:]
+ \begin{itemize}
+ \item du côté de \MP, \typeMP{path} ;
+ \item du côté de \mpgeomdd, \typeGDD{triangle}, \typeGDD{segment}, \typeGDD{vecteur},
+ \typeGDD{cercle}, \typeGDD{chemin}, ou
+ \typeGDD{courbe}.
+ \end{itemize}
+\end{description}\index{fermeture@\lstinline+fermeture+}
+\end{colourband}
+
+On pourra spécifier le \emph{crayon} utilisé pour les tracés avec la commande
+suivante:
+
+\begin{colourband}
+ \macro|avecCrayon(«taille»,«couleur»)|
+ \begin{description}
+ \item[\meta{taille}:] facteur d’échelle \typeMP{numeric} du \typeMP{pen}
+ \lstinline+pencircle+ de \MP{} utilisé ;
+ \item[\meta{couleur}:] couleur \typeMP{color} à utiliser.
+ \end{description}\index{avecCrayon@\lstinline+avecCrayon+}
+\end{colourband}
+
+Cette macro est un raccourci pour le \emph{classique} \texttt{withpen
+pencircle scaled ... withcolor ...}. On peut d’ailleurs évidemment toujours
+utiliser les commandes \MP{} pour le dessin.
+
+On peut représenter les objets de type \typeGDD{point}. Pour cela, on dispose
+d’une commande qui trace un petit cercle coloré à l’endroit du point. La
+commande est la suivante :
+
+\begin{colourband}
+\macro|pointe(«point»)|
+\begin{description}
+ \item[\meta{point}:] \typeGDD{point} ou \typeMP{pair}
+\end{description}\index{pointe@\lstinline+pointe+}
+\end{colourband}
+
+Cette macro utilise deux variables globales de \mpgeomdd qui sont
+\begin{colourband}
+\macro|gddTaillePoint|\indication{\typeMP{numeric}, valeur par défaut 3}
+\index{gddTaillePoint@\lstinline+gddTaillePoint+}
+\end{colourband}
+et
+\begin{colourband}
+\macro|gddCouleurPoint| \indication{\typeMP{color}, valeur par défaut \lstinline+white+}
+\index{gddCouleurPoint@\lstinline+gddCouleurPoint+}
+\end{colourband}
+
+\subsection{Contenir les tracés}
+
+Il est souvent nécessaire de restreindre les tracés à une zone du plan $\R^2$.
+Pour cela, \mpgeomdd fournit la commande \lstinline+Fenetre+:
+\begin{colourband}
+\macro|Fenetre(«Xmin»,«Ymin»,«Xmax»,«Ymin»)|
+\index{Fenetre@\lstinline+Fenetre+}
+\end{colourband}
+Cette fonction trace un rectangle dans deux sommets opposés sont les points
+\lstinline|(Xmin,Ymin)| et \lstinline|(Xmax,Ymax)| avec la couleur \MP{}
+\lstinline+background+ et découpe l’image courante autour de ce cadre (avec la
+commande \MP{} \lstinline+clip currentpicture+).
+
+
+\section{Les types}\label{sec:types}
+
+\mpgeomdd, fournit plusieurs types d'objets. Le type d'objet est
+stocké dans la table \variableGDD{gddT[]}, et les tables \variableGDD{gddA[]}
+à \variableGDD{gddF[]}, ainsi que la table \variableGDD{gddX} contiennent les propriétés des objets.
+
+Nous allons ici décrire chaque type de l'extension \mpgeomdd,
+leurs propriétés respectives, ainsi que des méthodes associées directement à
+l’objet.
+
+\subsection{Le type \typeGDD{point}}
+
+Ce type correspond au point de
+l'espace euclidien.
+
+\subsubsection{Constructeur}
+
+Pour être plus clair voici la fonction principale
+pour créer un tel objet :
+%
+\begin{mpcode}
+vardef Point(expr a,b) =
+ gddT[incr gddO] = "point";
+ gddA[gddO] = a; gddB[gddO] = b; gddO
+enddef;
+\end{mpcode}
+
+\begin{colourband}
+\macro|Point(«x»,«y»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{x}:] \typeMP{numeric}
+ \item[\meta{y}:] \typeMP{numeric}
+\end{description}\index{Point@\lstinline+Point+}
+\end{colourband}
+\bigskip
+
+
+Cette fonction \og{}retourne\fg{} le compteur \variableGDD{gdd0} et crée dans la
+table de type une entrée \typeGDD{point} et les attributs (coordonnées)
+correspondants \variableGDD{a} et \variableGDD{b} dans les tables
+\variableGDD{gddA} et \variableGDD{gddB}.
+
+Avec un tel type de fonctionnement, la plupart des manipulations se
+fait sur des \typeMP{numeric}s. En effet, pour déclarer un
+\typeGDD{point}, il suffit d'écrire
+\begin{mpcode}
+A = Point(2,3);
+\end{mpcode}
+\variableGDD{A} prend alors la valeur courante de \variableGDD{gddO}. C'est
+l'identifiant du point.
+
+On peut aussi définir un \typeGDD{point} par ses coordonnées \emph{polaires}
+avec la commande suivante.
+
+\begin{colourband}
+\macro|PointPolaire(«r»,«a»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{r}:] \typeMP{numeric}, module du point.
+ \item[\meta{a}:] \typeMP{numeric}, angle par rapport à l’axe des abscisses.
+\end{description}\index{Point@\lstinline+Point+}
+\end{colourband}
+\bigskip
+
+
+
+On peut définir un point dans un repère défini lui par un point
+d’origine et deux vecteurs avec la fonction suivante:
+\begin{colourband}
+\macro|PointDansRepere(«x»,«y»,«o»,«i»,«j»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{x}:] \typeMP{numeric}
+ \item[\meta{y}:] \typeMP{numeric}
+ \item[\meta{o}:] \typeGDD{Point} d’origine du repère
+ \item[\meta{i}:] \typeGDD{Vecteur} (ou \typeGDD{Point}) définissant l’axe des abscisses
+ \item[\meta{j}:] \typeGDD{Vecteur} (ou \typeGDD{Point}) définissant l’axe des ordonnées
+\end{description}\index{PointDansRepere@\lstinline+PointDansRepere+}
+\end{colourband}
+
+\bigskip
+
+On pourra alors définir un point comme ceci:
+Un vecteur se définit alors comme ceci (pas soucis de concision, on utilise ici
+des \typeGDD{Point}s qui devraient être des \typeGDD{Vecteur}s):
+\begin{mpcode}
+O = Point(0,0);
+I = Point(2,0);
+J = Point(0,3);
+A = PointDansRepere(2,3,O,I,J);
+\end{mpcode}
+
+
+\subsubsection{Macros associées}
+
+On peut récupérer les abscisse et ordonnée d’un point avec les commandes
+suivantes :
+\begin{colourband}
+\macro|Abscisse(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point}, \typeGDD{vecteur} ou \typeMP{pair}.
+\end{description}\index{Abscisse@\lstinline+Abscisse+}
+\end{colourband}
+
+\begin{colourband}
+\macro|Ordonnee(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point}, \typeGDD{vecteur} ou \typeMP{pair}.
+\end{description}\index{Ordonnee@\lstinline+Ordonnee+}
+\end{colourband}
+
+On pourra ajouter les abscisses, les ordonnées ou bien, à la manière des
+vecteurs, des points entre eux avec les commandes suivantes.
+\begin{colourband}
+\macro|AdditionAbscisses(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair}.
+\end{description}\index{AdditionAbscisses@\lstinline+AdditionAbscisses+}
+\end{colourband}
+\begin{colourband}
+\macro|AdditionOrdonnee(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair}.
+\end{description}\index{AdditionOrdonnee@\lstinline+AdditionOrdonnee+}
+\end{colourband}
+et
+\begin{colourband}
+\macro|Addition(«a»,«b»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair};
+ \item[\meta{b}:] \typeGDD{point} ou \typeMP{pair}.
+\end{description}\index{Addition@\lstinline+Addition+}
+\end{colourband}
+
+On peut aussi calculer la longueur entre deux points grâce à la commande
+suivante:
+\begin{colourband}
+\macro|Longueur(«a»,«b»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair};
+ \item[\meta{b}:] \typeGDD{point} ou \typeMP{pair}.
+\end{description}\index{Longueur@\lstinline+Longueur+}
+\end{colourband}
+
+On peut calculer le point équidistant de deux point, le milieu :
+\begin{colourband}
+\macro|Milieu(«a»,«b»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair};
+ \item[\meta{b}:] \typeGDD{point} ou \typeMP{pair}.
+\end{description}\index{Milieu@\lstinline+Milieu+}
+\end{colourband}
+
+On peut réaliser la rotation d’un point autour de l’origine $(0,0)$ avec la
+commande suivante:
+\begin{colourband}
+\macro|Rotation(«a»,«b»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair};
+ \item[\meta{b}:] \typeMP{numeric}, l’angle de rotation en radian.
+\end{description}\index{Rotation@\lstinline+Rotation+}
+\end{colourband}
+
+Si on veut réaliser la rotation d’un point autour d’un autre, on utilisera la
+commande suivante:
+\begin{colourband}
+\macro|RotationCentre(«a»,«b»,«c»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair};
+ \item[\meta{b}:] \typeGDD{point} ou \typeMP{pair};
+ \item[\meta{c}:] \typeMP{numeric}, l’angle de rotation en radian.
+\end{description}\index{RotationCentre@\lstinline+RotationCentre+}
+\end{colourband}
+
+On peut calculer l’isobarycentre d’une liste de points (ou de \typeMP{pair} de \MP) avec la commande suivante.
+\begin{colourband}
+\macro|IsoBarycentre(«a»,«b»,«c», etc.)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair};
+ \item[\meta{b}:] \typeGDD{point} ou \typeMP{pair}.
+\end{description}\index{IsoBarycentre@\lstinline+IsoBarycentre+}
+\end{colourband}
+
+On peut calculer le barycentre d’une liste de points associées à des poids (mais
+ici, il n’est pas possible d’utiliser des \typeMP{pair} de \MP).
+\begin{colourband}
+\macro|Barycentre((«A»,«a»),(«B»,«b»),(«C»,«c»), etc.)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{A}:] \typeGDD{point} ;
+ \item[\meta{a}:] \typeMP{numeric}, poids associé à \meta{A} ;
+ \item[\meta{B}:] \typeGDD{point} ;
+ \item[\meta{b}:] \typeMP{numeric}, poids associé à \meta{B} ;
+ \item[] etc.
+\end{description}\index{Barycentre@\lstinline+Barycentre+}
+\end{colourband}
+
+
+On peut déterminer la bissectrice d’un secteur angulaire défini par trois
+points. La fonction retourne une \typeGDD{droite}..
+\begin{colourband}
+\macro|Bissectrice(«A»,«B»,«C»)|\return{\typeGDD{droite}}
+\begin{description}
+ \item[\meta{A}:] \typeGDD{point} ;
+ \item[\meta{B}:] \typeGDD{point} ;
+ \item[\meta{C}:] \typeGDD{point} ;
+\end{description}\index{Bissectrice@\lstinline+Bissectrice+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,0);
+B = Point(0,0);
+C = Point(1,1);
+D = Bissectrice(A,B,C);
+trace D;
+marque.bot "A";
+marque.bot "B";
+marque.bot "C";
+Fenetre(-0.5,-0.5,2,2);
+endfig;
+\end{ExempleMP}
+
+
+Le type \typeGDD{point} est évidemment lié au type \MP{} \typeMP{pair}.
+
+\mpgeomdd fournit des macros qui permettent de passer de \typeGDD{point} à
+\typeMP{pair} et réciproquement.
+\begin{colourband}
+\macro|PointTOPair(«a»,«b»)|\return{\typeMP{pair}}
+\begin{description}
+ \item[\meta{a}:] \typeMP{numeric}, abscisse
+ \item[\meta{b}:] \typeMP{numeric}, ordonnée
+\end{description}\index{PointTOPair@\lstinline+PointTOPair+}
+\end{colourband}
+
+
+\begin{colourband}
+\macro|PairTOPoint(«p»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{p}:] \typeMP{pair}
+\end{description}\index{PairTOPoint@\lstinline+PairTOPoint+}
+\end{colourband}
+
+Ces deux commandes sont complétées par deux autres qui assure qu’un élément est
+d’un type donné:
+\begin{colourband}
+\macro|PairImp(«p»)|\return{\typeGDD{pair}}
+\begin{description}
+ \item[\meta{p}:] \typeGDD{point} ou \typeMP{pair}
+\end{description}\index{PairImp@\lstinline+PairImp+}
+\end{colourband}
+
+
+\begin{colourband}
+\macro|PointImp(«p»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{p}:] \typeGDD{point} ou \typeMP{pair}
+\end{description}\index{PointImp@\lstinline+PointImp+}
+\end{colourband}
+
+On peut aussi récupérer un point le long d’un objet \mpgeomdd (décris dans les
+sections suivantes). La macro suivante retourne un \typeGDD{point} le long du
+chemin (cyclique ou non) de l’objet le paramétrant entre 0 et 1.
+
+\begin{colourband}
+\macro|PointDe(«o»,«t»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{o}:] n’importe quel objet \mpgeomdd (même un \typeGDD{point} pour
+ lequel lui-même est retourné);
+ \item[\meta{t}:] \typeMP{numeric} compris entre 0 et 1 (qui paramètre le
+ chemin de l’objet entre 0 et 1).
+\end{description}\index{PointDe@\lstinline+PointDe+}
+\end{colourband}
+
+
+
+\subsection{Le type \typeGDD{vecteur}}
+
+Ce type correspond aux vecteurs
+définis à l'aide de deux coordonnées de l'espace euclidien.
+
+\subsubsection{Constructeurs}
+
+La fonction
+créatrice d'un tel objet est celle-ci
+%
+\begin{mpcode}
+vardef Vecteur(expr a,b) =
+ save n; n = incr gddO;
+ gddT[n] = "vecteur"; gddA[n] = a; gddB[n] = b; n
+enddef;
+\end{mpcode}
+
+\begin{colourband}
+\macro|Vecteur(«a»,«b»)|\return{\typeGDD{vecteur}}
+\begin{description}
+ \item[\meta{a}:] \typeMP{numeric}
+ \item[\meta{b}:] \typeMP{numeric}
+\end{description}\index{Vecteur@\lstinline+Vecteur+}
+\end{colourband}
+\bigskip
+
+Cette fonction a la même architecture que celle correspondante au
+\typeGDD{point} : elle retourne la valeur courante de \variableGDD{gddO}
+après incrémentation, puis affecte le type \typeGDD{vecteur} à
+l'entrée correspondante dans la table \variableGDD{gddT}.
+
+On peut aussi définir un vecteur à partir d’un \typeMP{pair} \MP.
+\begin{mpcode}
+vardef VecteurP(expr a) =
+ save n; n = incr gddO;
+ gddT[n] = "vecteur"; gddA[n] = xpart a; gddB[n] = ypart a; n
+enddef;
+\end{mpcode}
+
+\begin{colourband}
+\macro|VecteurP(«a»)|\return{\typeGDD{vecteur}}
+\begin{description}
+ \item[\meta{a}:] \typeMP{pair}
+\end{description}\index{VecteurP@\lstinline+VecteurP+}
+\end{colourband}
+\bigskip
+
+Un vecteur peut se définir alors comme ceci:
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+AB = Vecteur(2,3);
+pair a;
+a := (3,2);
+A = VecteurP(a);
+trace AB;
+trace A;
+endfig;
+\end{ExempleMP}
+
+\subsubsection{Macros associées}
+
+Comme les objets de \mpgeomdd sont des \typeMP{numeric}s, les opérations classiques
+de l’espace vectoriel ne peuvent pas s’écrire avec les simple caractères
+\lstinline-+-, \lstinline+-+, et \lstinline-*-.
+
+\begin{colourband}
+\macro|AdditionVecteur(«a»,«b»)|\return{\typeGDD{vecteur}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{vecteur}
+ \item[\meta{b}:] \typeGDD{vecteur}
+\end{description}\index{AdditionVecteur@\lstinline+AdditionVecteur+}
+\end{colourband}
+\bigskip
+
+
+\begin{colourband}
+\macro|SoustractionVecteur(«a»,«b»)|\return{\typeGDD{vecteur}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{vecteur}
+ \item[\meta{b}:] \typeGDD{vecteur}
+\end{description}\index{SoustractionVecteur@\lstinline+SoustractionVecteur+}
+\end{colourband}
+\bigskip
+
+
+\begin{colourband}
+\macro|ScalaireVecteur(«k»,«b»)|\return{\typeGDD{vecteur}}
+\begin{description}
+ \item[\meta{k}:] \typeMP{numeric}
+ \item[\meta{b}:] \typeGDD{vecteur}
+\end{description}\index{ScalaireVecteur@\lstinline+ScalaireVecteur+}
+\end{colourband}
+\bigskip
+
+On pourra alors faire les opérations classiques sur les vecteurs.
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+AB = Vecteur(2,3);
+BC = Vecteur(1,0);
+AC = AdditionVecteur(AB,BC);
+kAC = ScalaireVecteur(3.0,AC);
+trace AB;
+trace BC;
+trace AC;
+endfig;
+\end{ExempleMP}
+
+On peut aussi calculer le produit scalaire de deux vecteurs avec la commande
+suivante.
+
+\begin{colourband}
+\macro|ProduitScalaire(«a»,«b»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeMP{vecteur}
+ \item[\meta{b}:] \typeGDD{vecteur}
+\end{description}\index{ProduitScalaire@\lstinline+ProduitScalaire+}
+\end{colourband}
+\bigskip
+
+On peut aussi calculer la norme euclidienne d’un vecteur.
+\begin{colourband}
+\macro|Norme(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{vecteur}
+\end{description}\index{Norme@\lstinline+Norme+}
+\end{colourband}
+\bigskip
+
+La commande suivante permet d’obtenir l’angle, en radian, entre $[0,\pi]$ formé
+entre deux vecteurs. Si on note $u$ et $v$ les deux vecteurs de $\R^2$, l’angle
+calculé par la commande suivante est obtenu avec la formule suivante :
+\[\theta = \arccos \left(\frac{u\cdot v}{\|u\|\|v\|}\right).\]
+
+\begin{colourband}
+\macro|Angle(«a»,«b»)|\return{\typeMP{numeric} (dans $[0,\pi]$)}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{vecteur}
+ \item[\meta{b}:] \typeGDD{vecteur}
+\end{description}\index{Norme@\lstinline+Norme+}
+\end{colourband}
+\bigskip
+
+
+\subsection{Le type \typeGDD{segment}}
+Les segments sont
+définis par deux points de $\R^2$.
+
+
+\subsubsection{Contructeur}
+La fonction créatrice de cet objet est
+celle-ci
+\begin{mpcode}
+vardef Segment (expr a,b) =
+ save n; n = incr gddO;
+ gddT[n] = "segment"; gddA[n] = PointImp(a); gddB[n] = PointImp(b); n
+enddef;
+\end{mpcode}
+
+\begin{colourband}
+\macro|Segment(«a»,«b»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point}
+ \item[\meta{b}:] \typeGDD{point}
+\end{description}\index{Segment@\lstinline+Segment+}
+\end{colourband}
+
+\bigskip
+
+Un segment se définit alors comme ceci:
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(2,3);
+B = Point(4,5);
+C = Point(2,1);
+AB = Segment(A,B);
+BC = Segment(B,C);
+AC = Segment(A,C);
+fleche AB;
+fleche BC;
+fleche AC;
+endfig;
+\end{ExempleMP}
+
+\subsubsection{Macros associées}
+
+On peut calculer la longueur d’un segment avec la macro suivante.
+\begin{colourband}
+\macro|LongueurSegment(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{segment}
+\end{description}\index{LongueurSegment@\lstinline+LongueurSegment+}
+\end{colourband}
+
+On peut aussi convertir un segment en vecteur avec la macro suivante qui fait la
+différente des coordonnées des deux points définissant le segment.
+\begin{colourband}
+\macro|SegmentTOVecteur(«a»)|\return{\typeGDD{vecteur}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{segment}
+\end{description}\index{SegmentTOVecteur@\lstinline+SegmentTOVecteur+}
+\end{colourband}
+
+
+
+\subsection{Le type \typeGDD{droite}}
+Une droite est simplement définie par
+deux points.
+
+\subsubsection{Constructeur}
+
+Ainsi la fonction créatrice de cet objet est la suivante
+\begin{mpcode}
+vardef Droite (expr a,b) =
+ save n; n = incr gddO;
+ gddT[n] = "droite"; gddA[n] = PointImp(a); gddB[n] = PointImp(b); n
+enddef;
+\end{mpcode}
+\begin{colourband}
+\macro|Droite(«a»,«b»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point}
+ \item[\meta{b}:] \typeGDD{point}
+\end{description}\index{Droite@\lstinline+Droite+}
+\end{colourband}
+\bigskip
+
+Lors de la représentation des droites (voir section~\ref{sec:trace}), le
+caractère \emph{infini} de la droite est géré par la variable globale
+\lstinline+gddExtensionDroite+
+\index{gddExtensionDroite@\lstinline+gddExtensionDroite+}
+qui vaut 10 par défaut.
+
+\subsubsection{Macros associées}
+
+
+La macro suivante permet, sous forme d’un triplet, et donc d’une \typeMP{color},
+d’obtenir les coefficients d’une droite donnée. Pour une droite $(D)$, la macro
+donne le triplet $(u,v,w)\in\R^3$ tel que $\forall (x,y)\in(D)$, $ux+vy+w=0$.
+
+\begin{colourband}
+\macro|EquationDroite(«a»)|\return{\typeMP{color}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{droite}
+\end{description}\index{EquationDroite@\lstinline+EquationDroite+}
+\end{colourband}
+
+On peut calculer la projection d’un point sur une droite avec la commande
+suivante.
+
+\begin{colourband}
+\macro|ProjectionPointSurDroite(«p»,«a»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{p}:] \typeGDD{point}
+ \item[\meta{a}:] \typeGDD{droite}
+\end{description}\index{ProjectionPointSurDroite@\lstinline+ProjectionPointSurDroite+}
+\end{colourband}
+
+On peut obtenir l’ordonnée relative d’un point sur une droite avec la macro
+suivante.
+\begin{colourband}
+\macro|OrdonneeRelativePointDroite(«p»,«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{p}:] \typeGDD{point}
+ \item[\meta{a}:] \typeGDD{droite}
+\end{description}\index{OrdonneeRelativePointDroite@\lstinline+OrdonneeRelativePointDroite+}
+\end{colourband}
+
+Le calcul de la distance d’un point à une droite se fait avec la macro suivante.
+\begin{colourband}
+\macro|DistancePointDroite(«p»,«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{p}:] \typeGDD{point}
+ \item[\meta{a}:] \typeGDD{droite}
+\end{description}\index{DistancePointDroite@\lstinline+DistancePointDroite+}
+\end{colourband}
+
+La macro suivante permet d’obtenir la droite perpendiculaire à un droite passant
+par un point.
+\begin{colourband}
+\macro|DroitePerpendiculaire(«a»,«p»)|\return{\typeGDD{droite}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{droite}
+ \item[\meta{p}:] \typeGDD{point}
+\end{description}\index{DroitePerpendiculaire@\lstinline+DroitePerpendiculaire+}
+\end{colourband}
+
+On pourra obtenir le \typeGDD{point} d’intersection de deux droites avec la
+macro suivante.
+\begin{colourband}
+\macro|IntersectionDroites(«a»,«b»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{droite}
+ \item[\meta{b}:] \typeGDD{droite}
+\end{description}\index{IntersectionDroites@\lstinline+IntersectionDroites+}
+\end{colourband}
+
+La macro suivante permet de reporter un point sur une droite avec une certaine
+longueure, à la manière d’un compas.
+
+\begin{colourband}
+\macro|ReportSurDroite(«P»,«D»,«l»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{P}:] \typeGDD{point}
+ \item[\meta{D}:] \typeGDD{droite}
+ \item[\meta{l}:] \typeGDD{numeric}
+\end{description}\index{ReportSurDroite@\lstinline+ReportSurDroite+}
+\end{colourband}
+
+Voici un exemple permettant d’illustrer l’utilisation de quelques commandes
+relatives aux droites.
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(0,0);
+B = Point(3,2);
+AB = Droite(A,B);
+trace AB;
+pointe A;
+pointe B;
+C = Point(0,2);
+DC = DroitePerpendiculaire(AB,C);
+trace DC;
+pointe C;
+D = ProjectionPointSurDroite(C,AB);
+pointe D;
+Fenetre(-2,-2,4,4);
+endfig;
+\end{ExempleMP}
+
+
+
+
+
+\subsection{Le type \typeGDD{cercle}}
+Un cercle est défini par un point et un
+rayon.
+
+\subsubsection{Constructeurs}
+La fonction créatrice de base de cet objet est la suivante
+\begin{mpcode}
+vardef Cercle (expr a,b) =
+ save n; n = incr gddO;
+ gddT[n] = "cercle"; gddA[n] = PointImp(a); gddB[n] = b; n
+enddef;
+\end{mpcode}
+\begin{colourband}
+\macro|Cercle(«a»,«b»)|\return{\typeGDD{cercle}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair},
+ centre du cercle
+ \item[\meta{b}:] \typeMP{numeric}, rayon du cercle
+\end{description}\index{Cercle@\lstinline+Cercle+}
+\end{colourband}
+\bigskip
+
+
+Deux autres fonctions permettent de définir des cercles. La fonction
+\foncGDD{CercleCP} définit le cercle par un centre et un point par lequel passe
+le cercle.
+\begin{colourband}
+\macro|CercleCP(«a»,«b»)|\return{\typeGDD{cercle}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair},
+ centre du cercle
+ \item[\meta{b}:] \typeGDD{point},
+ tel que \meta{b}-\meta{a} est le rayon
+\end{description}\index{CercleCP@\lstinline+CercleCP+}
+\end{colourband}
+\bigskip
+
+
+
+On peut aussi définir un cercle par deux points définissant son diamètre. La
+fonction correspondante est la suivante
+
+\begin{colourband}
+\macro|CercleD(«a»,«b»)|\return{\typeGDD{cercle}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair}
+ \item[\meta{b}:] \typeGDD{point} ou \typeMP{pair},
+ tel que (\meta{a}--\meta{b}) est le diamètre du cercle
+\end{description}\index{CercleD@\lstinline+CercleD+}
+\end{colourband}
+\bigskip
+
+On peut aussi définir un cercle comme le cercle qui passe par trois points avec
+la macro suivante.
+
+\begin{colourband}
+\macro|CercleTroisPoints(«a»,«b»,«c»)|\return{\typeGDD{cercle}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair}
+ \item[\meta{b}:] \typeGDD{point} ou \typeMP{pair}
+ \item[\meta{c}:] \typeGDD{point} ou \typeMP{pair}
+\end{description}\index{CercleTroisPoints@\lstinline+CercleTroisPoints+}
+\end{colourband}
+\bigskip
+
+
+
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(3,1);
+B = Point(0,2);
+O = Point(0,0);
+r = 1.0;
+COr = Cercle(O,r);
+COA = CercleCP(O,A);
+CAB = CercleD(A,B);
+COAB = CercleTroisPoints(O,A,B);
+trace COr;
+trace COA;
+trace CAB;
+trace COAB;
+pointe A; pointe B; pointe O;
+endfig;
+\end{ExempleMP}
+
+\subsubsection{Macros associées}
+
+De nombreuses macros sont associées aux cercles.
+
+On pourra récupérer le rayon d’un cercle avec la commande suivante.
+
+
+\begin{colourband}
+\macro|Rayon(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{cercle}
+\end{description}\index{Rayon@\lstinline+Rayon+}
+\end{colourband}
+\bigskip
+
+On pourra obtenir le centre (\typeGDD{point}) d’un cercle avec la commande :
+\begin{colourband}
+\macro|Centre(«a»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{cercle}, \typeGDD{ellipse} ou \typeGDD{hyperbole}
+\end{description}\index{Centre@\lstinline+Centre+}
+\end{colourband}
+\bigskip
+
+On peut calculer l’intersection entre deux cercles grâce à la macro suivante.
+
+\begin{colourband}
+\macro|IntersectionCercles(«a»,«b»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{cercle}
+ \item[\meta{b}:] \typeGDD{cercle}
+\end{description}\index{IntersectionCercles@\lstinline+IntersectionCercles+}
+\end{colourband}
+\bigskip
+
+Cette macro ne donnera qu’un seul point d’intersection. Pour obtenir les deux
+points d’intersection, il faudra inverser l’ordre d’appel sur les cercles comme
+l’exemple suivant l’illustre.
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(0,0);
+CA = Cercle(A,1);
+B = Point(1.5,0);
+CB = Cercle(B,2);
+D1 = IntersectionCercles(CA,CB);
+D2 = IntersectionCercles(CB,CA);
+trace CA; trace CB;
+pointe A; pointe B; pointe D1; pointe D2;
+endfig;
+\end{ExempleMP}
+
+\mpgeomdd fournit aussi une macro permettant d’obtenir les intersections entre une
+droite et un cercle.
+
+\begin{colourband}
+\macro|IntersectionDroiteCercle(«d»,«c»,«n»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{d}:] \typeGDD{droite}
+ \item[\meta{c}:] \typeGDD{cercle}
+ \item[\meta{n}:] \typeMP{numeric} qui vaut 1 ou 2 suivant le point
+ d’intersection que l’on souhaite (s’il n’existe qu’un point d’intersection
+ alors les deux valeurs renvoient le même point)
+\end{description}\index{IntersectionDroiteCercle@\lstinline+IntersectionDroiteCercle+}
+\end{colourband}
+\bigskip
+
+L’exemple suivant permet d’illuster cette macro.
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(2,2);
+C_A = Cercle(A,1);
+B = Point(0,1);
+C = Point(4,2);
+BC = Droite(B,C);
+E1 = IntersectionDroiteCercle(BC,C_A,1);
+trace C_A;
+trace BC dashed evenly;
+pointe A; pointe B; pointe C; pointe E1;
+Fenetre(-0.5,-0.5,5,4);
+endfig;
+\end{ExempleMP}
+
+
+
+On peut obtenir les tangentes intérieures et extérieures communes à deux cercles
+avec les deux macros suivantes. Là encore, comme il existe deux tangentes, pour
+obtenir les deux, on inversera l’ordre d’appel des deux cercles.
+
+\begin{colourband}
+\macro|TangenteCommuneExterieure(«a»,«b»)|\return{\typeGDD{droite}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{cercle}
+ \item[\meta{b}:] \typeGDD{cercle}
+\end{description}\index{TangenteCommuneExterieure@\lstinline+TangenteCommuneExterieure+}
+\end{colourband}
+\bigskip
+
+
+\begin{colourband}
+\macro|TangenteCommuneInterieure(«a»,«b»)|\return{\typeGDD{droite}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{cercle}
+ \item[\meta{b}:] \typeGDD{cercle}
+\end{description}\index{TangenteCommuneInterieure@\lstinline+TangenteCommuneInterieure+}
+\end{colourband}
+\bigskip
+
+L’exemple suivante illustre l’utilisation de ces deux macros.
+\begin{ExempleMP}[sidebyside=false]
+input geom2d;
+beginfig(1);
+C1 = Cercle((-2,0),2);
+C2 = Cercle((1.5,0),1);
+T1 = TangenteCommuneExterieure(C1,C2);
+T2 = TangenteCommuneExterieure(C2,C1);
+T3 = TangenteCommuneInterieure(C1,C2);
+T4 = TangenteCommuneInterieure(C2,C1);
+trace C1; trace C2;
+trace T1; trace T2;
+trace T3; trace T4;
+
+Fenetre(-5,-3,6,3);
+endfig;
+\end{ExempleMP}
+
+La macro suivante permet de calculer l’axe radical (\typeGDD{droite}) de deux
+cercles\footnote{La méthode de construction a été largement inspirée du code de
+T.~Thurston dans son document \emph{Drawing with \MP}.}.
+\begin{colourband}
+\macro|AxeRadical(«a»,«b»)|\return{\typeGDD{droite}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{cercle}
+ \item[\meta{b}:] \typeGDD{cercle}
+\end{description}\index{AxeRadical@\lstinline+AxeRadical+}
+\end{colourband}
+\bigskip
+
+La macro suivante permet d’obtenir le centre radical de trois cercles.
+\begin{colourband}
+\macro|CentreRadical(«a»,«b»,«c»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{cercle}
+ \item[\meta{b}:] \typeGDD{cercle}
+ \item[\meta{c}:] \typeGDD{cercle}
+\end{description}\index{CentreRadical@\lstinline+CentreRadical+}
+\end{colourband}
+\bigskip
+
+La macro suivante permet de calculer l’axe de similitude de trois cercles.
+\begin{colourband}
+\macro|AxeDeSimilitude(«a»,«b»,«c»)|\return{\typeGDD{droite}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{cercle}
+ \item[\meta{b}:] \typeGDD{cercle}
+ \item[\meta{c}:] \typeGDD{cercle}
+\end{description}\index{AxeDeSimilitude@\lstinline+AxeDeSimilitude+}
+\end{colourband}
+\bigskip
+
+\subsection{Le type \typeGDD{ellipse}}
+\subsubsection{Contructeurs}
+
+Les ellipses peuvent être définies de plusieurs façons. Tout d’abord, on peut la
+définir avec son centre, un des points de l’ellipse sur le grand axe (appelé
+vertex), et un des points de l’ellipse sur le petit axe (appelé co-vertex).
+Cependant, lors de la création d’une ellipse de nombreux attribus sont calculés.
+
+Le code du contructeur est le suivant:
+\begin{mpcode}
+vardef Ellipse(expr C,A,B) =
+ % C : centre
+ % A : vertex
+ % B : co-vertex
+ save n,a,b,c,e,_tmp,slope;
+ pair _tmp;
+ n = incr gddO;
+ gddT[n] = "ellipse"; gddA[n] = PointImp(C); gddB[n] = PointImp(A);
+ gddC[n] = PointImp(B);
+ % calcul des deux foyers
+ a = Longueur(C,A);
+ b = Longueur(C,B);
+ c = sqrt(a**2-b**2);
+ e = c/a;
+ _tmp = e*(Pt(A)-Pt(C));
+ % les foyers
+ gddD[n] = PairTOPoint(Pt(C)+_tmp);
+ gddE[n] = PairTOPoint(Pt(C)-_tmp);
+ gddX[n][1] = a;
+ gddX[n][2] = b;
+ gddX[n][3] = e;
+ % angle du demi grand axe
+ slope = angle(PairImp(A)-PairImp(C));
+ gddX[n][4] = slope;
+ n
+enddef;
+\end{mpcode}
+
+\begin{colourband}
+\macro|Ellipse(«c»,«a»,«b»)|\return{\typeGDD{ellipse}}
+\begin{description}
+ \item[\meta{c}:] \typeGDD{point} ou \typeMP{pair}, le centre
+ \item[\meta{a}:] \typeGDD{point} ou \typeMP{pair}, le vertex
+ \item[\meta{b}:] \typeGDD{point} ou \typeMP{pair}, le co-vertex
+\end{description}\index{Ellipse@\lstinline+Ellipse+}
+\end{colourband}
+\bigskip
+
+Cette macro s’utilise comme le montre l’exemple suivant.
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+C = Point(0,0);
+A = Point(3,1);
+B = Rotation((1.5,0.5),Pi/2);
+E = Ellipse(C,A,B);
+trace E;
+pointe A; pointe B; pointe C;
+endfig;
+\end{ExempleMP}
+
+On pourra définir une ellipse avec la donnée de ses deux foyers et du demi
+grand-axe avec la commande suivante:
+\begin{colourband}
+\macro|EllipseF(«A»,«B»,«a»)|\return{\typeGDD{ellipse}}
+\begin{description}
+ \item[\meta{A}:] \typeGDD{point} ou \typeMP{pair}, premier foyer
+ \item[\meta{B}:] \typeGDD{point} ou \typeMP{pair}, deuxième foyer
+ \item[\meta{a}:] \typeGDD{numeric}, le demi grand-axe
+\end{description}\index{EllipseF@\lstinline+EllipseF+}
+\end{colourband}
+\bigskip
+
+
+Cette macro s’utilise comme le montre l’exemple suivant.
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+F1 = Point(3,1);
+F2 = Point(1.5,0.5);
+E = EllipseF(F1,F2,1.7);
+trace E;
+pointe F1; pointe F2;
+endfig;
+\end{ExempleMP}
+
+\subsubsection{Macros associées}
+
+On pourra obtenir le centre (\typeGDD{point}) d’un cercle avec la commande :
+\begin{colourband}
+ \macro|Centre(«a»)|\return{\typeGDD{point}}
+ \begin{description}
+ \item[\meta{a}:] \typeGDD{cercle}, \typeGDD{ellipse} ou \typeGDD{hyperbole}
+ \end{description}\index{Centre@\lstinline+Centre+}
+\end{colourband}
+
+On obtient le vertex et le co-vertex avec les commandes suivantes:
+\begin{colourband}
+\macro|Vertex(«a»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}
+\end{description}\index{Vertex@\lstinline+Vertex+}
+\end{colourband}
+\bigskip
+
+\begin{colourband}
+\macro|CoVertex(«a»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}
+\end{description}\index{CoVertex@\lstinline+CoVertex+}
+\end{colourband}
+\bigskip
+
+La commande suivante permet d’obtenir les deux foyer suivant l’entier passé en
+argument.
+\begin{colourband}
+\macro|Foyer(«a»,«n»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}
+ \item[\meta{n}:] \typeMP{numeric}, entier qui vaut 1 ou 2 pour obtenir chaque
+ foyer
+\end{description}\index{Foyer@\lstinline+Foyer+}
+\end{colourband}
+\bigskip
+
+On peut obtenir le demi grand-axe et le demi petit-axe avec les commandes
+suivantes.
+\begin{colourband}
+\macro|DemiGrandAxe(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}
+\end{description}\index{DemiGrandAxe@\lstinline+DemiGrandAxe+}
+\end{colourband}
+\bigskip
+
+
+\begin{colourband}
+\macro|DemiPetitAxe(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}
+\end{description}\index{DemiPetitAxe@\lstinline+DemiPetitAxe+}
+\end{colourband}
+\bigskip
+
+On obtient l’excentricité, souvent notée $e$, avec la commande suivante.
+
+\begin{colourband}
+\macro|Excentricite(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}, \typeGDD{parabole} ou \typeGDD{hyperbole}
+\end{description}\index{Excentricite@\lstinline+Excentricite+}
+\end{colourband}
+\bigskip
+
+Pour obtenir l’inclinaison (coefficient directeur de la droite passant par les
+foyers de l’ellipse), on utilisera la commande suivante.
+
+\begin{colourband}
+\macro|Inclinaison(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}, \typeGDD{parabole} ou \typeGDD{hyperbole}
+\end{description}\index{Inclinaison@\lstinline+Inclinaison+}
+\end{colourband}
+\bigskip
+
+Pour obtenir la tangente (\typeGDD{droite}) à un point de l’ellipse, on
+utilisera la commande suivante.
+
+\begin{colourband}
+\macro|TangenteEllipse(«e»,«p»)|\return{\typeGDD{droite}}
+\begin{description}
+ \item[\meta{e}:] \typeGDD{ellipse}
+ \item[\meta{p}:] \typeGDD{point} ou \typeGDD{pair}
+\end{description}\index{TangenteEllipse@\lstinline+TangenteEllipse+}
+\end{colourband}
+\bigskip
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+F1 = Point(3,1);
+F2 = Point(1.5,0.5);
+E := EllipseF(F1,F2,2.4);
+pointe F1; pointe F2;
+trace E;
+M' := PointDe(E,0.5);
+D := TangenteEllipse(E,M');
+trace D;
+pointe M';
+pointe Foyer(E,1);
+pointe Foyer(E,2);
+Fenetre(-0.2,-2.5,6,4);
+endfig;
+\end{ExempleMP}
+
+
+Pour obtenir les tangentes (\typeGDD{droite}) passant par un point extérieur à
+l’ellipse, on utilisera la commande suivante. Si le point choisi n’est pas
+extérieur à l’ellipse, alors il y aura une erreur de compilation.
+
+\begin{colourband}
+\macro|TangenteExterieureEllipse(«e»,«p»,«n»)|\return{\typeGDD{droite}}
+\begin{description}
+ \item[\meta{e}:] \typeGDD{ellipse}
+ \item[\meta{p}:] \typeGDD{point} ou \typeGDD{pair}
+ \item[\meta{n}:] \typeMP{numeric} qui vaut 1 ou 2 pour choisir la tangente
+ parmi les deux possibles
+\end{description}\index{TangenteExterieureEllipse@\lstinline+TangenteExterieureEllipse+}
+\end{colourband}
+\bigskip
+
+Les points de tangence sont accessibles comme deuxième point de la définition de
+la \typeGDD{droite} grâce à la table \variableGDD{gddB[]}.
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+F1 = Point(3,1);
+F2 = Point(1.5,0.5);
+E := EllipseF(F1,F2,2.4);
+pointe F1; pointe F2;
+trace E;
+M := Point(4,3);
+D1 := TangenteExterieureEllipse(E,M,1);
+trace D1;
+pointe gddB[D1];
+D2 := TangenteExterieureEllipse(E,M,2);
+trace D2;
+pointe gddB[D2];
+pointe M;
+pointe Foyer(E,1);
+pointe Foyer(E,2);
+Fenetre(-0.2,-2.5,6,4);
+endfig;
+\end{ExempleMP}
+
+\subsection{Le type \typeGDD{parabole}}
+
+Le constructeur de base de la parabole défini cette objet à partir du foyer et
+de la directrice.
+
+Le code du contructeur est le suivant:
+\begin{mpcode}
+vardef ParaboleFD(expr F,D) =
+ % F : foyer (point)
+ % D : directrice (droite)
+ save u, v, w, d, i, n,_tmp,slope;
+ pair _tmp;
+ n = incr gddO;
+ (u,v,w) = EquationDroite(D);
+ % ordonnée relative
+ d := u * gddA[F] + v * gddB[F] + w;
+ gddT[n] := "parabole";
+ gddX[n][1] := D; % on stock la directrice
+ gddX[n][2] := D; % on stock la directrice (compatibilité avec hyperbole)
+ % sommet
+ _tmp := (((-d/2)*(u,v)) shifted PairImp(F));
+ gddB[n] = PointImp(_tmp);
+ gddC[n] = PointImp(_tmp);
+ % le foyer (doublé pour compatibilité)
+ gddD[n] := F;
+ gddE[n] := F;
+ gddX[n][3] := 1.0; % excentricité
+ % angle du demi grand axe
+ slope = angle(PairImp(gddA[D])-PairImp(gddB[D]))+90;
+ gddX[n][4] = slope;
+ i := -gddC2Dparam-1;
+ gddP[n] := (
+ ((i*(v,-u)+((i*i-d*d)/(2d))*(u,v))
+ for i:= -gddC2Dparam upto gddC2Dparam:
+ ..(i*(v,-u)+((i*i-d*d)/(2d))*(u,v))
+ endfor)) shifted PairImp(F);
+ n
+enddef;
+\end{mpcode}
+
+\begin{colourband}
+ \macro|ParaboleFD(«f»,«d»)|\return{\typeGDD{chemin}}
+ \begin{description}
+ \item[\meta{f}:] est le foyer (\typeGDD{point}) de la parabole;
+ \item[\meta{d}:] est la directrice (\typeGDD{droite}) de la parabole.
+ \end{description}
+ \index{ParaboleFD@\lstinline+ParaboleFD+}
+\end{colourband}
+
+Lors de la représentation d’une parabole, le caractère \emph{infini} est géré
+par la variable globale \lstinline+gddC2Dparam+ qui vaut 15 par défaut.
+
+\subsubsection{Fonctions associées}
+
+
+On obtient l’excentricité, souvent notée $e$, avec la commande suivante.
+
+\begin{colourband}
+\macro|Excentricite(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}, \typeGDD{parabole} ou \typeGDD{hyperbole}
+\end{description}\index{Excentricite@\lstinline+Excentricite+}
+\end{colourband}
+\bigskip
+
+
+Pour obtenir l’inclinaison (coefficient directeur de la droite axe de symétrie
+de la parabole), on utilisera la commande suivante:
+
+\begin{colourband}
+\macro|Inclinaison(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}, \typeGDD{parabole} ou \typeGDD{hyperbole}
+\end{description}\index{Inclinaison@\lstinline+Inclinaison+}
+\end{colourband}
+\bigskip
+
+On peut obtenir le sommet de la parabole avec la commande suivante:
+
+\begin{colourband}
+\macro|Sommet(«a»,«n»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{parabole} ou \typeGDD{hyperbole}
+ \item[\meta{n}:] 1 ou 2 (\typeMP{numeric}), argument utile pour l’hyperbole
+ qui possède deux sommets. Ici, peut importe la valeur de \meta{n}, l’unique
+ sommet sera donné.
+\end{description}\index{Sommet@\lstinline+Sommet+}
+\end{colourband}
+\bigskip
+
+On peut obtenir la directrice de la parabole avec la commande suivante:
+
+\begin{colourband}
+\macro|Directrice(«a»,«n»)|\return{\typeGDD{droite}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{parabole} ou \typeGDD{hyperbole}
+ \item[\meta{n}:] 1 ou 2 (\typeMP{numeric}), argument utile pour l’hyperbole
+ qui possède deux directrices. Ici, peut importe la valeur de \meta{n},
+ l’unique directrice sera donnée.
+\end{description}\index{Directrice@\lstinline+Directrice+}
+\end{colourband}
+\bigskip
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(0,0);
+B = Point(3,2);
+AB = Droite(A,B);
+F = Point(-1,1);
+Para = ParaboleFD(F,AB);
+trace AB;
+trace Para;
+pointe Sommet(Para,1);
+pointe F;
+Fenetre(-4,-5,2,5);
+endfig;
+\end{ExempleMP}
+
+
+\subsection{Le type \typeGDD{hyperbole}}
+
+Le constructeur de base de la parabole défini cette objet à partir du foyer et
+de la directrice.
+
+Le code du contructeur est le suivant:
+\begin{mpcode}
+vardef HyperboleFD(expr F,D,e) =
+ % F : foyer (point)
+ % D : directrice (droite)
+ % e : exentricité (numeric)
+ % pm : +1 ou -1 pour les deux branches
+ save u, v, w, d, i, n,_tmp,slope,aa,bb;
+ pair _tmp;
+ n = incr gddO;
+
+ (u,v,w) = EquationDroite(D);
+ d := u * gddA[F] + v * gddB[F] + w;
+ gddT[n] := "hyperbole";
+
+ % sommets
+ _tmp := -(d+1*sqrt(e*e*d*d))/(e*e-1)*(u,v)shifted (ProduitScalaire(F,Vecteur(v,-u))*(v,-u));
+ gddB[n] := PointImp(_tmp);
+ _tmp := -(d-1*sqrt(e*e*d*d))/(e*e-1)*(u,v)shifted
+ (ProduitScalaire(F,Vecteur(v,-u))*(v,-u));
+ gddC[n] := PointImp(_tmp);
+ % centre comme milieu des deux sommets
+ gddA[n] = Milieu(gddB[n],gddC[n]);
+ % le foyer (doublé pour compatibilité)
+ gddD[n] := F;
+ gddE[n] := RotationCentre(F, gddA[n], Pi);
+ gddX[n][3] := e; % excentricité
+ % directrices
+ gddX[n][1] := D; % on stock la directrice
+ gddX[n][2] := Droite(RotationCentre(gddA[D], gddA[n], Pi),RotationCentre(gddB[D], gddA[n], Pi));
+ % angle de l’axe
+ slope = angle(PairImp(gddA[D])-PairImp(gddB[D]))+90;
+ gddX[n][4] = slope;
+ % cercle principale
+ gddX[n][5] = CercleD(gddB[n],gddC[n]);
+ % asymptotes
+ aa = IntersectionDroiteCercle(D,gddX[n][5],1);
+ bb = IntersectionDroiteCercle(D,gddX[n][5],2);
+ gddX[n][6] = Droite(gddA[n],aa);
+ gddX[n][7] = Droite(gddA[n],bb);
+ % tracés des moitiées
+ i := -gddC2Dparam-1;
+ gddPX[n][1] := (
+ (
+ (i*(v,-u)-(d+sqrt(e*e*d*d+i*i*(e*e-1)))/(e*e-1)*(u,v))
+ for i:= -gddC2Dparam upto gddC2Dparam:
+ ..(i*(v,-u)-(d+sqrt(e*e*d*d+i*i*(e*e-1)))/(e*e-1)*(u,v))
+ endfor
+ ) shifted (ProduitScalaire(F,Vecteur(v,-u))*(v,-u))
+ );
+ gddPX[n][2] := (
+ (
+ (i*(v,-u)-(d-sqrt(e*e*d*d+i*i*(e*e-1)))/(e*e-1)*(u,v))
+ for i:= -gddC2Dparam upto gddC2Dparam:
+ ..(i*(v,-u)-(d-sqrt(e*e*d*d+i*i*(e*e-1)))/(e*e-1)*(u,v))
+ endfor
+ ) shifted (ProduitScalaire(F,Vecteur(v,-u))*(v,-u))
+ );
+ n
+enddef;
+\end{mpcode}
+
+On peut voir dans ce constructeur l’utilisation de la table de \typeMP{path}
+étendu \variableGDD{gddPX[][]} qui permet d’associer plusieurs \typeMP{path}s à
+un seul objet.
+
+\begin{colourband}
+ \macro|HyperboleFD(«f»,«d»,«e»)|\return{\typeGDD{chemin}}
+ \begin{description}
+ \item[\meta{f}:] est le foyer (\typeGDD{point}) de la parabole;
+ \item[\meta{d}:] est la directrice (\typeGDD{droite}) de la parabole;
+ \item[\meta{e}:] est l’excentricité de l’hyperbole.
+ \end{description}
+ \index{HyperboleFD@\lstinline+HyperboleFD+}
+\end{colourband}
+
+\subsubsection{Fonctions associées}
+
+On pourra obtenir le centre (\typeGDD{point}) d’un cercle avec la commande :
+\begin{colourband}
+ \macro|Centre(«a»)|\return{\typeGDD{point}}
+ \begin{description}
+ \item[\meta{a}:] \typeGDD{cercle}, \typeGDD{ellipse} ou \typeGDD{hyperbole}
+ \end{description}\index{Centre@\lstinline+Centre+}
+\end{colourband}
+
+
+On obtient l’excentricité, souvent notée $e$, avec la commande suivante.
+
+\begin{colourband}
+\macro|Excentricite(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}, \typeGDD{parabole} ou \typeGDD{hyperbole}
+\end{description}\index{Excentricite@\lstinline+Excentricite+}
+\end{colourband}
+\bigskip
+
+
+Pour obtenir l’inclinaison (coefficient directeur de la droite passant par les
+foyers de l’hyperbole), on utilisera la commande suivante.
+
+\begin{colourband}
+\macro|Inclinaison(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{ellipse}, \typeGDD{parabole} ou \typeGDD{hyperbole}
+\end{description}\index{Inclinaison@\lstinline+Inclinaison+}
+\end{colourband}
+\bigskip
+
+On peut obtenir les sommets de l’hyperbole avec la commande suivante:
+
+\begin{colourband}
+\macro|Sommet(«a»,«n»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{parabole} ou \typeGDD{hyperbole}
+ \item[\meta{n}:] 1 ou 2 (\typeMP{numeric}), pour choisir l’un des deux sommets.
+\end{description}\index{Sommet@\lstinline+Sommet+}
+\end{colourband}
+\bigskip
+
+On peut obtenir les directrices de l’hyperbole avec la commande suivante:
+
+\begin{colourband}
+\macro|Directrice(«a»,«n»)|\return{\typeGDD{droite}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{parabole} ou \typeGDD{hyperbole}
+ \item[\meta{n}:] 1 ou 2 (\typeMP{numeric}), pour choisir l’une des deux
+ directrices.
+\end{description}\index{Directrice@\lstinline+Directrice+}
+\end{colourband}
+\bigskip
+
+Pour obtenir le \emph{cercle principal} de l’hyperbole, on pourra utiliser la
+commande suivante:
+
+
+\begin{colourband}
+ \macro|CerclePrincipale(«h»)|\return{\typeGDD{cercle}}
+ \begin{description}
+ \item[\meta{h}:] \typeGDD{hyperbole}
+ \end{description}\index{CerclePrincipale@\lstinline+CerclePrincipale+}
+\end{colourband}
+\bigskip
+
+On pourra aussi obtenir les deux asymptotes de l’hyperbole avec le commande
+suivante:
+
+\begin{colourband}
+ \macro|AsymptoteHyperbole(«h»,«n»)|\return{\typeGDD{droite}}
+ \begin{description}
+ \item[\meta{h}:] \typeGDD{hyperbole}
+ \item[\meta{n}:] 1 ou 2 (\typeMP{numeric}), pour choisir l’une des deux
+ asymptotes.
+ \end{description}\index{AsymptoteHyperbole@\lstinline+AsymptoteHyperbole+}
+\end{colourband}
+\bigskip
+
+Parce que une hyperbole est constituée de deux parties disjointes, on ne peut
+pas, comme pour les autres objets \mpgeomdd, utiliser directement la command
+\lstinline+trace+ directement sur l’objet. Il faudra utiliser la commande
+suivante pour obtenir le \typeMP{path} associé à une des deux parties de
+l’hyperbole.
+
+\begin{colourband}
+ \macro|DemieHyperbole(«h»,«n»)|\return{\typeGDD{path}}
+ \begin{description}
+ \item[\meta{h}:] \typeGDD{hyperbole}
+ \item[\meta{n}:] 1 ou 2 (\typeMP{numeric}), pour choisir l’une des deux
+ parties.
+ \end{description}\index{DemieHyperbole@\lstinline+DemieHyperbole+}
+\end{colourband}
+\bigskip
+
+
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(0,0);
+B = Point(3,2);
+AB = Droite(A,B);
+F = Point(-1,1);
+Hyper = HyperboleFD(F,AB,1.5);
+trace AB;
+trace DemieHyperbole(Hyper,1);
+trace DemieHyperbole(Hyper,2);
+trace Directrice(Hyper,2);
+trace CerclePrincipale(Hyper) dashed evenly;
+trace AsymptoteHyperbole(Hyper,1) dashed evenly;
+trace AsymptoteHyperbole(Hyper,2) dashed evenly;
+pointe Centre(Hyper);
+pointe Foyer(Hyper,1);
+pointe Foyer(Hyper,2);
+pointe Sommet(Hyper,1);
+pointe Sommet(Hyper,2);
+Fenetre(-3,-5,3,5);
+endfig;
+\end{ExempleMP}
+
+
+\subsection{Le type \typeGDD{triangle}}
+
+Les triangles sont définis par trois
+points de $\R^2$.
+
+\subsubsection{Constructeur}
+La fonction créatrice de cet objet est la suivante
+\begin{mpcode}
+vardef Triangle (expr a,b,c) =
+ save n; n = incr gddO; gddT[n] = "triangle";
+ gddA[n] = PointImp(a); gddB[n] = PointImp(b); gddC[n] = PointImp(c); n
+enddef;
+\end{mpcode}
+
+\begin{colourband}
+\macro|Triangle(«a»,«b»,«c»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{point}
+ \item[\meta{b}:] \typeGDD{point}
+ \item[\meta{c}:] \typeGDD{point}
+\end{description}\index{Triangle@\lstinline+Triangle+}
+\end{colourband}
+
+
+\bigskip
+
+Ici, on voit l’appel à la troisième table \variableGDD{gddC} pour stocker le
+troisième point.
+
+Un triangle se définit alors comme ceci:
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(3,1);
+B = Point(1,3);
+C = Point(0,0);
+ABC = Triangle(A,B,C);
+trace ABC;
+endfig;
+\end{ExempleMP}
+
+\subsubsection{Macros associées}
+
+La macro suivante permet de calculer l’aire d’un triangle.
+\begin{colourband}
+\macro|AireTriangle(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{triangle}
+\end{description}\index{AireTriangle@\lstinline+AireTriangle+}
+\end{colourband}
+
+On peut calculer aussi l’orthocentre d’un triangle avec la commande suivante.
+\begin{colourband}
+\macro|Orthocentre(«a»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{triangle}
+\end{description}\index{Orthocentre@\lstinline+Orthocentre+}
+\end{colourband}
+
+La macro suivante calcul le cercle inscrit d’un triangle.
+\begin{colourband}
+\macro|CercleInscrit(«a»)|\return{\typeGDD{cercle}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{triangle}
+\end{description}\index{CercleInscrit@\lstinline+CercleInscrit+}
+\end{colourband}
+
+On peut aussi obtenir le cercle circonscrit avec la macro suivante.
+\begin{colourband}
+\macro|CercleCirconscrit(«a»)|\return{\typeGDD{cercle}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{triangle}
+\end{description}\index{CercleCirconscrit@\lstinline+CercleCirconscrit+}
+\end{colourband}
+
+On peut aussi calculer les cercles exinscrits. Soit $A$, $B$ et $C$ trois points
+définissant un triangle $ABC$\footnote{Évidemment, les points peuvent s’appeler
+autrement.}. La commande suivante permet d’obtenir, au choix, un des trois
+cercles exinscrits.
+\begin{colourband}
+\macro|CercleExinscrit(«a»,«n»)|\return{\typeGDD{cercle}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{triangle}
+ \item[\meta{n}:] \typeMP{numeric} qui vaut 1, 2 ou 3. Si \meta{n}$=1$, c’est
+ le cercle exinscrit tangent au côté $[BC]$ du triangle, si \meta{n}$=2$, c’est
+ celui tangent au côté $[AC]$ et si \meta{n}$=1$, c’est celui tangent au côté $[AB]$.
+\end{description}\index{CercleExinscrit@\lstinline+CercleExinscrit+}
+\end{colourband}
+
+On peut aussi obtenir le cercle d’Euler d’un triangle avec la commande suivante.
+\begin{colourband}
+\macro|CercleEuler(«a»)|\return{\typeGDD{cercle}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{triangle}
+\end{description}\index{CercleEuler@\lstinline+CercleEuler+}
+\end{colourband}
+
+Voici un exemple d’illustration des quelques unes des macros relatives aux
+triangles.
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(3,1);
+B = Point(1,3);
+C = Point(0,0);
+AB = Droite(A,B);
+BC = Droite(B,C);
+ABC = Triangle(A,B,C);
+trace AB dashed evenly;
+trace BC dashed evenly;
+trace ABC avecCrayon(1.5,black);
+Euler = CercleEuler(ABC);
+trace Euler avecCrayon(1,DarkRed);
+C_E1 = CercleExinscrit(ABC,2);
+trace C_E1 avecCrayon(1,LightBlue);
+C_C = CercleCirconscrit(ABC);
+trace C_C avecCrayon(1,LightCoral);
+Fenetre(-1,-4,4,4);
+endfig;
+\end{ExempleMP}
+
+\subsection{Le type \typeGDD{polygone}}
+Les triangles sont définis par $N$
+points de $\R^2$.
+
+\subsubsection{Constructeurs}
+
+La fonction créatrice de cet objet est la suivante
+\begin{mpcode}
+vardef Polygone (text plist) =
+ save n,_point,i; n = incr gddO; gddT[n] = "polygone";
+ i:=1;
+ for _point = plist:
+ gddX[gddO][i] = PointImp(_point);
+ i:=i+1;
+ endfor
+ gddA[n] = i-1; % nombre de côté
+ gddB[n] = IsoBarycentre(plist); % centre
+ n
+enddef;
+\end{mpcode}
+
+\begin{colourband}
+\macro|Polygone(«liste»)|\return{\typeGDD{polygone}}
+\begin{description}
+ \item[\meta{liste}:] est une liste de \typeGDD{point} ou de \typeMP{pair}
+\end{description}\index{Polygone@\lstinline+Polygone+}
+\end{colourband}
+
+
+\bigskip
+
+Ici, on voit l’appel à la \emph{double} table \variableGDD{gddX} pour stocker
+les $N$ points.
+
+Un polygone se définit alors comme ceci:
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(2,0);
+B = Point(3,1);
+C = Point(0,2);
+D = Point(0,0);
+P = Polygone(A,B,C,D);
+trace P;
+endfig;
+\end{ExempleMP}
+
+On pourra aussi construire des polygones réguliers avec la commande suivante.
+\begin{colourband}
+\macro|PolygoneRegulier(«N»,«rayon»,«rotation»,«translation»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{N}:] entier (\typeMP{numeric}) indiquant le nombre de points ;
+ \item[\meta{rayon}:] \typeMP{numeric}, rayon du cercle circonscrit ;
+ \item[\meta{rotation}:] \typeMP{numeric}, rotation du polygone ;
+ \item[\meta{translation}:] \typeGDD(point) ou \typeGDD{vecteur} (ou même
+ \typeMP{pair}), déplacement du centre du polygone.
+\end{description}\index{PolygoneRegulier@\lstinline+PolygoneRegulier+}
+\end{colourband}
+
+\begin{ExempleMP}
+ input geom2d;
+ beginfig(1);
+ P = PolygoneRegulier(7,3,0,origine);
+ trace P;
+ endfig;
+ \end{ExempleMP}
+
+\subsubsection{Macros associées}
+
+On pourra obtenir le nombre de côté d’un polygone avec la commande suivante.
+
+\begin{colourband}
+\macro|NombreCotesPolygone(«a»)|\return{\typeMP{numeric}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{polygone}
+\end{description}\index{NombreCotesPolygone@\lstinline+NombreCotesPolygone+}
+\end{colourband}
+\bigskip
+
+On pourra avoir accès aux différents sommets du polygone, numérotés à partir de
+1, avec la macro suivante.
+
+\begin{colourband}
+\macro|PointPolygone(«a»,«i»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{a}:] \typeGDD{polygone}
+ \item[\meta{i}:] \typeMP{numeric}, entier plus grand que 1, permettant
+ d’accéder au $i$\ieme{} point du polygone
+\end{description}\index{PointPolygone@\lstinline+PointPolygone+}
+\end{colourband}
+ \bigskip
+
+\subsection{Le type \typeGDD{chemin}} Pour ce type particulier, \mpgeomdd stocke
+le \typeMP{path} dans la table \variableGDD{gddP} réservée. Ainsi la fonction
+créatrice de ce type d’objet est la suivante
+\begin{mpcode}
+vardef Chemin (expr p) =
+gddT[incr gddO] = "chemin"; gddP[gddO] = p; gddO
+enddef;
+\end{mpcode}
+\begin{colourband}
+\macro|Chemin(«p»)|\return{\typeGDD{chemin}}
+\begin{description}
+ \item[\meta{p}:] un \typeMP{path} de \MP
+\end{description}\index{Chemin@\lstinline+Chemin+}
+\end{colourband}
+
+
+\subsubsection{Macros associées}
+
+La macro suivante contruit, à partir d’une liste de \typeGDD{point}s, une ligne
+brisée de type \typeGDD{chemin}.
+
+\begin{colourband}
+ \macro|LigneBrisee(«liste»)|\return{\typeGDD{chemin}}
+ \begin{description}
+ \item[\meta{liste}:] est une liste de \typeGDD{point} ou de \typeMP{pair}
+ \end{description}\index{LigneBrisee@\lstinline+LigneBrisee+}
+\end{colourband}
+
+
+\subsection{Le type \typeGDD{courbe}}
+
+Pour ce type particulier, \mpgeomdd stocke
+une chaine de caractère (un nom de fichier à exploiter avec l’extension
+\fichier{graph.mp}) dans la table \variableGDD{gddS} réservée.
+
+\subsubsection{Constructeur}
+
+Ainsi la fonction
+créatrice de ce type d’objet est la suivante
+\begin{mpcode}
+vardef CourbeDat (expr s) =
+ gddT[incr gddO] = "courbe"; gddS[gddO] = s; gddO
+enddef;
+\end{mpcode}
+\begin{colourband}
+\macro|CourbeDat(«s»)|\return{\typeGDD{courbe}}
+\begin{description}
+ \item[\meta{s}:] un nom de fichier sous forme de \typeMP{string} de \MP
+\end{description}\index{CourbeDat@\lstinline+CourbeDat+}
+\end{colourband}
+
+\bigskip
+
+\section{Arc de cercle}
+
+Avec \mpgeomdd{}, quelques commandes permettent de travailler avec les arcs de
+cercle. Tout d’abord, on peut décider de ne représenter qu’un arc de cercle d’un
+\typeGDD{cercle} précédemment défini. Ceci se fait avec la commande suivante qui
+prend en argument un \typeGDD{cercle} et deux angles en radian, et retourne un
+\typeMP{path} de \MP{} correspondant à l’arc de cercle compris entre les deux
+angles donnés (l’angle 0 étant parallèle à l’axe $Ox$).
+
+\begin{colourband}
+\macro|gddTraceArcDeCercle(«C»,«a»,«b»)|\return{\typeMP{path}}
+\begin{description}
+ \item[\meta{C}:] \typeGDD{cercle} dont on souhaite représenter un arc.
+ \item[\meta{a}:] premier angle en radian (\typeMP{numeric}).
+ \item[\meta{b}:] deuxième angle en radian (\typeMP{numeric}).
+\end{description}\index{gddTraceArcDeCercle@\lstinline+gddTraceArcDeCercle+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+C = Cercle(origine,2);
+trace C;
+trace gddTraceArcDeCercle(C,Pi/3,Pi) avecCrayon(2,DarkRed);
+endfig;
+\end{ExempleMP}
+
+On peut aussi définir un objet \typeGDD{chemin}. Pour cela on pourra utiliser
+les deux commandes suivantes. La première permet de définir un arc de cercle à
+partir d’un point, d’un rayon et de deux angles.
+
+\begin{colourband}
+\macro|Arc(«P»,«r»,«a»,«b»)|\return{\typeGDD{chemin}}
+\begin{description}
+ \item[\meta{P}:] \typeGDD{point} ou \typeMP{pair} centre de l’arc de cercle.
+ \item[\meta{r}:] rayon de l’arc de cercle (\typeMP{numeric}).
+ \item[\meta{a}:] premier angle en radian (\typeMP{numeric}).
+ \item[\meta{b}:] premier angle en radian (\typeMP{numeric}).
+\end{description}\index{Arc@\lstinline+Arc+}
+\end{colourband}
+
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(2,2);
+Ac = Arc(A,2,Pi/3,Pi);
+pointe A;
+trace Ac;
+endfig;
+\end{ExempleMP}
+
+La deuxième commande définissant un \typeGDD{chemin} est la suivante. Elle prend
+comme arguments trois points, notons les $C$, $A$ et $B$ : le centre de l’arc de
+cercle $C$, et les points $A$ et $B$. Elle prend ensuite comme argument le rayon
+de l’arc défini entre les segments $[C,A]$ et $[C,B]$.
+
+\begin{colourband}
+\macro|ArcEntrePoints(«P»,«r»,«A»,«B»,«s»)|\return{\typeGDD{chemin}}
+\begin{description}
+ \item[\meta{P}:] \typeGDD{point} ou \typeMP{pair} centre de l’arc de cercle.
+ \item[\meta{r}:] rayon de l’arc de cercle (\typeMP{numeric}).
+ \item[\meta{A}:] premier \typeGDD{point} ou \typeMP{pair}.
+ \item[\meta{B}:] deuxième \typeGDD{point} ou \typeMP{pair}.
+ \item[\meta{s}:] \typeMP{numeric}, $-1$ ou $1$ suivant le sens choisi.
+\end{description}\index{Arc@\lstinline+Arc+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+C = Point(0,0);
+A = Point(2,2);
+B = Point(0,3);
+Cab = ArcEntrePoints(C,1,A,B,1);
+Cba = ArcEntrePoints(C,1,A,B,-1);
+trace Segment(C,A);
+trace Segment(C,B);
+pointe A; pointe B; pointe C;
+fleche Cab;
+fleche Cba avecCrayon(1,DarkRed);
+endfig;
+\end{ExempleMP}
+
+
+\section{Quelques transformations}
+
+\subsection{Homothétie}
+
+On peut réaliser une homothétie sur n’importe quel objet \mpgeomdd avec la commande
+suivante.
+
+\begin{colourband}
+\macro|Homothetie(«p»,«o»,«k»)|\return{du même type que \meta{p}}
+\begin{description}
+ \item[\meta{p}:] un objet \mpgeomdd.
+ \item[\meta{o}:] \typeGDD{point} ou \typeMP{pair}, centre de l’homothétie.
+ \item[\meta{k}:] \typeMP{numeric}, facteur de l’homothétie.
+\end{description}\index{Homothetie@\lstinline+Homothetie+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,2);
+B = Point(0,2);
+C_B = Cercle(B,1);
+T = Triangle((1,1),(0,0),(0,1));
+C_H = Homothetie(C_B, A, 2);
+T_H = Homothetie(T, A ,-1);
+trace C_B; trace C_H;
+trace T; trace T_H;
+pointe A; pointe B;
+endfig;
+\end{ExempleMP}
+
+\subsection{Symétrie axiale}
+
+On peut réaliser une symétrie axiale sur n’importe quel objet \mpgeomdd avec la
+commande suivante.
+
+\begin{colourband}
+\macro|SymetrieAxiale(«p»,«d»)|\return{du même type que \meta{p}}
+\begin{description}
+ \item[\meta{p}:] un objet \mpgeomdd.
+ \item[\meta{d}:] \typeGDD{droite} définissant l’axe de symétrie.
+\end{description}\index{SymetrieAxiale@\lstinline+SymetrieAxiale+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,2);
+B = Point(0,2);
+C_B = Cercle(B,1);
+T = Triangle((1,1),(0,0),(0,1));
+D = Droite((-1,0),(3,-1));
+C_H = SymetrieAxiale(C_B, D);
+T_H = SymetrieAxiale(T, D);
+trace C_B; trace C_H;
+trace T; trace T_H;
+trace D;
+pointe A; pointe B;
+Fenetre(-2.5,-3.5,3,3.2);
+endfig;
+\end{ExempleMP}
+
+\subsection{Symétrie centrale}
+
+On peut réaliser une symétrie centrale sur n’importe quel objet \mpgeomdd avec la
+commande suivante.
+
+\begin{colourband}
+\macro|SymetrieCentrale(«p»,«d»)|\return{du même type que \meta{p}}
+\begin{description}
+ \item[\meta{p}:] un objet \mpgeomdd.
+ \item[\meta{d}:] \typeGDD{point} définissant le centre de symétrie.
+\end{description}\index{SymetrieCentrale@\lstinline+SymetrieCentrale+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,2);
+B = Point(0,2);
+C_B = Cercle(B,1);
+T = Triangle((1,1),(0,0),(0,1));
+D = Point(-1,0);
+C_H = SymetrieCentrale(C_B, D);
+T_H = SymetrieCentrale(T, D);
+trace C_B; trace C_H;
+trace T; trace T_H;
+pointe D;
+pointe A; pointe B;
+Fenetre(-3.5,-3.5,3,3.2);
+endfig;
+\end{ExempleMP}
+
+\subsection{Inversion}
+
+On peut calculer l’inversion d’un point, d’un cercle ou d’une droite par rapport à un cercle avec la macro
+suivante.
+\begin{colourband}
+\macro|Inversion(«p»,«c»)|\return{\typeGDD{point}}
+\begin{description}
+ \item[\meta{p}:] \typeGDD{point}, \typeGDD{cercle} ou \typeGDD{droite}
+ \item[\meta{c}:] \typeGDD{cercle}
+\end{description}\index{Inversion@\lstinline+Inversion+}
+\end{colourband}
+\bigskip
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+ A = Point(2,2);
+ C = Cercle(A,2);
+ trace C;
+ marque.rt "A";
+ B = Point(-0.5,1);
+ D = Inversion(B,C);
+ drawoptions(withcolor DarkRed);
+ marque.rt "B"; marque.rt "D";
+
+ drawoptions(withcolor DarkBlue);
+ E = Point(3,1);
+ CE = Cercle(E,0.5);
+ trace CE;
+ marque.rt "E";
+ iCE = Inversion(CE,C);
+ trace iCE;
+
+
+ drawoptions(withcolor DarkGreen);
+ d = Droite((3,3),(4,2));
+ trace d;
+ Cd = Inversion(d,C);
+ trace Cd;
+ Fenetre(-1,-1,5.5,6);
+endfig;
+\end{ExempleMP}
+
+
+\section{Annotations et labels}
+
+\subsection{Signes}
+
+\mpgeomdd fournit la macro suivante pour marquer un angle droit formé par trois
+points:
+\begin{colourband}
+\macro|SigneOrtho(«a»,«b»,«c»,«x»)|
+\begin{description}
+ \item[\meta{a},\meta{b},\meta{c}:] sont les trois \typeGDD{point}s formant
+ l’angle droit $\widehat{ABC}$.
+ \item[\meta{x}:] est la \og{}taille\fg{} (\typeMP{numeric}) du signe d’orthogonalité.
+\end{description}\index{SigneOrtho@\lstinline+SigneOrtho+}
+\end{colourband}
+
+On peut aussi réaliser des marques entre deux points ou sur un segment, un
+vecteur, ou tout type d’objet. Pour cela, la première macro est la suivante:
+\begin{colourband}
+\macro|Marque(«a»,«b»,«n»)|
+\begin{description}
+ \item[\meta{a}:] premier \typeGDD{point} formant
+ le segment à marquer;
+ \item[\meta{b}:] deuxième \typeGDD{point} formant
+ le segment à marquer;
+ \item[\meta{n}:] est le type (\typeMP{numeric}) de marque, il y en a quatre
+ \meta{n}$=1$, $2$, $3$ ou $4$.
+\end{description}\index{Marque@\lstinline+Marque+}
+\end{colourband}
+
+On peut aussi marquer n’importe quel type de trait avec la macro suivante:
+\begin{colourband}
+\macro|MarqueTrait(«a»,«n»)|
+\begin{description}
+ \item[\meta{a}:] est n’importe quel objet \mpgeomdd ou même un \typeMP{path} \MP;
+ \item[\meta{n}:] est le type (\typeMP{numeric}) de marque, il y en a quatre
+ \meta{n}$=1$, $2$, $3$ ou $4$.
+\end{description}\index{MarqueTrait@\lstinline+MarqueTrait+}
+\end{colourband}
+
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(4,0);
+B = Point(0,0);
+C = Point(0,2);
+trace Segment(B,A);
+trace Segment(B,C);
+marque.bot "A";
+marque.bot "B";
+marque.lft "C";
+trace SigneOrtho(A,B,C,0.5);
+trace Marque(A,B,1);
+trace MarqueTrait(Segment(B,C),3);
+endfig;
+\end{ExempleMP}
+
+
+\subsection{Labels}
+
+Comme le code produit avec \mpgeomdd est un code \MP{}\cite{ctan-metapost}, on peut utiliser les outils
+classiques de labélisation. Cependant, pour permettre plus de flexibilité (et
+notamment une compatibilité avec \hologo{LuaLaTeX} et
+\package{luamplib}~\cite{ctan-luamplib} ou
+\package{minim-mp}~\cite{ctan-minim-mp}), si le code est compilé avec \MP{},
+alors le package~\package{latexmp}~\cite{ctan-latexmp} est chargé et fournit la
+commande \lstinline+textext()+.
+
+De plus, \mpgeomdd fournit quelques commandes pour se faciliter la vie.
+
+On peut marquer les points avec la commande suivante. Cette commande
+\emph{pointe} le point (avec la commande \lstinline+pointe+, voir
+section~\ref{sec:trace}) et inscrit un label.
+\begin{colourband}
+\macro|marque.«place» "«nom»"|
+\begin{description}
+ \item[\meta{place}:] peut être les classiques placement de \MP{} :
+ \lstinline+top+, \lstinline+bot+, \lstinline+rt+,
+ \lstinline+lft+,+\lstinline+urt+, \lstinline+ulft+, \lstinline+lrt+, \lstinline+llft+.
+ \item[\meta{nom}:] entre double quote, doit être un nom de variable de
+ point. Le nom sera composé en mode mathématique (entre \lstinline+$+). Si le
+ nom contient un \lstinline+_+, tout ce qui sera après sera mis en
+ indice (ex. \lstinline+A_be+ deviendra $A_{be}$). Si le nom est
+ \lstinline+alpha+, \lstinline+beta+, \lstinline+gamma+ ou \lstinline+delta+,
+ alors le résultat donnera la lettre grecque composée en mode mathématique.
+\end{description}\index{marque@\lstinline+marque+}
+\end{colourband}
+
+
+\mpgeomdd fournit aussi une adaptation au classique \lstinline+label+ de \MP{}.
+
+\begin{colourband}
+\macro|gddLabel.«place»(«materiel»,«point»)|
+\begin{description}
+ \item[\meta{place}:] peut être les classiques placement de \MP{} :
+ \lstinline+top+, \lstinline+bot+, \lstinline+rt+,
+ \lstinline+lft+,+\lstinline+urt+, \lstinline+ulft+, \lstinline+lrt+, \lstinline+llft+.
+ \item[\meta{materiel}:] classiquement ce qu’on donne à \lstinline+label+, une
+ chaîne de caractères, ou une \typeMP{picture} (qui peut-être produite par
+ exemple avec \lstinline+btex ... etex+ ou, puisque \package{latexmp} est
+ chargé par \mpgeomdd, \lstinline+textext()+).
+ \item[\meta{point}:] doit être un \typeGDD{point} de \mpgeomdd.
+\end{description}\index{gddLabel@\lstinline+gddLabel+}
+\end{colourband}
+
+On peut aussi étiquetter un \typeGDD{chemin}, une \typeGDD{courbe} ou un
+\typeMP{path} avec la macro suivante:
+
+\begin{colourband}
+\macro|EtiquetteChemin.«place»(«materiel»,«chemin»,«position»)|
+\begin{description}
+ \item[\meta{place}:] peut être les classiques placement de \MP{} :
+ \lstinline+top+, \lstinline+bot+, \lstinline+rt+,
+ \lstinline+lft+,+\lstinline+urt+, \lstinline+ulft+, \lstinline+lrt+, \lstinline+llft+.
+ \item[\meta{materiel}:] classiquement ce qu’on donne à \lstinline+label+, une
+ chaîne de caractères, ou une \typeMP{picture} (qui peut-être produite par
+ exemple avec \lstinline+btex ... etex+ ou, puisque \package{latexmp} est
+ chargé par \mpgeomdd, \lstinline+textext()+).
+ \item[\meta{chemin}:] doit être un \typeGDD{chemin}, une \typeGDD{courbe}, ou
+ un \typeMP{path}.
+\end{description}\index{EtiquetteChemin@\lstinline+EtiquetteChemin+}
+\end{colourband}
+
+
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(0,0);
+B_23 = Point(3,3);
+alpha = Point(0,2);
+trace Segment(A,B_23);
+C = Milieu(A,B_23);
+pointe C;
+gddLabel.top(textext("Milieu"),C);
+marque.top "A";
+marque.urt "B_23";
+marque.llft "alpha";
+P = Chemin(Pt(A)..Pt(alpha)..Pt(B_23));
+trace P;
+EtiquetteChemin.top("Test",P,0.6);
+endfig;
+\end{ExempleMP}
+
+
+\section{Repère}
+
+\mpgeomdd fournit un ensemble de commandes permettant de faciliter le dessin de
+repère.
+
+La commande principale est la définition du repère, c’est-à-dire la boîte dans
+laquelle le dessin sera représenté.
+\begin{colourband}
+ \macro|Repere(«l»,«h»,«ox»,«oy»,«ux»,«uy»)|
+ \begin{description}
+ \item[\meta{l}:] \typeMP{numeric}, largeur du repère (en unité \lstinline+gddU+).
+ \item[\meta{h}:] \typeMP{numeric}, hauteur du repère (en unité \lstinline+gddU+).
+ \item[\meta{ox}:] \typeMP{numeric}, distance (en unité \lstinline+gddU+) de
+ l’origine (\typeGDD{point} $(0,0)$) par rapport au bord gauche.
+ \item[\meta{oy}:] \typeMP{numeric}, distance (en unité \lstinline+gddU+) de
+ l’origine (\typeGDD{point} $(0,0)$) par rapport au bord bas.
+ \item[\meta{ux}:] \typeMP{numeric}, unité de l’axe $(Ox)$ (en unité \lstinline+gddU+).
+ \item[\meta{uy}:] \typeMP{numeric}, unité de l’axe $(Oy)$ (en unité \lstinline+gddU+).
+ \end{description}\index{Repere@\lstinline+Repere+}
+\end{colourband}
+
+Ce commande ne retourne, ni ne trace rien. Elle sert à spécifier quelques
+variables internes de définition du dessin. Elle modifie d’ailleurs le
+comportement de la macro \lstinline+gddEnPlace+ (voir
+page~\pageref{gddEnPlace}). Noter que cette commande impose le fait que
+l’origine (c’est-à-dire le \typeGDD{point} $(0,0)$) soit à l’intérieur du
+repère.
+
+Cette macro s’accompagne de deux autres, elles aussi \emph{silencieuses}, ne
+servant qu’à :
+\begin{itemize}
+\item sauvegarder la \typeMP{picture} courante ;
+\item construire une \typeMP{picture} avec le contenu se trouvant entre
+\lstinline+Debut+ et \lstinline+Fin+ ;
+\item rogner (avec \lstinline+clip+) la \typeMP{picture} aux cadre du repère
+construit ;
+\item ajouter la \typeMP{picture} courant à celle sauvegarder ;
+\item enfin rétablir le
+fonctionnement de \lstinline+gddEnPlace+ comme avant l’utilisation de
+\lstinline+Repere+.
+\end{itemize}
+
+Ces deux commandes sont appelées \lstinline+Debut+ et
+\lstinline+Fin+.
+
+\begin{colourband}
+\macro|Debut|
+\index{Debut@\lstinline+Debut+}
+\end{colourband}
+
+
+\begin{colourband}
+\macro|Fin|
+\index{Fin@\lstinline+Fin+}
+\end{colourband}
+
+Ainsi, il est très simple d’illustrer le fait qu’à un changement de base
+orthogonale prêt, un cercle est une ellipse.
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,1);
+CA = Cercle(A,2);
+Repere(5,5,1,1,1,0.5);
+Debut;
+trace CA;
+Fin;
+endfig;
+\end{ExempleMP}
+
+On dispose de deux commandes pour tracer les axes du repère. La première trace
+les axes passant par l’origine.
+\begin{colourband}
+\macro|Axes|\indication{trace un essemble d’éléments sur le repère}
+\index{Axes@\lstinline+Axes+}
+\end{colourband}
+
+Cette commande inscrit aussi les labels des axes des abscisses et des ordonnées
+qui sont stockées dans les variables globales dédiées suivantes:
+\begin{colourband}
+\macro|gddXlabel|\indication{\typeMP{string}, valeur par défaut \lstinline+"$x$"+}
+\index{gddXlabel@\lstinline+gddXlabel+}
+\end{colourband}
+
+\begin{colourband}
+\macro|gddYlabel|\indication{\typeMP{string}, valeur par défaut \lstinline+"$y$"+}
+\index{gddYlabel@\lstinline+gddYlabel+}
+\end{colourband}
+
+Attention, ces commandes doivent s’utiliser avant l’appel à \lstinline+Debut+.
+
+L’exemple suivant permet d’illustrer le tracé des axes.
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,1);
+CA = Cercle(A,2);
+Repere(5,5,1,1,1,1);
+gddYlabel:="$z$";
+Axes;
+Debut;
+trace CA;
+Fin;
+endfig;
+\end{ExempleMP}
+
+On pourra aussi définir un repère en utilisant une syntaxe permettant de
+spécifier les abscisses et les ordonnées extrêmales.
+
+\begin{colourband}
+ \macro|RepereMinMax(«xmin»,«xmax»,«ymin»,«ymax»,«ux»,«uy»)|
+ \begin{description}
+ \item[\meta{xmin}:] \typeMP{numeric}, abscisse minimum (en unité \lstinline+gddU+).
+ \item[\meta{xmax}:] \typeMP{numeric}, abscisse maximum (en unité \lstinline+gddU+).
+ \item[\meta{ymin}:] \typeMP{numeric}, ordonnée minimum (en unité \lstinline+gddU+).
+ \item[\meta{ymax}:] \typeMP{numeric}, ordonnée maximum (en unité \lstinline+gddU+).
+ \item[\meta{ux}:] \typeMP{numeric}, unité de l’axe $(Ox)$ (en unité \lstinline+gddU+).
+ \item[\meta{uy}:] \typeMP{numeric}, unité de l’axe $(Oy)$ (en unité \lstinline+gddU+).
+ \end{description}\index{RepereMinMax@\lstinline+RepereMinMax+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,1);
+CA = Cercle(A,2);
+RepereMinMax(-1,4,-1,4,1,1);
+Axes;
+Debut;
+trace CA;
+Fin;
+endfig;
+\end{ExempleMP}
+
+\mpgeomdd fournit aussi de quoi tracer les axes sur le bord du cadre avec la
+commande suivante.
+\begin{colourband}
+\macro|AxesBords|\indication{trace un essemble d’éléments sur le repère}
+\index{AxesBords@\lstinline+AxesBords+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,1);
+CA = Cercle(A,2);
+RepereMinMax(-1,4,-1,4,1,1);
+AxesBords;
+Debut;
+trace CA;
+Fin;
+endfig;
+\end{ExempleMP}
+
+Les commandes suivantes permettent de graduer les axes (classiques ou sur le
+bord). Là encore, ce sont des commandes qui n’ont pas d’arguments ni ne
+retournent rien et qui tracent.
+
+\begin{colourband}
+\macro|Graduations|\indication{trace un essemble d’éléments sur le repère}
+\index{Graduations@\lstinline+Graduations+}
+\end{colourband}
+
+
+\begin{colourband}
+\macro|GraduationsBords|\indication{trace un essemble d’éléments sur le repère}
+\index{GraduationsBords@\lstinline+GraduationsBords+}
+\end{colourband}
+
+On utilisera la version en cohérence avec les axes choisis.
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,1);
+CA = Cercle(A,2);
+RepereMinMax(-1,4,-1,4,1,1);
+AxesBords;
+GraduationsBords;
+Debut;
+trace CA;
+Fin;
+endfig;
+\end{ExempleMP}
+
+Si on désire marqué les unités, \mpgeomdd{} propose la macro suivante (qui n’est
+utilisable que si l’on ne place pas les axes sur le bords).
+\begin{colourband}
+\macro|Unites(«unité»)|\indication{trace un essemble d’éléments sur le repère}
+\begin{description}
+ \item[\meta{unité}:] \typeMP{numeric}, valeur à inscrire sur les deux axes.
+\end{description}
+\index{Unites@\lstinline+Unites+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,1);
+CA = Cercle(A,2);
+RepereMinMax(-1,4,-1,4,1,1);
+Axes;
+Debut;
+ Graduations;
+ Unites(2);
+ trace CA;
+Fin;
+endfig;
+\end{ExempleMP}
+
+On peut aussi ajouter une grille sur notre repère avec la macro suivante.
+\begin{colourband}
+\macro|GrilleRepere|\indication{trace un essemble d’éléments sur le repère}
+\index{GrilleRepere@\lstinline+GrilleRepere+}
+\end{colourband}
+Dans l’exemple suivant, on règle la couleur de la grille avec la commande
+\hologo{MetaPost} \lstinline+drawoptions+.
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,1);
+CA = Cercle(A,2);
+RepereMinMax(-1,4,-1,4,1,1);
+drawoptions(withcolor LightGrey);
+GrilleRepere;
+drawoptions();
+Axes;
+Debut;
+ Graduations;
+ Unites(1);
+ trace CA;
+Fin;
+endfig;
+\end{ExempleMP}
+On pourra aussi ajouter un cadre au repère avec la macro suivante.
+\begin{colourband}
+ \macro|CadreRepere|\return{\typeMP{path}}
+ \index{CadreRepere@\lstinline+CadreRepere+}
+\end{colourband}
+ Dans l’exemple suivant, on règle la couleur de la grille avec la commande
+ \hologo{MetaPost} \lstinline+drawoptions+.
+ \begin{ExempleMP}
+input geom2d;
+beginfig(1);
+A = Point(1,1);
+CA = Cercle(A,2);
+RepereMinMax(-1,4,-1,4,1,1);
+drawoptions(withcolor LightGrey);
+GrilleRepere;
+drawoptions();
+Axes;
+Debut;
+ Graduations;
+ Unites(1);
+ trace CA;
+ trace CadreRepere withcolor OrangeRed;
+Fin;
+endfig;
+ \end{ExempleMP}
+
+\section{Quelques constantes et fonctions mathématiques}
+
+\mpgeomdd définit deux constantes mathématiques \lstinline+Pi+ et \lstinline+_E+
+\index{Pi@\lstinline+Pi+}\index{_E@\lstinline+_E+} pour les constantes
+$\pi\simeq 3.14159265$ et $\mathrm{e}=2.71828183$.
+
+De plus, le package définit quelques fonctions mathématiques de la variable
+rééelle :
+\begin{colourband}
+\macro|sin(«x»)| \index{sin@\lstinline+sin+}
+\macro|cos(«x»)| \index{cos@\lstinline+cos+}
+\macro|tan(«x»)| \index{tan@\lstinline+tan+}
+\macro|exp(«x»)| \index{exp@\lstinline+exp+}
+\macro|ln(«x»)| \index{ln@\lstinline+ln+}
+\macro|ch(«x»)| \index{ch@\lstinline+ch+}
+\macro|sh(«x»)| \index{sh@\lstinline+sh+}
+\macro|th(«x»)| \index{th@\lstinline+th+}
+\macro|arcsin(«x»)| \index{arcsin@\lstinline+arcsin+}
+\macro|arccos(«x»)| \index{arccos@\lstinline+arccos+}
+\macro|arctan(«x»)| \index{arctan@\lstinline+arctan+}
+\end{colourband}
+
+\section{Représentation de courbes et de fonctions}
+
+\mpgeomdd{} fournit aussi quelques macros facilitant la représentation simple de
+courbes et de fonctions mathématiques.
+
+\subsection{Fonction de la variable réelle}
+
+Pour représenter une fonction de la variable réelle, on utilisera la macro
+suivante:
+\begin{colourband}
+ \macro|Representation(«fonction»)(«ti»,«tf»,«n»)|\return{\typeMP{path}}
+ \begin{description}
+ \item[\meta{fonction}:] est une macro \MP{} qui définit la fonction
+ mathématique d’une variable réelle que l’on souhaite represénter ;
+ \item[\meta{ti}:] est la valeur (\typeMP{numeric}) initiale de la variable à
+ partir de laquelle on souhaite construire la représentation de la fonction ;
+ \item[\meta{tf}:] est la valeur (\typeMP{numeric}) finale de la variable
+ jusqu’à laquelle on souhaite construire la représentation de la fonction ;
+ \item[\meta{n}:] est le nombre de pas (\typeMP{numeric}) utilisé pour la
+ discrétisation de la représentation.
+ \end{description}
+ \index{Representation@\lstinline+Representation+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+beginfig(1);
+RepereMinMax(-2Pi,2Pi,-1.1,1.1,0.4,1);
+Axes;
+Debut;
+ Graduations;
+ trace Representation(cos,-2Pi,2Pi,100);
+Fin;
+endfig;
+ \end{ExempleMP}
+
+\subsection{Courbe plane}
+
+Pour représenter une courbe plane définie par deux fonctions décrivant les
+abscisse et ordonnée en fonction d’un paramètre, on utilisera la macro suivante:
+\begin{colourband}
+ \macro|Courbe(«fct_abscisse»)(«fct_ordonnee»)(«ti»,«tf»,«n»)|\return{\typeMP{path}}
+ \begin{description}
+ \item[\meta{fct\_abscisse}:] est une macro \MP{} qui définit la fonction
+ mathématique d’une variable réelle décrivant l’évolution de l’abscisse des
+ points de la courbe que l’on souhaite représenter ;
+ \item[\meta{fct\_ordonnee}:] est une macro \MP{} qui définit la fonction
+ mathématique d’une variable réelle décrivant l’évolution de l’ordonnée des
+ points de la courbe que l’on souhaite représenter ;
+ \item[\meta{ti}:] est la valeur (\typeMP{numeric}) initiale de la variable à
+ partir de laquelle on souhaite construire la représentation de la fonction ;
+ \item[\meta{tf}:] est la valeur (\typeMP{numeric}) finale de la variable
+ jusqu’à laquelle on souhaite construire la représentation de la fonction ;
+ \item[\meta{n}:] est le nombre de pas (\typeMP{numeric}) utilisé pour la
+ discrétisation de la représentation.
+ \end{description}
+ \index{Courbe@\lstinline+Courbe+}
+\end{colourband}
+
+\begin{ExempleMP}
+input geom2d;
+vardef f_a(expr t)= cos(t) enddef;
+vardef f_o(expr t)= sin(2*t) enddef;
+
+beginfig(1);
+RepereMinMax(-1.1,1.1,-1.1,1.1,2,2);
+Axes;
+Debut;
+ Graduations;
+ trace Courbe(f_a,f_o,-2Pi,2Pi,100);
+Fin;
+endfig;
+ \end{ExempleMP}
+
+ Pour représenter une courbe plane définie par une fonction décrivant les
+ coordonées polaires en fonction d’un paramètre, on utilisera la macro suivante:
+ \begin{colourband}
+ \macro|CourbeEnPolaires(«fonction»)(«ti»,«tf»,«n»)|\return{\typeMP{path}}
+ \begin{description}
+ \item[\meta{fonction}:] est une macro \MP{} qui définit la fonction
+ mathématique d’une variable réelle décrivant l’évolution des coordonnées polaires des
+ points de la courbe que l’on souhaite représenter ;
+ \item[\meta{ti}:] est la valeur (\typeMP{numeric}) initiale de la variable à
+ partir de laquelle on souhaite construire la représentation de la fonction ;
+ \item[\meta{tf}:] est la valeur (\typeMP{numeric}) finale de la variable
+ jusqu’à laquelle on souhaite construire la représentation de la fonction ;
+ \item[\meta{n}:] est le nombre de pas (\typeMP{numeric}) utilisé pour la
+ discrétisation de la représentation.
+ \end{description}
+ \index{CourbeEnPolaires@\lstinline+CourbeEnPolaires+}
+ \end{colourband}
+
+ \begin{ExempleMP}
+input geom2d;
+a := 2;
+vardef cardioide(expr t)= a*(1+cos(t)) enddef;
+beginfig(1);
+RepereMinMax(-1.1,4.1,-2.8,2.8,1,1);
+Axes;
+Debut;
+ Graduations;
+ trace CourbeEnPolaires(cardioide,0,2Pi,100);
+Fin;
+endfig;
+ \end{ExempleMP}
+
+
+\subsection{Champs de vecteurs}
+
+\mpgeomdd fournit des macros pour la représentation des champs de vecteurs.
+
+Tout d’abord, on peut tracer des champs de vecteurs associée à une équation
+différentielle du premier ordre pour une fonction $y$ de la variable $x$:
+\[y'=F(x,y).\]
+La macro associée est la suivante:
+\begin{colourband}
+ \macro|ChampVecteurs(«fonction»)(«x»,«y»,«px»,«py»,«dx»,«couleur»)|\return{\typeMP{path}}
+ \begin{description}
+ \item[\meta{fonction}:] est une macro \MP{} qui définit une fonction
+ mathématique de $\R^2$ dans $\R$ ;
+ \item[\meta{x}:] est une valeur (\typeMP{numeric}), en unité \variableGDD{gddU}, qui permet de décaler la
+ grille des vecteurs suivant la direction $x$, les points étant tous les
+ \meta{x}$+i$\meta{px} pour $i$ entier ;
+ \item[\meta{y}:] est une valeur (\typeMP{numeric}), en unité \variableGDD{gddU}, qui permet de décaler la
+ grille des vecteurs suivant la direction $y$, les points étant tous les
+ \meta{y}$+i$\meta{py} pour $i$ entier ;
+ \item[\meta{px}:] est la valeur (\typeMP{numeric}), en unité
+ \variableGDD{gddU}, du pas de la grille suivant l’axe $x$ pour
+ la représentation des vecteurs ;
+ \item[\meta{py}:] est la valeur (\typeMP{numeric}), en unité
+ \variableGDD{gddU}, du pas de la grille suivant l’axe $y$ pour
+ la représentation des vecteurs ;
+ \item[\meta{dx}:] est la norme (\typeMP{numeric}), en unité
+ \variableGDD{gddU}, des vecteurs du champ de vecteur ;
+ \item[\meta{couleur}:] est la couleur (\typeMP{color}) utilisée pour tracer
+ les vecteurs.
+ \end{description}
+ \index{ChampVecteurs@\lstinline+ChampVecteurs+}
+\end{colourband}
+
+Comme cette macro utilise la macro \lstinline+drawarrow+ de \MP{}, il faudra
+jouer avec le paramètre \lstinline+ahlength+ pour régler la taille du triangle
+des flêches (voir~\cite{ctan-metapost}).
+
+\begin{ExempleMP}
+input geom2d;
+vardef F(expr x,y) = x - 2 * x * y enddef;
+vardef f(expr x) = 1/2 + a * exp(- x*x) enddef;
+beginfig(1);
+RepereMinMax(-2.5,2.5,-2.8,2.8,1,1);
+Axes;
+Debut;
+Graduations;
+ahlength := 1;
+ChampVecteurs(F,0,0,0.2,0.2,0.1,0.5white);
+% Courbes intégrales
+for n = 0 upto 16:
+ a := (n/2) - 4;
+ trace Representation(f,-2.5,2.5,50)
+ avecCrayon(1,(0.7,0.2,0.2));
+endfor
+Fin;
+endfig;
+ \end{ExempleMP}
+
+Sur le même modèle, on peut tracer des champs de vecteurs d’une fonction de
+$\R^2$ dans $\R^2$.
+La macro associée est la suivante:
+\begin{colourband}
+ \macro|ChampVecteursDD(«fonction»)(«x»,«y»,«px»,«py»,«dx»,«couleur»)|\return{\typeMP{path}}
+ \begin{description}
+ \item[\meta{fonction}:] est une macro \MP{} qui définit une fonction
+ mathématique de $\R^2$ dans $\R^2$ (donc qui retourne une \typeMP{pair}) ;
+ \item[\meta{x}:] est une valeur (\typeMP{numeric}), en unité \variableGDD{gddU}, qui permet de décaler la
+ grille des vecteurs suivant la direction $x$, les points étant tous les
+ \meta{x}$+i$\meta{px} pour $i$ entier ;
+ \item[\meta{y}:] est une valeur (\typeMP{numeric}), en unité \variableGDD{gddU}, qui permet de décaler la
+ grille des vecteurs suivant la direction $y$, les points étant tous les
+ \meta{y}$+i$\meta{py} pour $i$ entier ;
+ \item[\meta{px}:] est la valeur (\typeMP{numeric}), en unité
+ \variableGDD{gddU}, du pas de la grille suivant l’axe $x$ pour
+ la représentation des vecteurs ;
+ \item[\meta{py}:] est la valeur (\typeMP{numeric}), en unité
+ \variableGDD{gddU}, du pas de la grille suivant l’axe $y$ pour
+ la représentation des vecteurs ;
+ \item[\meta{dx}:] est la norme (\typeMP{numeric}), en unité
+ \variableGDD{gddU}, des vecteurs du champ de vecteur ;
+ \item[\meta{couleur}:] est la couleur (\typeMP{color}) utilisée pour tracer
+ les vecteurs.
+ \end{description}
+ \index{ChampVecteursDD@\lstinline+ChampVecteursDD+}
+\end{colourband}
+
+ \begin{ExempleMP}[sidebyside=false]
+input geom2d;
+gddXlabel := "$\theta$";
+gddYlabel := "$\dot\theta$";
+numeric b,c;
+b:=0.5;
+c=1.0;
+
+vardef F(expr x,y) = (y,-b*y-c*sin(x)) enddef;
+
+beginfig(1);
+Repere(10,6,2,4,2,2);
+Axes;
+Unites(1);
+Debut;
+Graduations;
+trajectoire := CourbeDat("solution0",0);
+ChampVecteursDD(F,0.5,0.5,0.2,0.2,0.15,0.5white);
+trace trajectoire avecCrayon(1,(0.7,0.2,0.2));
+pointe Point(0,0) avecCrayon(1,(0.7,0.2,0.2));
+pointe Point(3.1415,0) avecCrayon(1,(0.7,0.2,0.2));
+Fin;
+endfig;
+ \end{ExempleMP}
+
+
+
+
+\section{Couleurs \texttt{svgnames}}
+
+\begin{mplibcode}
+input exemples/svgnames/palette.mp
+\end{mplibcode}
+
+
+
+\pagestyle{empty}
+\begin{landscape}
+ \section{Galerie}
+ \subsection{Repère et tangentes extérieure}
+ \begin{minipage}{0.5\linewidth}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/cercles/cercles2.mp;
+ \end{mplibcode}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{0.5\linewidth}
+ \lstinputlisting[basicstyle=\ttfamily\small]{exemples/cercles/cercles2.mp}
+ \end{minipage}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Vecteur dans un repère}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/reperes/reperes2.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/reperes/reperes2.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Théorème de Pascale}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/divers/pascalline.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/divers/pascalline.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Hyperbole}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/coniques/hyper.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/coniques/hyper.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Astroïde comme enveloppe de droites}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/courbes/cp01.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/courbes/cp01.mp}
+ \end{multicols}
+\end{landscape}
+
+
+\begin{landscape}
+ \subsection{Courbe de Lissajous}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/courbes/cp02.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/courbes/cp02.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Étude de fonctions}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/courbes/cp05.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/courbes/cp05.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Le bicorne}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/courbes/cp08.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/courbes/cp08.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Une fonction et ses dérivées}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/fonctions/fonction2.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/fonctions/fonction2.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Cardioïde}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/polaires/pol02.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/polaires/pol02.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Axe de similitude}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/cercles/axessimilitude.mp;
+ \end{mplibcode}
+ \end{center}
+ \begin{multicols}{2}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/cercles/axessimilitude.mp}
+ \end{multicols}
+\end{landscape}
+
+
+\begin{landscape}
+ \subsection{Tracé d’une cubique}
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/cubiques/K001.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/cubiques/K001.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Apollonius}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/triangles/apollonius.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/triangles/apollonius.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Épure d’ogive}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/construction/ogiveentiers.mp;
+ \end{mplibcode}
+ \end{center}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/construction/ogiveentiers.mp}
+ \end{multicols}
+\end{landscape}
+
+\begin{landscape}
+ \subsection{Triangle \og{}pédale\fg{}}
+
+ Figure 21 de~\cite{toeplitz}.
+ \begin{center}
+ \begin{mplibcode}
+ input exemples/triangles/pedale.mp;
+ \end{mplibcode}
+ \end{center}
+ \begin{multicols}{2}
+ \lstinputlisting[basicstyle=\ttfamily\scriptsize]{exemples/triangles/pedale.mp}
+ \end{multicols}
+\end{landscape}
+
+\printbibliography
+\addcontentsline{toc}{section}{Références}%Including it as a chapter
+\printindex
+\addcontentsline{toc}{section}{Index}%Including it as a chapter
+
+
+\end{document}
Property changes on: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/mp-geom2d-doc.tex
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/metapost/mp-geom2d/solution0.dat
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/mp-geom2d/solution0.dat (rev 0)
+++ trunk/Master/texmf-dist/doc/metapost/mp-geom2d/solution0.dat 2024-10-14 19:15:06 UTC (rev 72550)
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Added: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-arc.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-arc.mp (rev 0)
+++ trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-arc.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,56 @@
+%%% --------------------------------------------------------------------------
+%%% Arcs de cercles
+%%% --------------------------------------------------------------------------
+
+vardef Arc(expr c,r,a,b) =
+ % c: centre de l’arc (point ou pair)
+ % r: rayon (numeric)
+ % a: angle de départ (numeric)
+ % b: angle d’arrivée (numeric)
+ save n,centre,pas; n = incr gddO;
+ gddT[n] = "chemin";
+ pair centre; centre = PairImp(c); pas =(b-a)/10;
+ gddP[n]:=(centre+r*(cos(a),sin(a))) for i=0 upto 10: ..
+ (centre+r*(cos(a+i*pas),sin(a+i*pas))) endfor;
+ n
+enddef;
+
+vardef ArcEntrePoints(expr C, r, A, B,s) =
+ % C : centre de l’arc (point ou pair)
+ % r : rayon (numeric)
+ % A : point ou pair de départ de l’arc
+ % B : point ou pair d’arrivée
+ % s : sens 1 ou -1
+ save n,cercle,t; n = incr gddO;
+ gddT[n] = "chemin";
+ numeric t[];
+ path cercle;
+ cercle := fullcircle scaled 2r shifted PairImp(C);
+ (t1,t2) = cercle intersectiontimes (PairImp(C)--5[PairImp(C),PairImp(A)]);
+ (t3,t4) = cercle intersectiontimes (PairImp(C)--5[PairImp(C),PairImp(B)]);
+
+ if(t1<t3):
+ t5 = t1;
+ t6 = t3;
+ else:
+ t5 = t3;
+ t6 = t1;
+ fi
+ if(s=1):
+ gddP[n] := subpath (t5,t6) of cercle;
+ else:
+ gddP[n] := subpath (t5,t6-8) of cercle;
+ fi
+ n
+enddef;
+
+
+% obtenir seulement une partie d’un cercle déjà défini
+vardef gddTraceArcDeCercle(expr C,r,d)=
+ % C : cercle 4
+ % r : premier angle en radian
+ % d : deuxième angle en radian
+ (subpath(r/Pi*4,d/Pi*4) of gddTraceObjet(C))
+enddef;
+
+endinput
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-arc.mp
___________________________________________________________________
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+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-c2d.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-c2d.mp (rev 0)
+++ trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-c2d.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,300 @@
+%%% --------------------------------------------------------------------------
+%%% mp-gdd %%% Courbes du second degré
+%%% --------------------------------------------------------------------------
+
+gddC2Dparam := 15; % pour les tracés des parabole et hyperbole
+
+% macros factorisées
+
+vardef Foyer(expr c,n) =
+ % c : ellipse, parabole, hyperbole
+ % n : 1 ou 2
+ if(n=1):
+ gddD[c]
+ else:
+ if(gddT[c]="parabole"): % si parabole c’est le même foyer
+ gddD[c]
+ else:
+ gddE[c]
+ fi
+ fi
+enddef;
+
+vardef Excentricite(expr c)=
+ gddX[c][3]
+enddef;
+
+vardef Inclinaison(expr c)=
+ gddX[c][4]
+enddef;
+
+% Ellipse ----------------------------------------------------------------------
+
+vardef Ellipse(expr C,A,B) =
+ % C : centre
+ % A : vertex
+ % B : co-vertex
+ save n,a,b,c,e,_tmp,slope;
+ pair _tmp;
+ n = incr gddO;
+ gddT[n] = "ellipse"; gddA[n] = PointImp(C); gddB[n] = PointImp(A);
+ gddC[n] = PointImp(B);
+ % calcul des deux foyers
+ a = Longueur(C,A);
+ b = Longueur(C,B);
+ c = sqrt(a**2-b**2);
+ e = c/a;
+ _tmp = e*(Pt(A)-Pt(C));
+ % les foyers
+ gddD[n] = PairTOPoint(Pt(C)+_tmp);
+ gddE[n] = PairTOPoint(Pt(C)-_tmp);
+ gddX[n][1] = a;
+ gddX[n][2] = b;
+ gddX[n][3] = e;
+ % angle du demi grand axe
+ slope = angle(PairImp(A)-PairImp(C));
+ gddX[n][4] = slope;
+ n
+enddef;
+
+vardef EllipseF(expr A,B,a) =
+ % A : foyer 1
+ % B : foyer 2
+ save n,b,c,e,_tmp,slope;
+ pair _tmp;
+ n = incr gddO;
+ gddT[n] = "ellipse";
+ % Foyers
+ gddD[n] = PointImp(A);
+ gddE[n] = PointImp(B);
+ % centre
+ gddA[n] = Milieu(A,B);
+ % La distance entre les deux foyers est égale à 2c
+ c = Longueur(A,B)/2;
+ if(c>a):
+ errmessage("le demi grand axe est trop petit");
+ fi
+ e = c/a;
+
+ b = sqrt(a**2-c**2);
+
+ % vertex et co-vertex
+ _tmp := 1.0/c*(Pt(B)-Pt(gddA[n]));
+ gddB[n] = PairTOPoint(Pt(gddA[n])+a*_tmp);
+ gddC[n] = PairTOPoint(Pt(gddA[n])+b*Pt(Rotation(_tmp,Pi/2)));
+ gddX[n][1] = a;
+ gddX[n][2] = b;
+ gddX[n][3] = e;
+ % angle du demi grand axe
+ slope = angle(PairImp(gddB[n])-PairImp(gddA[n]));
+ gddX[n][4] = slope;
+ n
+enddef;
+
+
+
+vardef Vertex(expr c) =
+ gddB[c]
+enddef;
+
+vardef Covertex(expr c) =
+ gddC[c]
+enddef;
+
+
+
+vardef DemiGrandAxe(expr c)=
+ gddX[c][1]
+enddef;
+
+vardef DemiPetitAxe(expr c)=
+ gddX[c][2]
+enddef;
+
+
+
+
+vardef TangenteEllipse(expr e,p) =
+ % détermine la tangente à une ellipse e au point p
+ % appartenant à l’ellipse
+ % par la méthode de la bissectrice
+ save F,Fp,M,B;
+ F = Foyer(e,1);
+ Fp = Foyer(e,2);
+ M = PointImp(p);
+ B = Bissectrice(F,M,Fp);
+ DroitePerpendiculaire(B,M)
+enddef;
+
+vardef TangenteExterieureEllipse(expr ell, p,n) =
+ % ell : ellipse
+ % p : point
+ % n : 1 ou 2 pour choisir la tangente
+ % http://choumac44.free.fr/NGEOMETRIE/Ellipse.htm
+ % Du point p comme centre tracer un arc de cercle de rayon PF'
+ % Du foyer F comme centre tracer un arc de cercle de rayon 2a
+ % l'intersection des 2 arcs donne le point T
+ % Tracer la droite TF puis la droite TF' et sa médiatrice , l'intersection de
+ % la médiatrice et la droite TF nous donne le point ( M ) ( contact avec la
+ % courbe) -> ici on laisse MetaPost trouver l’intersection segment,ellipse
+ save F,P,T,C,Ip,U,DU,M;
+ P = PointImp(p);
+ if(n=1):
+ F1 = Foyer(ell,1);
+ F2 = Foyer(ell,2);
+ else:
+ F1 = Foyer(ell,2);
+ F2 = Foyer(ell,1);
+ fi
+ C1 = CercleCP(P,F1);
+ C2 = Cercle(F2,2*DemiGrandAxe(ell));
+ T1 = IntersectionCercles(C1,C2);
+ T2 = IntersectionCercles(C2,C1);
+ if(Longueur(F1,T1)<Longueur(F1,T2)):
+ U = T1;
+ else:
+ U = T2;
+ fi
+ DU = Segment(F2,U);
+ pair Ip;
+ Ip := (gddTraceObjet(DU)) intersectionpoint (gddTraceObjet(ell));
+ M = PointImp(Ip);
+ Droite(P,M)
+enddef;
+
+
+%%% Paraboles ----------------------------------------------------------------
+
+% Parabole par Foyer-Directrice.
+
+
+
+vardef ParaboleFD(expr F,D) =
+ % F : foyer (point)
+ % D : directrice (droite)
+ save u, v, w, d, i, n,_tmp,slope;
+ pair _tmp;
+ n = incr gddO;
+ (u,v,w) = EquationDroite(D);
+ % ordonnée relative
+ d := u * gddA[F] + v * gddB[F] + w;
+ gddT[n] := "parabole";
+ gddX[n][1] := D; % on stock la directrice
+ gddX[n][2] := D; % on stock la directrice (compatibilité avec hyperbole)
+ % sommet
+ _tmp := (((-d/2)*(u,v)) shifted PairImp(F));
+ gddB[n] = PointImp(_tmp);
+ gddC[n] = PointImp(_tmp);
+ % le foyer (doublé pour compatibilité)
+ gddD[n] := F;
+ gddE[n] := F;
+ gddX[n][3] := 1.0; % excentricité
+ % angle du demi grand axe
+ slope = angle(PairImp(gddA[D])-PairImp(gddB[D]))+90;
+ gddX[n][4] = slope;
+ i := -gddC2Dparam-1;
+ gddP[n] := (
+ ((i*(v,-u)+((i*i-d*d)/(2d))*(u,v))
+ for i:= -gddC2Dparam upto gddC2Dparam:
+ ..(i*(v,-u)+((i*i-d*d)/(2d))*(u,v))
+ endfor)) shifted PairImp(F);
+ n
+enddef;
+
+% Parabole par Foyer-Sommet
+vardef ParaboleFS(expr F,S) =
+enddef;
+
+
+%% Hyperbole ----------------------------------------------------------
+
+vardef HyperboleFD(expr F,D,e) =
+ % F : foyer (point)
+ % D : directrice (droite)
+ % e : exentricité (numeric)
+ % pm : +1 ou -1 pour les deux branches
+ save u, v, w, d, i, n,_tmp,slope,aa,bb;
+ pair _tmp;
+ n = incr gddO;
+
+ (u,v,w) = EquationDroite(D);
+ d := u * gddA[F] + v * gddB[F] + w;
+ gddT[n] := "hyperbole";
+
+ % sommets
+ _tmp := -(d+1*sqrt(e*e*d*d))/(e*e-1)*(u,v)shifted (ProduitScalaire(F,Vecteur(v,-u))*(v,-u));
+ gddB[n] := PointImp(_tmp);
+ _tmp := -(d-1*sqrt(e*e*d*d))/(e*e-1)*(u,v)shifted
+ (ProduitScalaire(F,Vecteur(v,-u))*(v,-u));
+ gddC[n] := PointImp(_tmp);
+ % centre comme milieu des deux sommets
+ gddA[n] = Milieu(gddB[n],gddC[n]);
+ % le foyer (doublé pour compatibilité)
+ gddD[n] := F;
+ gddE[n] := RotationCentre(F, gddA[n], Pi);
+ gddX[n][3] := e; % excentricité
+ % directrices
+ gddX[n][1] := D; % on stock la directrice
+ gddX[n][2] := Droite(RotationCentre(gddA[D], gddA[n], Pi),RotationCentre(gddB[D], gddA[n], Pi));
+ % angle de l’axe
+ slope = angle(PairImp(gddA[D])-PairImp(gddB[D]))+90;
+ gddX[n][4] = slope;
+ % cercle principale
+ gddX[n][5] = CercleD(gddB[n],gddC[n]);
+ % asymptotes
+ aa = IntersectionDroiteCercle(D,gddX[n][5],1);
+ bb = IntersectionDroiteCercle(D,gddX[n][5],2);
+ gddX[n][6] = Droite(gddA[n],aa);
+ gddX[n][7] = Droite(gddA[n],bb);
+ % tracés des moitiées
+ i := -gddC2Dparam-1;
+ gddPX[n][1] := (
+ (
+ (i*(v,-u)-(d+sqrt(e*e*d*d+i*i*(e*e-1)))/(e*e-1)*(u,v))
+ for i:= -gddC2Dparam upto gddC2Dparam:
+ ..(i*(v,-u)-(d+sqrt(e*e*d*d+i*i*(e*e-1)))/(e*e-1)*(u,v))
+ endfor
+ ) shifted (ProduitScalaire(F,Vecteur(v,-u))*(v,-u))
+ );
+ gddPX[n][2] := (
+ (
+ (i*(v,-u)-(d-sqrt(e*e*d*d+i*i*(e*e-1)))/(e*e-1)*(u,v))
+ for i:= -gddC2Dparam upto gddC2Dparam:
+ ..(i*(v,-u)-(d-sqrt(e*e*d*d+i*i*(e*e-1)))/(e*e-1)*(u,v))
+ endfor
+ ) shifted (ProduitScalaire(F,Vecteur(v,-u))*(v,-u))
+ );
+ n
+enddef;
+
+vardef CerclePrincipale(expr h)=
+ %h : hyperbole
+ gddX[h][5]
+enddef;
+
+vardef AsymptoteHyperbole(expr h,n)=
+ % h : hyperbole
+ % n : 1 ou 2 pour choisir l’hyperbole
+ gddX[h][5+n]
+enddef;
+
+vardef DemieHyperbole(expr h,n)=
+ gddPX[h][n]
+enddef;
+
+% sommet
+vardef Sommet(expr p,n) =
+ % p : parabole ou hyperbole
+ % n : 1 ou 2, choisir un des sommets (le même pour la parabole)
+ if n=1:
+ gddB[p]
+ else:
+ gddC[p]
+ fi
+enddef;
+
+vardef Directrice(expr p,n) =
+ % p : parabole ou hyperbole
+ gddX[p][n]
+enddef;
+endinput
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-c2d.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-fct.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-fct.mp (rev 0)
+++ trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-fct.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,22 @@
+numeric Pi;
+numeric _E;
+
+Pi := 3.14159265;
+_E := 2.71828183;
+
+vardef sin(expr x) = sind(x/Pi*180) enddef;
+vardef cos(expr x) = cosd(x/Pi*180) enddef;
+vardef tan(expr x) = sin(x)/cos(x) enddef;
+
+vardef exp(expr x) = _E**x enddef;
+
+vardef ln(expr x) = mlog(x)/256 enddef;
+vardef ch(expr x) = (_E**x + _E**(-x))/2 enddef;
+vardef sh(expr x) = (_E**x - _E**(-x))/2 enddef;
+vardef th(expr x) = (_E**(2*x) - 1)/(_E**(2*x) + 1) enddef;
+
+vardef arcsin(expr t) = angle((sqrt(1-t**2),t)) / 180 * Pi enddef;
+vardef arccos(expr t) = angle(t,(sqrt(1-t**2))) / 180 * Pi enddef;
+vardef arctan(expr t) = angle(1,t) / 180 * Pi enddef;
+
+endinput
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-fct.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-lbl.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-lbl.mp (rev 0)
+++ trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-lbl.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,84 @@
+
+string lblS[];
+lblS[0] = "alpha";
+lblS[1] = "beta";
+lblS[2] = "gamma";
+lblS[3] = "delta";
+lblN = 3;
+
+
+vardef lTEX primary s =
+ textext("$"&scanchaine_label(s)&"$")
+enddef;
+
+vardef gddLabel.@#(expr s,p) =
+ % comme label mais qui s’applique à un point
+ % s : matériel de l’annotation
+ % p : point mpgdd
+ label.@#(s,Pt(p) gddEnPlace)
+enddef;
+
+vardef Etiquette.@#(expr s,t,p) = label.@#(textext(s) scaled t,p gddEnPlace) enddef;
+
+vardef EtiquetteChemin.@#(expr s,p,pos) = % label, chemin, position
+ save chemin;
+ path chemin;
+ if path p:
+ chemin:=p;
+ else:
+ chemin:=gddP[p]; % fonction pour chemin et courbe
+ fi;
+ label.@#(textext(s), _milieuChemin(chemin,pos) gddEnPlace)
+enddef;
+
+vardef _milieuChemin(expr p,pos) = % p est du type path
+ save midtime;
+ midtime = arctime (pos*(arclength(p))) of p;
+ point infinity of (subpath (0,midtime) of p)
+enddef;
+
+vardef FICHIER primary s =
+ save _s; string _s; _s = "input " & s;
+ scantokens _s
+enddef;
+
+vardef m_arque.@# expr p =
+ pointe p;
+ label.@#(gddL[p] scaled gddTailleLabel,PointTOPair(p) gddEnPlace);
+enddef;
+
+vardef m_a_rque.@# expr p =
+ pointe(scantokens p);
+ label.@#(lTEX(p) scaled gddTailleLabel,PointTOPair(scantokens p) gddEnPlace);
+enddef;
+
+vardef marque.@# expr p =
+ if string p: m_a_rque.@# p else: m_arque.@# p fi
+enddef;
+
+
+
+vardef scanchaine_label(expr s) =
+ save d,m,f,c,l,flag,i; string d,m,f,c;
+ d := ""; m := ""; f := "";
+ l = length(s); flag := 0;
+ for i:=0 upto l:
+ c := substring (i,i+1) of s;
+ if c = "'":
+ f := f & c; flag := 2;
+ elseif c = "_":
+ flag := 1;
+ else:
+ if flag = 0:
+ d := d & c
+ else:
+ m := m & c
+ fi;
+ fi
+ endfor;
+ for i:=0 upto lblN:
+ if d = lblS[i]: d := "\" & d fi
+ endfor;
+ d := d & "_{" & m & "}" & f; d
+enddef;
+endinput
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-lbl.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-main.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-main.mp (rev 0)
+++ trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-main.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,1051 @@
+
+
+%%% ----------------------------------------------------------------------------
+%%% Déclarations
+%%% ----------------------------------------------------------------------------
+
+numeric gddA[];
+numeric gddB[];
+numeric gddC[];
+numeric gddD[];
+numeric gddE[];
+numeric gddF[];
+numeric gddX[][];
+picture gddL[]; % Table des labels TeX (btex .. etex)
+numeric gddO; % Compteur des objets
+path gddP[]; % Table des chemins (paths internes)
+path gddPX[][]; % Tables des chemins étendues
+string gddS[]; % Table des chaînes (noms de fichiers)
+string gddT[]; % Table des types
+numeric gddU; % Unité graphique
+string gddW; % Chaîne spécifiant le placement des objets
+
+%%% ----------------------------------------------------------------------------
+%%% Initialisations
+%%% ----------------------------------------------------------------------------
+
+% Initialisation de gddO -------------------------------------------------------
+gddO := 0;
+
+% Valeur par défaut de gddU ----------------------------------------------------
+gddU := 1cm;
+
+% Initialisation de gddW et procédure associée ---------------------------------
+gddW = "scaled gddU";
+def gddEnPlace = scantokens gddW enddef;
+
+%%% ----------------------------------------------------------------------------
+%%% Définition des objets
+%%% ----------------------------------------------------------------------------
+
+% Point ------------------------------------------------------------------------
+vardef Point(expr a,b) =
+ gddT[incr gddO] = "point";
+ gddA[gddO] = a; gddB[gddO] = b; gddO
+enddef;
+
+vardef PointPolaire(expr r,a) =
+ % r : rayon
+ % a : angle en radian
+ gddT[incr gddO] = "point";
+ gddA[gddO] = r*cos(a); gddB[gddO] = r*sin(a); gddO
+enddef;
+
+vardef PointDansRepere(expr x,y,o,i,j) =
+ gddT[incr gddO] = "point";
+ gddA[gddO] = gddA[o] + x*(gddA[i]-gddA[o]) + y*(gddA[j]-gddA[o]);
+ gddB[gddO] = gddB[o] + x*(gddB[i]-gddB[o]) + y*(gddB[j]-gddB[o]);
+ gddO
+enddef;
+
+vardef CoordonneesRepere(expr m,o,i,j) =
+ save x,y; numeric x,y;
+ gddA[m] = (gddA[i]-gddA[o])*x + (gddA[j]-gddA[o])*y + gddA[o];
+ gddB[m] = (gddB[i]-gddB[o])*x + (gddB[j]-gddB[o])*y + gddB[o];
+ (x,y)
+enddef;
+
+vardef Milieu(expr a,b) =
+ gddT[incr gddO] = "point";
+ gddA[gddO] = 0.5*(gddA[a]+gddA[b]);
+ gddB[gddO] = 0.5*(gddB[a]+gddB[b]);
+ gddO
+enddef;
+
+vardef Rotation(expr A, a) =
+ % A : point
+ % a : angle
+ save _tmp,n;
+ n = incr gddO;
+ _tmp = PointImp(A);
+ gddT[n] = "point";
+ gddA[n] = cos(a)*gddA[_tmp]-sin(a)*gddB[_tmp];
+ gddB[n] = sin(a)*gddA[_tmp]+cos(a)*gddB[_tmp];
+ n
+enddef;
+
+vardef RotationCentre(expr A, C, a) =
+ % A : point
+ % C : point centre de la rotation
+ % a : angle
+ save _tmp,_tmp,n;
+ n = incr gddO;
+ _tmp1 = PointImp(A);
+ _tmp2 = PointImp(C);
+ gddT[n] = "point";
+ gddA[n] = cos(a)*(gddA[_tmp1]-gddA[_tmp2])-sin(a)*(gddB[_tmp1]-gddB[_tmp2])+gddA[_tmp2];
+ gddB[n] = sin(a)*(gddA[_tmp1]-gddA[_tmp2])+cos(a)*(gddB[_tmp1]-gddB[_tmp2])+gddB[_tmp2];
+ n
+enddef;
+
+vardef IsoBarycentre(text t) =
+ save n, G;
+ pair G; numeric n;
+ G := origin; n:=0;
+ for a=t:
+ G:=G+PairImp(a);
+ n:=n+1;
+ endfor;
+ PointImp(G/n)
+enddef;
+
+vardef Barycentre(text t) =
+ % liste sous la forme (A,a),(B,b),(C,c), etc.
+ save n, Gs;
+ pair G; numeric n;
+ G := origin; n:=0;
+ for a=t:
+ G:=G+((ypart a)*Pt(xpart a));
+ n:=n+(ypart a);
+ endfor;
+ PointImp(G/n)
+enddef;
+
+
+% Transformations pair <-> Point -----------------------------------------------
+def PointTOPair(expr a) = (gddA[a],gddB[a]) enddef;
+def PairTOPoint(expr p) = Point(xpart p,ypart p) enddef;
+def PairImp(expr a) = if pair a: a else: PointTOPair(a) fi enddef;
+def PointImp(expr a) = if pair a: PairTOPoint(a) else: a fi enddef;
+def Pt(expr a) = (gddA[a],gddB[a]) enddef;
+def PtR(expr a) = (gddA[a],gddB[a]) gddEnPlace enddef;
+
+% Transformations pair <-> Point -----------------------------------------------
+def VecteurTOPair(expr a) = (gddA[a],gddB[a]) enddef;
+def PairTOVecteur(expr p) = Vecteur(xpart p,ypart p) enddef;
+
+% Abscisse et ordonnées --------------------------------------------------------
+vardef Abscisse(expr a) = if pair a: xpart a else: gddA[a] fi enddef;
+vardef Ordonnee(expr a) = if pair a: ypart a else: gddB[a] fi enddef;
+
+
+% Addition ---------------------------------------------------------------------
+vardef AdditionAbscisses(expr a,b) = if pair a: xpart a else: gddA[a] fi + if pair b: xpart b else: gddA[b] fi enddef;
+vardef AdditionOrdonnees(expr a,b) = if pair a: ypart a else: gddB[a] fi + if pair b: ypart b else: gddB[b] fi enddef;
+vardef Addition(expr a,b) =
+ gddT[incr gddO] = "point";
+ gddA[gddO] = AdditionAbscisses(a,b);
+ gddB[gddO] = AdditionOrdonnees(a,b);
+ gddO
+enddef;
+
+vardef Longueur (expr a,b) =
+ abs(PairImp(a)-PairImp(b))
+enddef;
+
+vardef Bissectrice(expr a,b,c) =
+ % bisectrice du secteur angulaire défini par les points (abc)
+ save dba,dbc,ap,cp;
+ dba = Droite(b,a);
+ dbc = Droite(b,c);
+ ap = ReportSurDroite(b,dba,2);
+ cp = ReportSurDroite(b,dbc,2);
+ %% C'est une bonne idée cette procédure ReportSurDroite !
+ %% Pour obtenir la bissectrice il suffit de prendre la droite qui joint
+ %% le sommet au milieu du segment dont les extrémités sont les reports.
+ %% Ainsi le cas où les droites (b,a) et (b,c) sont confondues est traité.
+ Droite(b,Milieu(ap,cp))
+enddef;
+
+% Vecteur ----------------------------------------------------------------------
+vardef Vecteur (expr a,b) =
+ save n; n = incr gddO;
+ gddT[n] = "vecteur"; gddA[n] = a; gddB[n] = b; n
+enddef;
+
+vardef VecteurP (expr a) =
+ % définition d’un vecteur à partir d’un pair
+ save n; n = incr gddO;
+ gddT[n] = "vecteur"; gddA[n] =xpart a; gddB[n] = ypart a; n
+enddef;
+
+vardef ScalaireVecteur (expr k,a) =
+ % multiplication par un scalaire
+ % k : scalaire
+ % a : vecteur
+ save x,y;
+ x = k*gddA[a];
+ y = k*gddB[a];
+ Vecteur(x,y)
+enddef;
+
+vardef AdditionVecteur (expr u,v) =
+ save n,x,y; n = incr gddO;
+ gddT[n] = "vecteur";
+ x = gddA[u]+gddA[v];
+ y = gddB[u]+gddB[v];
+ gddA[n] = x; gddB[n] = y; n
+enddef;
+
+vardef SoustractionVecteur (expr u,v) =
+ save n,x,y; n = incr gddO;
+ gddT[n] = "vecteur";
+ x = gddA[u]-gddA[v];
+ y = gddB[u]-gddB[v];
+ gddA[n] = x; gddB[n] = y; n
+enddef;
+
+
+vardef ProduitScalaire (expr u,v)=
+ (gddA[u]*gddA[v]+gddB[u]*gddB[v])
+enddef;
+
+vardef Norme (expr s) =
+ sqrt(gddA[s]**2+gddB[s]**2)
+enddef;
+
+vardef VecteursAngle (expr u,v)=
+ arccos((ProduitScalaire(u,v))/(Norme(u)*Norme(v)))
+enddef;
+
+% Segment ----------------------------------------------------------------------
+vardef Segment (expr a,b) =
+ save n; n = incr gddO;
+ gddT[n] = "segment"; gddA[n] = PointImp(a); gddB[n] = PointImp(b); n
+enddef;
+
+vardef LongueurSegment (expr s) =
+ abs(Pt(gddA[s])-Pt(gddB[s]))
+enddef;
+
+vardef SegmentTOVecteur (expr s)=
+ VecteurP(Pt(gddB[s])-Pt(gddA[s]))
+enddef;
+
+
+% Triangle ---------------------------------------------------------------------
+vardef Triangle (expr a,b,c) =
+ save n; n = incr gddO; gddT[n] = "triangle";
+ gddA[n] = PointImp(a); gddB[n] = PointImp(b); gddC[n] = PointImp(c); n
+enddef;
+
+% Drawing with Metapost, Thurston
+vardef Orthocentre (expr t) =
+ save A,B,C,D,p,q;
+ pair A,B,C,D,p,q;
+ A = PointTOPair(gddA[t]);
+ B = PointTOPair(gddB[t]);
+ C = PointTOPair(gddC[t]);
+ p = whatever[B,C] ; A-p = whatever*(B-C) rotated 90;
+ q = whatever[C,A] ; B-q = whatever*(C-A) rotated 90;
+ D = whatever[A,p] = whatever[B,q];
+ PairTOPoint(D)
+enddef;
+
+
+
+vardef AireTriangle ( expr t) =
+ save droite,h,l;
+ droite = Droite(gddA[t],gddB[t]);
+ h = ProjectionPointSurDroite(gddC[t],droite);
+ l = Longueur(gddC[t],h);
+ (Longueur(gddA[t],gddB[t])*l/2.0)
+enddef;
+
+vardef CercleInscrit(expr t) =
+ save AB,BC,CA,a,b,c,I,Aire,rayon;
+ c = Longueur(gddA[t],gddB[t]);
+ a = Longueur(gddB[t],gddC[t]);
+ b = Longueur(gddC[t],gddA[t]);
+ I = Barycentre((gddA[t],a),(gddB[t],b),(gddC[t],c));
+ Aire = AireTriangle(t);
+ rayon = 2*Aire/(a+b+c);
+ Cercle(I,rayon)
+enddef;
+
+
+vardef CercleExinscrit(expr t,n) =
+ % t : gdd triangle
+ % s : 1,2 ou 3 pour choisir AB, BC ou CA
+ save AB,BC,CA,a,b,c,I,p,Aire,rayon;
+ c = Longueur(gddA[t],gddB[t]);
+ a = Longueur(gddB[t],gddC[t]);
+ b = Longueur(gddC[t],gddA[t]);
+ p = (a+b+c)/2.0;
+ Aire = AireTriangle(t);
+ if(n=1):
+ rayon = Aire/(p-a);
+ I = Barycentre((gddA[t],-a),(gddB[t],b),(gddC[t],c));
+ elseif(n=2):
+ rayon = Aire/(p-b);
+ I = Barycentre((gddA[t],a),(gddB[t],-b),(gddC[t],c));
+ elseif(n=3):
+ rayon = Aire/(p-c);
+ I = Barycentre((gddA[t],a),(gddB[t],b),(gddC[t],-c));
+ fi
+ Cercle(I,rayon)
+enddef;
+
+vardef CercleCirconscrit(expr t) =
+ % t : gdd triangle
+ CercleTroisPoints(gddA[t],gddB[t],gddC[t])
+enddef;
+
+vardef CercleEuler(expr t) =
+ % t : gdd triangle
+ % cercle des neuf points
+ save D,C,N,r;
+ pair N;
+ D = Orthocentre(t);
+ C = CercleCirconscrit(t);
+ N = 0.5[Pt(D),Pt(Centre(C))];
+ r = abs(N-1/2[Pt(gddA[t]),Pt(gddB[t])]); % un des neuf points est le
+ % milieu de [A,B]
+ Cercle(N,r)
+enddef;
+
+
+% Polygones --------------------------------------------------------------------
+vardef Polygone (text plist) =
+ save n,_point,i; n = incr gddO; gddT[n] = "polygone";
+ i:=1;
+ for _point = plist:
+ gddX[gddO][i] = PointImp(_point);
+ i:=i+1;
+ endfor
+ gddB[n] = i-1; % nombre de côté
+ gddA[n] = IsoBarycentre(plist); % centre
+ n
+enddef;
+
+vardef PolygoneRegulier (expr N,s,r,t)=
+ % N : (entier) nombre de côtés
+ % s : (numeric) rayon du cercle circonscrit
+ % r : (numeric en degré) rotation du polygone (premier point
+ % commence sur l’axe des abscisses)
+ % t : (pair ou point) translation
+ save n,_point,i; n = incr gddO; gddT[n] = "polygone";
+ pair _point;
+ for i=1 upto N:
+ _point := (s*cos((2*Pi/N)*(i-1)+r/180*Pi),s*sin((2*Pi/N)*(i-1)+r/180*Pi))+PairImp(t);
+ gddX[n][i] = PointImp(_point);
+ endfor
+ gddB[n] = N; % nombre de côtés
+ gddA[n] = PointImp(t); % centre
+ n
+enddef;
+
+def NombreCotesPolygone(expr p) =
+ gddA[p]
+enddef;
+
+def PointPolygone(expr p,i) =
+ gddX[p][i]
+enddef;
+
+% Droite -----------------------------------------------------------------------
+vardef Droite (expr a,b) =
+ save n; n = incr gddO;
+ gddT[n] = "droite"; gddA[n] = PointImp(a); gddB[n] = PointImp(b); n
+enddef;
+
+% Équation de droite : triplet (u,v,w) tel que ux+vy+w=0 -----------------------
+% L'équation rendue est normalisée !
+vardef EquationDroite(expr d) =
+ save u, v, w, n;
+ u := gddB[gddB[d]] - gddB[gddA[d]];
+ v := gddA[gddA[d]] - gddA[gddB[d]];
+ w := - u * gddA[gddA[d]] - v * gddB[gddA[d]];
+ n := u ++ v;
+ (u/n,v/n,w/n)
+enddef;
+
+% Ordonnée relative à une droite orientée --------------------------------------
+vardef OrdonneeRelativePointDroite(expr p, d) =
+ savec u, v, w;
+ (u,v,w) = EquationDroite(d);
+ u * gddA[p] + v * gddB[p] + w
+enddef;
+
+% Distance d'un point à une droite ---------------------------------------------
+def DistancePointDroite(expr p, d) =
+ abs(OrdonneeRelativePointDroite(p, d))
+enddef;
+
+% Projection d'un point sur une droite -----------------------------------------
+vardef ProjectionPointSurDroite(expr p, d) =
+ save u,v,w, l;
+ (u,v,w) = EquationDroite(d);
+ l := - u * gddA[p] - v * gddB[p] - w;
+ Point(gddA[p] + l * u, gddB[p] + l * v)
+enddef;
+
+% Droite perpendicalaire -------------------------------------------------------
+
+vardef DroitePerpendiculaire (expr D,p) =
+ % D : droite par rapport à laquelle on doit être perpendiculaire
+ % p : point par lequel doit passer la droite
+ save n,_t,A,B,v,pP,pD; n = incr gddO;
+ pair _t,A,B,v,q;
+ A := Pt(gddA[D]);
+ B := Pt(gddB[D]);
+ v := B-A; v := (-(ypart v), xpart v); %% Vecteur normal à B-A
+ q := Pt(p) + v;
+ Droite(p,q)
+enddef;
+
+vardef ReportSurDroite(expr P,D,d) =
+ % P : point de départ du segment
+ % D : droite sur laquelle construire le point
+ % d : longueure du segment
+ save n,_t; n = incr gddO;
+ pair _t;
+ _t := PairImp(P)+d*unitvector(Pt(gddB[D])-Pt(gddA[D]));
+ gddT[n] = "point"; gddA[n] = xpart _t; gddB[n] = ypart _t; n
+enddef;
+
+% Intersection de deux droites -------------------------------------------------
+vardef IntersectionDroites (expr a,b) =
+ save _p;
+ pair _p;
+ _p := mpIntersectionDroites(Pt(gddA[a]),Pt(gddB[a]),Pt(gddA[b]),Pt(gddB[b]));
+ PairTOPoint(_p)
+enddef;
+
+% Cercles ----------------------------------------------------------------------
+vardef Cercle (expr a,b) =
+ save n; n = incr gddO;
+ gddT[n] = "cercle"; gddA[n] = PointImp(a); gddB[n] = b; n
+enddef;
+
+
+vardef Rayon(expr c) =
+ gddB[c]
+enddef;
+
+
+vardef CercleCP(expr a,b) = Cercle(a,abs(Pt(a)-Pt(b))) enddef;
+vardef CercleD(expr a,b) = CercleCP(Milieu(a,b),a) enddef;
+
+% Drawing with MetaPost Thurston
+vardef CercleTroisPoints(expr A, B, C) =
+ save o; pair o;
+ o = whatever * (Pt(A)-Pt(B)) rotated 90 shifted 1/2 [Pt(A),Pt(B)] = whatever * (Pt(B)-Pt(C)) rotated 90 shifted 1/2 [Pt(B),Pt(C)];
+ Cercle(o,abs(Pt(A)-o))
+enddef;
+
+vardef AxeDeSimilitude(expr a,b,c) =
+ % Axe de similitude de trois cercles
+ save T,E;
+ numeric T[],E[];
+ T1 = TangenteCommuneExterieure(a,b);
+ T2 = TangenteCommuneExterieure(b,a);
+ T3 = TangenteCommuneExterieure(b,c);
+ T4 = TangenteCommuneExterieure(c,b);
+ E1 = IntersectionDroites(T1,T2);
+ E2 = IntersectionDroites(T3,T4);
+ Droite(E1,E2)
+enddef;
+
+
+
+% Tangente commune extérieure à deux cercles -----------------------------------
+vardef TangenteCommuneExterieure(expr a, b) =
+ save O, A, d, f; pair O, A;
+ O = (gddB[a]/(gddB[a]-gddB[b]))[Pt(gddA[a]),Pt(gddA[b])]; % Centre de l'homothétie
+ d = abs(O-Pt(gddA[a]));
+ f := if gddA[a] < gddA[b] : 1 else: -1 fi;
+ A = Pt(gddA[a]) rotatedaround(O,angle(d+-+gddB[a],f*gddB[a]));
+ Droite(O,A)
+enddef;
+
+% Tangente commune intérieure à deux cercles -----------------------------------
+vardef TangenteCommuneInterieure(expr a, b) =
+ save O, A, d, f; pair O, A;
+ O = (gddB[a]/(gddB[a]+gddB[b]))[Pt(gddA[a]),Pt(gddA[b])]; % Centre de l'homothétie
+ d = abs(O-Pt(gddA[a]));
+ f := if gddA[a] < gddA[b] : 1 else: -1 fi;
+ A = Pt(gddA[a]) rotatedaround(O,angle(d+-+gddB[a],f*gddB[a]));
+ Droite(O,A)
+enddef;
+
+
+% Intersection de deux cercles -------------------------------------------------
+vardef IntersectionCercles (expr a, b) =
+ save d, x, y, u; pair u;
+ u = unitvector(Pt(gddA[b])-Pt(gddA[a]));
+ d = abs(Pt(gddA[a])-Pt(gddA[b]));
+ x = (gddB[a]**2-gddB[b]**2+d**2)/(2d);
+ y = gddB[a]+-+x;
+ PairTOPoint(Pt(gddA[a])+x*u+y*(u rotated 90))
+enddef;
+
+
+
+% Intersection d’une droite et d’un cercle ------------------------------------
+vardef IntersectionDroiteCercle (expr D, CC, n) =
+ % D : droite
+ % CC : cercle
+ % n : identification du point 1 ou 2, le même si point unique
+ % résolution par le calcul
+ save a,b,c,Xc,Yc,R,A,B,C,Delta,Xp,Yp;
+ numeric a,b,c,Xc,Yc,R,A,B,C,Delta,Xp,Yp;
+ (a,b,c) = EquationDroite(D);
+ (Xc,Yc) = Pt(Centre(CC));
+ R := Rayon(CC);
+ if(b=0): % si la droite est verticale
+ Xp := xpart Pt(gddA[D]);
+ A := 1;
+ B := 2*(-Yc);
+ C := Yc**2+(Xp-Xc)**2-R**2;
+ Delta := B**2-4*A*C;
+ if(Delta>0):
+ if(n=1):
+ Yp := (-B - sqrt(Delta))/(2*A);
+ elseif(n=2):
+ Yp := (-B + sqrt(Delta))/(2*A);
+ fi
+ elseif(Delta=0):
+ Yp := -B/(2*A);
+ fi
+ else:
+ if(abs(a/b)<8): % si la droite est suffisamment horizontale
+ A := 1+(-a/b)**2;
+ B := 2*((-a/b)*(-c/b-Yc)-Xc);
+ C := Xc**2+(-c/b-Yc)**2-R**2;
+ Delta := B**2-4*A*C;
+ if(Delta>0):
+ if(n=1):
+ Xp := (-B - sqrt(Delta))/(2*A);
+ Yp := (-a/b*Xp-c/b);
+ elseif(n=2):
+ Xp := (-B + sqrt(Delta))/(2*A);
+ Yp := (-a/b*Xp-c/b);
+ fi
+ elseif(Delta=0):
+ Xp := -B/(2*A);
+ Yp := -a/b*Xp-c/b;
+ fi
+ else: % sinon
+ A := 1+(b/a)**2;
+ B := 2*((b/a)*(c/a+Xc)-Yc);
+ C := Yc**2+(c/a+Xc)**2-R**2;
+ Delta := B**2-4*A*C;
+ if(Delta>0):
+ if(n=1):
+ Yp := (-B - sqrt(Delta))/(2*A);
+ Xp := (-b/a*Yp-c/a);
+ elseif(n=2):
+ Yp := (-B + sqrt(Delta))/(2*A);
+ Xp := (-b/a*Yp-c/a);
+ fi
+ elseif(Delta=0):
+ Yp := -B/(2*A);
+ Xp := -b/a*Yp-c/a;
+ fi
+ fi
+ fi
+ Point(Xp,Yp)
+enddef;
+
+
+% Inversion par rapport à un cercle -------------------------------------------
+vardef Inversion (expr P, C) =
+ save O,r,s,Cc,Pp,rr,Co,Po,ro,M,iM,R;
+ O = Centre(C);
+ r = Rayon(C);
+ if(gddT[P]="point"):
+ s = r / Longueur(P,O);
+ PairTOPoint(Pt(O) + (Pt(P) - Pt(O)) * s * s)
+ elseif(gddT[P]="cercle"):
+ Cc = Centre(P);
+ rr = Rayon(P);
+ if(Longueur(O,Cc)=rr): % si le cercle objet passe par le centre du cercle
+ % % d’inversion
+ % point du cercle sur rayon passant par les deux centre
+ M = PairTOPoint(Pt(Cc)+Pt(Cc)-Pt(O));
+ % inversion de ce point
+ iM = Inversion(M,C);
+ R = Droite(O,iM);
+ DroitePerpendiculaire(R,iM)
+ else:
+ Pp = PairTOPoint(Pt(Cc)+rr*right);
+ Co = Inversion(Cc,C);
+ Po = Inversion(Pp,C);
+ CercleCP(Co,Po)
+ fi
+ elseif(gddT[P]="droite"):
+ R = DroitePerpendiculaire(P,O);
+ iM = IntersectionDroites(R,P);
+ M = Inversion(iM,C);
+ Cc = Milieu(O,M);
+ CercleCP(Cc,O)
+ fi
+enddef;
+
+
+% Axe radical entre deux cercles -----------------------------------------------
+% drawing with metapost Thurston
+vardef AxeRadical (expr CA, CB) =
+ save O,ra,rb,d,t,C_CA,C_CB,_p,_q;
+ pair _p,_q;
+ ra = Rayon(CA);
+ rb = Rayon(CB);
+ C_CA = Centre(CA);
+ C_CB = Centre(CB);
+ d = abs(Pt(C_CA) - Pt(C_CB));
+ 2t = 1 + (ra+rb) / d * (ra-rb) / d;
+ _p := up scaled 2*gddU
+ rotated angle (Pt(C_CB) - Pt(C_CA))
+ shifted t[Pt(C_CA), Pt(C_CB)];
+ _q := down scaled 2*gddU
+ rotated angle (Pt(C_CB) - Pt(C_CA))
+ shifted t[Pt(C_CA), Pt(C_CB)];
+ Droite(_p,_q)
+enddef;
+
+% Centre radical de trois cercles ---------------------------------------------
+% drawing with metapost Thurston
+vardef CentreRadical (expr CA, CB, CC) =
+ save DAB,DAC;
+ DAB = AxeRadical(CA,CB);
+ DAC = AxeRadical(CA,CC);
+ IntersectionDroites(DAB,DAC)
+enddef;
+
+vardef Centre(expr c) =
+ % pour cercle, ellipse et polygone
+ if((gddT[c] = "ellipse") or (gddT[c] = "cercle") or (gddT[c] = "polygone") or (gddT[c] = "hyperbole")):
+ gddA[c]
+ fi
+enddef;
+
+% Chemin -----------------------------------------------------------------------
+vardef Chemin (expr p) =
+ gddT[incr gddO] = "chemin"; gddP[gddO] = p; gddO
+enddef;
+
+vardef LigneBrisee(text t)=
+ save n, _p,a,i;
+ path _p;
+ i:=0;
+ for a=t:
+ if(i=0):
+ _p:=PairImp(a);
+ else:
+ _p:=_p--PairImp(a);
+ fi
+ i:=i+1;
+ endfor;
+ Chemin(_p)
+enddef;
+
+% Courbe -----------------------------------------------------------------------
+vardef CourbeDat (expr s, c) =
+ % c = 1 ou 0, selon que la courbe doit être fermée ou pas !
+ gddT[incr gddO] = "courbe"; gddS[gddO] = s; gddA[gddO] = c; gddO
+enddef;
+
+% Homothétie ------------------------------------------------------------------
+vardef HomothetiePoint (expr p,o,k) =
+ % p : point
+ % o : centre homothetie
+ % k : facteur
+ save OP,OM;
+ pair OP,OM;
+ OP = PairImp(p)-PairImp(o);
+ OM = k*OP;
+ PairTOPoint(PairImp(o)+OM)
+enddef;
+
+
+vardef Homothetie (expr p,o,k) =
+ % p : objet
+ % o : centre homothetie
+ % k : facteur
+ save A,B,C,R,_p,X,n;
+ numeric X[];
+ pair _p;
+ if((gddT[p]="point")):
+ HomothetiePoint(p,o,k)
+ elseif((gddT[p]="vecteur")):
+ A = HomothetiePoint(p,o,k);
+ Vecteur(gddA[A],gddB[A])
+ elseif((gddT[p]="segment")):
+ A = HomothetiePoint(gddA[p],o,k);
+ B = HomothetiePoint(gddB[p],o,k);
+ Segment(A,B)
+ elseif((gddT[p]="droite")):
+ A = HomothetiePoint(gddA[p],o,k);
+ B = HomothetiePoint(gddB[p],o,k);
+ Droite(A,B)
+ elseif(gddT[p]="triangle"):
+ A = HomothetiePoint(gddA[p],o,k);
+ B = HomothetiePoint(gddB[p],o,k);
+ C = HomothetiePoint(gddC[p],o,k);
+ Triangle(A,B,C)
+ elseif(gddT[p]="cercle"):
+ A = HomothetiePoint(gddA[p],o,k);
+ R = k*Rayon(p);
+ Cercle(A,R)
+ elseif(gddT[p]="ellipse"):
+ % homothetie des foyers
+ A = HomothetiePoint(gddD[p],o,k);
+ B = HomothetiePoint(gddE[p],o,k);
+ % echelle du demi grand axe
+ R = k*gddX[p][1];
+ EllipseF(A,B,R)
+ elseif(gddT[p]="parabole"):
+ A = HomothetiePoint(Foyer(p,1),o,k);
+ B = Directrice(p,1);
+ C = Homothetie(B,o,k);
+ ParaboleFD(A,C)
+ elseif(gddT[p]="hyperbole"):
+ A = HomothetiePoint(Foyer(p,1),o,k);
+ B = Directrice(p,1);
+ C = Homothetie(B,o,k);
+ HyperboleFD(A,C)
+ elseif(gddT[p]="polygone"):
+ % reprise du constructeur
+ n = incr gddO; gddT[n] = "polygone";
+ for i=1 upto gddA[p]:
+ gddX[n][i] := HomothetiePoint(gddX[p][i],o,k);
+ endfor
+ gddA[n] := gddA[p]; % nombre de côté
+ gddB[n] := HomothetiePoint(gddB[p],o,k); % centre
+ n
+ elseif(gddT[p]="chemin"):
+ _p := PairImp(o);
+ Chemin(((gddP[p] shifted (-_p)) scaled k) shifted _p)
+ fi
+enddef;
+
+% Symétrie ------------------------------------------------------------------
+vardef SymetrieAxialePoint (expr p,d) =
+ % p : point
+ % d : axe de symétrie
+ save O,l,D;
+ O = ProjectionPointSurDroite(p,d);
+ l = Longueur(p,O);
+ D = Droite(p,O);
+ ReportSurDroite(p,D,2*l)
+enddef;
+
+
+vardef SymetrieAxiale (expr p,d) =
+ % p : objet
+ % d : axe de symétrie
+ save A,B,C,R,_p,X,n;
+ numeric X[];
+ pair _p;
+ if((gddT[p]="point")):
+ SymetrieAxialePoint(p,d)
+ elseif((gddT[p]="vecteur")):
+ A = SymetrieAxialePoint(p,d);
+ Vecteur(gddA[A],gddB[A])
+ elseif((gddT[p]="segment")):
+ A = SymetrieAxialePoint(gddA[p],d);
+ B = SymetrieAxialePoint(gddB[p],d);
+ Segment(A,B)
+ elseif((gddT[p]="droite")):
+ A = SymetrieAxialePoint(gddA[p],d);
+ B = SymetrieAxialePoint(gddB[p],d);
+ Droite(A,B)
+ elseif(gddT[p]="triangle"):
+ A = SymetrieAxialePoint(gddA[p],d);
+ B = SymetrieAxialePoint(gddB[p],d);
+ C = SymetrieAxialePoint(gddC[p],d);
+ Triangle(A,B,C)
+ elseif(gddT[p]="cercle"):
+ A = SymetrieAxialePoint(gddA[p],d);
+ R = Rayon(p);
+ Cercle(A,R)
+ elseif(gddT[p]="ellipse"):
+ % homothetie des foyers
+ A = SymetrieAxialePoint(gddD[p],d);
+ B = SymetrieAxialePoint(gddE[p],d);
+ % echelle du demi grand axe
+ R = gddX[p][1];
+ EllipseF(A,B,R)
+ elseif(gddT[p]="parabole"):
+ A = SymetrieAxialePoint(Foyer(p,1),d);
+ B = Directrice(p,1);
+ C = SymetrieAxiale(B,d);
+ ParaboleFD(A,C)
+ elseif(gddT[p]="hyperbole"):
+ A = SymetrieAxialePoint(Foyer(p,1),d);
+ B = Directrice(p,1);
+ C = SymetrieAxiale(B,d);
+ HyperboleFD(A,C)
+ elseif(gddT[p]="polygone"):
+ % reprise du constructeur
+ n = incr gddO; gddT[n] = "polygone";
+ for i=1 upto gddA[p]:
+ gddX[n][i] := SymetrieAxialePoint(gddX[p][i],d);
+ endfor
+ gddA[n] := gddA[p]; % nombre de côté
+ gddB[n] := SymetrieAxialePoint(gddB[p],d); % centre
+ n
+ fi
+enddef;
+
+% Symétrie ------------------------------------------------------------------
+vardef SymetrieCentralePoint (expr p,d) =
+ % p : point
+ % d : point centre de symétrie
+ save O,l,D;
+ RotationCentre(p,d,Pi)
+enddef;
+
+
+vardef SymetrieCentrale (expr p,d) =
+ % p : objet
+ % d : point centre de symétrie
+ save A,B,C,R,X,n;
+ numeric X[];
+ if((gddT[p]="point")):
+ SymetrieCentralePoint(p,d)
+ elseif((gddT[p]="vecteur")):
+ A = SymetrieCentralePoint(p,d);
+ Vecteur(gddA[A],gddB[A])
+ elseif((gddT[p]="segment")):
+ A = SymetrieCentralePoint(gddA[p],d);
+ B = SymetrieCentralePoint(gddB[p],d);
+ Segment(A,B)
+ elseif((gddT[p]="droite")):
+ A = SymetrieCentralePoint(gddA[p],d);
+ B = SymetrieCentralePoint(gddB[p],d);
+ Droite(A,B)
+ elseif(gddT[p]="triangle"):
+ A = SymetrieCentralePoint(gddA[p],d);
+ B = SymetrieCentralePoint(gddB[p],d);
+ C = SymetrieCentralePoint(gddC[p],d);
+ Triangle(A,B,C)
+ elseif(gddT[p]="cercle"):
+ A = SymetrieCentralePoint(gddA[p],d);
+ R = Rayon(p);
+ Cercle(A,R)
+ elseif(gddT[p]="ellipse"):
+ % homothetie des foyers
+ A = SymetrieCentralePoint(gddD[p],d);
+ B = SymetrieCentralePoint(gddE[p],d);
+ % echelle du demi grand axe
+ R = gddX[p][1];
+ EllipseF(A,B,R)
+ elseif(gddT[p]="parabole"):
+ A = SymetrieCentralePoint(Foyer(p,1),d);
+ B = Directrice(p,1);
+ C = SymetrieCentrale(B,d);
+ ParaboleFD(A,C)
+ elseif(gddT[p]="hyperbole"):
+ A = SymetrieCentralePoint(Foyer(p,1),d);
+ B = Directrice(p,1);
+ C = SymetrieCentrale(B,d);
+ HyperboleFD(A,C)
+ elseif(gddT[p]="polygone"):
+ % reprise du constructeur
+ n = incr gddO; gddT[n] = "polygone";
+ for i=1 upto gddA[p]:
+ gddX[n][i] := SymetrieCentralePoint(gddX[p][i],d);
+ endfor
+ gddA[n] := gddA[p]; % nombre de côté
+ gddB[n] := SymetrieCentralePoint(gddB[p],d); % centre
+ n
+ fi
+enddef;
+
+vardef PointDe(expr o,t)=
+ % t: paramètre le long de l’objet entre 0 et 1
+ % o: objet mpgdd
+ save _l,_t,_p;
+ path _p;
+ if((gddT[o]="point")):
+ o
+ else:
+ _p := gddTraceObjet(o);
+ _l := length(_p);
+ PointImp(point (t*_l) of _p)
+ fi
+enddef;
+
+%%% ----------------------------------------------------------------------------
+%%% Définitions liées au repère
+%%% ----------------------------------------------------------------------------
+
+% Définition de l'origine ------------------------------------------------------
+origine = Point(0,0);
+
+% Définition des axes ----------------------------------------------------------
+AxeOx = Droite(origin,right);
+AxeOy = Droite(origin,up);
+
+%%% ----------------------------------------------------------------------------
+%%% Calculs MetaPost
+%%% ----------------------------------------------------------------------------
+
+vardef mpIntersectionDroites (expr a,b,c,d) =
+ save t; pair t; t = whatever [a,b]; t = whatever [c,d]; t
+enddef;
+
+%%% --------------------------------------------------------------------------
+%%% Tracés des courbes
+%%% --------------------------------------------------------------------------
+vardef gddTraceCourbe (expr f, c) =
+ save s; gdata(f, s, if i>1:..fi (scantokens s1,scantokens s2)) if c>0:..cycle fi
+enddef;
+
+%%% ----------------------------------------------------------------------------
+%%% Tracés des objets
+%%% ----------------------------------------------------------------------------
+
+gddExtensionDroite := 10;
+
+
+def gddTracePolygone expr o=
+%show "test";
+ for i=1 upto gddB[o]:
+ PointTOPair(gddX[o][i])--
+ endfor
+ cycle
+enddef;
+
+def gddTraceEllipse expr o=
+ (fullcircle xscaled (2*gddX[o][1]) yscaled (2*gddX[o][2])) rotated gddX[o][4] shifted PairImp(gddA[o])
+enddef;
+
+def gddTraceObjet expr o =
+ if gddT[o] = "triangle":
+ PointTOPair(gddA[o])--PointTOPair(gddB[o])--
+ PointTOPair(gddC[o])--cycle
+ elseif (gddT[o] = "segment") :
+ PointTOPair(gddA[o])--PointTOPair(gddB[o])
+ elseif (gddT[o] = "vecteur"):
+ (0,0)--(gddA[o],gddB[o])
+ elseif gddT[o] = "droite":
+ (gddExtensionDroite [ PointTOPair(gddA[o]), PointTOPair(gddB[o]) ]) --
+ (gddExtensionDroite [ PointTOPair(gddB[o]), PointTOPair(gddA[o]) ])
+ elseif gddT[o] = "cercle":
+ fullcircle scaled (gddB[o]*2) shifted PointTOPair(gddA[o])
+ elseif gddT[o] = "ellipse":
+ gddTraceEllipse (o)
+ elseif ((gddT[o] = "chemin") or (gddT[o] = "parabole")):
+ gddP[o]
+ elseif gddT[o] = "courbe":
+ %message "This is a debug message.";
+ gddTraceCourbe (gddS[o] & ".dat", gddA[o])
+ elseif gddT[o] = "polygone":
+ gddTracePolygone (o)
+ fi
+enddef;
+
+def trace expr p =
+ if path p or picture p or pair p: draw (p)
+ elseif gddT[p] = "vecteur": drawarrow (gddTraceObjet p)
+ else: draw (gddTraceObjet p)
+ fi
+ gddEnPlace
+enddef;
+
+def fleche expr p =
+ if path p or picture p: drawarrow (p)
+ else: drawarrow (gddTraceObjet p)
+ fi gddEnPlace
+enddef;
+
+def colorie expr p =
+ if path p: fill p else: fill (gddTraceObjet p) fi gddEnPlace
+enddef;
+
+def fermeture expr p =
+ if path p: p else: (gddTraceObjet p) fi -- cycle
+enddef;
+
+def avecCrayon(expr t,c) = withpen pencircle scaled t withcolor c enddef;
+
+%%% --------------------------------------------------------------------------
+%%% Marque et label des points
+%%% --------------------------------------------------------------------------
+gddTaillePoint := 3; % Diamètre des cercles marquant un point.
+color gddCouleurPoint; % Couleur de fond de la marque d'un point.
+gddCouleurPoint := white;
+gddTailleLabel := 1; % Taille d'un label.
+
+
+def gddPointe(expr p) =
+ fill (fullcircle scaled gddTaillePoint) shifted (p gddEnPlace)
+ withcolor gddCouleurPoint;
+ draw (fullcircle scaled gddTaillePoint) shifted (p gddEnPlace)
+enddef;
+
+def pointe expr p =
+ gddPointe(if pair p: p else: PointTOPair(p) fi)
+enddef;
+
+
+
+%%% --------------------------------------------------------------------------
+%%% Signes
+%%% --------------------------------------------------------------------------
+def SigneOrtho(expr a,b,c,x) =
+ (Pt(b) + x * unitvector(Pt(a)-Pt(b)))
+ -- (Pt(b) + x * unitvector(Pt(a) - Pt(b))
+ + x * unitvector(Pt(c) - Pt(b)))
+ -- (Pt(b) + x * unitvector(Pt(c) - Pt(b)))
+enddef;
+
+picture gdd_marque[];
+gdd_marque1 = image(draw (-7,-7)--(7,7));
+gdd_marque2 = image(draw (-7,-7)--(7,7); draw (-7,7)--(7,-7));
+gdd_marque3 = image(draw (-9,-7)--(5,7); draw (-5,-7)--(9,7);
+ draw (-7,7)--(7,-7));
+gdd_marque4 = image(draw (-9,-7)--(5,7); draw (-5,-7)--(9,7);
+ draw (-9,7)--(5,-7); draw (-5,7)--(9,-7));
+
+def Marque(expr a,b,n) =
+ gdd_marque[n] rotated angle(PairImp(b)-PairImp(a)) scaled (0.5/gddU)
+ shifted 0.5[PairImp(a),PairImp(b)]
+enddef;
+
+vardef MarqueTrait(expr s,n) =
+ save chemin;
+ path chemin;
+ if path s:
+ chemin:=s;
+ elseif(numeric s):
+ chemin:= gddTraceObjet(s)
+ fi;
+ gdd_marque[n] scaled (0.5/gddU)
+ shifted _milieuChemin(chemin,0.5)
+enddef;
+
+%%% --------------------------------------------------------------------------
+%%% Fenêtrage
+%%% --------------------------------------------------------------------------
+
+def Fenetre(expr xg,yg,xd,yd) =
+ gddXG := xg;
+ gddYB := yg;
+ gddXD := xd;
+ gddYH := yd;
+ extra_endfig := "gddFenetre;" & extra_endfig;
+enddef;
+
+def gddFenetre =
+ clip currentpicture to
+ ((gddXG,gddYB)--(gddXG,gddYH)--(gddXD,gddYH)--(gddXD,gddYB)--cycle)
+ gddEnPlace;
+ draw ((gddXG,gddYB)--(gddXG,gddYH)--(gddXD,gddYH)--(gddXD,gddYB)--cycle)
+ gddEnPlace withpen pencircle scaled 1 withcolor background;
+enddef;
+
+endinput
Property changes on: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-main.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-plt.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-plt.mp (rev 0)
+++ trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-plt.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,97 @@
+%
+% Courbe param�tr�e
+% ------------------------------------------------------------------------------
+vardef Courbe(suffix fx)(suffix fy)(expr ti,tf,n) =
+ save fpas; fpas := (tf-ti)/n;
+ (fx(ti),fy(ti)) for i=1 upto n: ..(fx(ti+i*fpas),fy(ti+i*fpas)) endfor
+enddef;
+
+%
+% Repr�sentation de fonction
+% ------------------------------------------------------------------------------
+vardef Representation(suffix f)(expr ti,tf,n) =
+ save fpas;
+ fpas := (tf-ti)/n;
+ (ti,f(ti)) for i=1 upto n: ..(ti+i*fpas,f(ti+i*fpas)) endfor
+enddef;
+
+%
+% Courbe en polaire
+% ------------------------------------------------------------------------------
+vardef CourbeEnPolaires(suffix r)(expr ti,tf,n) =
+ save fpas,t;
+ fpas := (tf-ti)/n;
+ r(ti)*(cos(ti),sin(ti))
+ for i=1 upto n: hide(t:=ti+i*fpas) .. r(t)*(cos(t),sin(t)) endfor
+enddef;
+
+%
+% Champs de vecteurs
+% ------------------------------------------------------------------------------
+vardef ChampVecteurs(suffix f)(expr x,y,px,py,dx,couleur) =
+ for i = 0 upto (x - repXmin)/px:
+ for j = 0 upto (y - repYmin)/py:
+ drawarrow
+ (((0,0)--dx*unitvector((1,f(x-i*px,y-j*py))))
+ shifted (x-i*px,y-j*py)) gddEnPlace
+ withcolor couleur;
+ endfor
+ for j = 0 upto (repYmax - y)/py:
+ drawarrow
+ (((0,0)--dx*unitvector((1,f(x-i*px,y+j*py))))
+ shifted (x-i*px,y+j*py)) gddEnPlace
+ withcolor couleur;
+ endfor
+ endfor
+ for i = 0 upto (repXmax - x)/px:
+ for j = 0 upto (y - repYmin)/py:
+ drawarrow
+ (((0,0)--dx*unitvector((1,f(x+i*px,y-j*py))))
+ shifted (x+i*px,y-j*px)) gddEnPlace
+ withcolor couleur;
+ endfor
+ for j = 0 upto (repYmax - y)/py:
+ drawarrow
+ (((0,0)--dx*unitvector((1,f(x+i*px,y+j*py))))
+ shifted (x+i*px,y+j*py)) gddEnPlace
+ withcolor couleur;
+ endfor
+ endfor
+enddef;
+
+
+%
+% Champs de vecteurs f R^2 -> R^2
+% ------------------------------------------------------------------------------
+vardef ChampVecteursDD(suffix f)(expr x,y,px,py,dx,couleur) =
+ for i = 0 upto (x - repXmin)/px:
+ for j = 0 upto (y - repYmin)/py:
+ drawarrow
+ (((0,0)--dx*unitvector(f(x-i*px,y-j*py)))
+ shifted (x-i*px,y-j*py)) gddEnPlace
+ withcolor couleur;
+ endfor
+ for j = 0 upto (repYmax - y)/py:
+ drawarrow
+ (((0,0)--dx*unitvector(f(x-i*px,y+j*py)))
+ shifted (x-i*px,y+j*py)) gddEnPlace
+ withcolor couleur;
+ endfor
+ endfor
+ for i = 0 upto (repXmax - x)/px:
+ for j = 0 upto (y - repYmin)/py:
+ drawarrow
+ (((0,0)--dx*unitvector(f(x+i*px,y-j*py)))
+ shifted (x+i*px,y-j*px)) gddEnPlace
+ withcolor couleur;
+ endfor
+ for j = 0 upto (repYmax - y)/py:
+ drawarrow
+ (((0,0)--dx*unitvector(f(x+i*px,y+j*py)))
+ shifted (x+i*px,y+j*py)) gddEnPlace
+ withcolor couleur;
+ endfor
+ endfor
+enddef;
+
+endinput;
Property changes on: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-plt.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-rep.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-rep.mp (rev 0)
+++ trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-rep.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,136 @@
+picture repSavePict;
+string repSaveW;
+
+% x and y labels
+string gddXlabel;
+gddXlabel := "$x$";
+string gddYlabel;
+gddYlabel := "$y$";
+
+def Repere(expr l,h,ox,oy,ux,uy) =
+ repLargeur := l; repHauteur := h;
+ repOX := ox ; repOY := oy;
+ repXmin := - ox / ux; repXmax := repXmin + l / ux;
+ repYmin := - oy / uy; repYmax := repYmin + h / uy;
+ repUX := ux; repUY := uy;
+ repSaveW := gddW;
+ gddW := "xscaled repUX yscaled repUY shifted (repOX,repOY) scaled gddU";
+enddef;
+
+def RepereMinMax(expr xmin,xmax,ymin,ymax,ux,uy) =
+ repLargeur := (xmax-xmin)*ux; repHauteur := (ymax-ymin)*uy;
+ repOX := -xmin*ux ; repOY := -ymin*uy;
+ repXmin := xmin; repXmax := xmax;
+ repYmin := ymin; repYmax := ymax;
+ repUX := ux; repUY := uy;
+ repSaveW := gddW;
+ gddW := "xscaled repUX yscaled repUY shifted (repOX,repOY) scaled gddU";
+enddef;
+
+def Debut =
+ repSavePict := currentpicture; currentpicture := nullpicture;
+enddef;
+
+def repClip =
+ clip currentpicture to (%
+ ((0,0)--(repLargeur,0)--(repLargeur,repHauteur)--(0,repHauteur)--cycle)
+ scaled gddU);
+enddef;
+
+def repStroke (expr c) =
+ draw ((0,0)--(repLargeur,0)--(repLargeur,repHauteur)--(0,repHauteur)--cycle)
+ scaled gddU withcolor c;
+enddef;
+
+def Fin =
+ repClip;
+ addto repSavePict also currentpicture; currentpicture := repSavePict;
+ gddW := repSaveW;
+enddef;
+
+def Axes =
+ drawarrow ((repXmin,0)--(repXmax,0)) gddEnPlace;
+ drawarrow ((0,repYmin)--(0,repYmax)) gddEnPlace;
+ label.lrt(textext(gddXlabel),(repXmax,0) gddEnPlace);
+ label.ulft(textext(gddYlabel),(0,repYmax) gddEnPlace);
+enddef;
+
+def AxesBords =
+ drawarrow ((repXmin,repYmin)--(repXmax,repYmin)) gddEnPlace;
+ drawarrow ((repXmin,repYmin)--(repXmin,repYmax)) gddEnPlace;
+ label.lrt(textext(gddXlabel),(repXmax,repYmin) gddEnPlace);
+ label.ulft(textext(gddYlabel),(repXmin,repYmax) gddEnPlace);
+enddef;
+
+
+vardef Graduations =
+ save xmin, xmax, ymin, ymax;
+ xmin = round(repXmin); xmax = round(repXmax) ;
+ ymin = round(repYmin); ymax = round(repYmax) ;
+ SequenceTirets((xmin,0),(1,0),(0,-4),xmax-xmin);
+ SequenceTirets((xmin+0.5,0),(1,0),(0,-2),xmax-xmin);
+ SequenceTirets((0,ymin),(0,1),(-4,0),ymax-ymin+1);
+ SequenceTirets((0,ymin+0.5),(0,1),(-2,0),ymax-ymin);
+enddef;
+
+
+vardef GraduationsBords =
+ save xmin, xmax, ymin, ymax;
+ xmin = round(repXmin); xmax = round(repXmax) ;
+ ymin = round(repYmin); ymax = round(repYmax) ;
+ SequenceTirets((xmin,repYmin),(1,0),(0,+4),xmax-xmin);
+ SequenceTirets((xmin+0.5,repYmin),(1,0),(0,+2),xmax-xmin);
+ SequenceTirets((repXmin,ymin),(0,1),(+4,0),ymax-ymin);
+ SequenceTirets((repXmin,ymin+0.5),(0,1),(+2,0),ymax-ymin);
+enddef;
+
+def ClipRepere =
+ extra_endfig := extra_endfig & "repClip;";
+enddef;
+
+%
+% SequenceTirets
+% ------------------------------------------------------------------------------
+vardef SequenceTirets(expr o,p,t,n) text a=
+ save ot; pair ot; ot := o gddEnPlace;
+ for i:=1 upto n:
+ % tiret
+ draw ot -- (ot shifted t) a;
+ % avancement
+ ot := (o + i*p) gddEnPlace;
+ endfor
+enddef;
+
+vardef Unites(expr t) =
+ label.bot(textext("$+"&decimal(t)&"$"),(t,-(3/gddU/repUY)) gddEnPlace);
+ label.lft(textext("$+"&decimal(t)&"$"),(-(3/gddU/repUX),t) gddEnPlace);
+enddef;
+
+%vardef ValeursGraduations =
+% label.bot(textext("$+"&decimal(t)&"$"),(t,-(3/gddU/repUY)) gddEnPlace);
+% label.lft(textext("$+"&decimal(t)&"$"),(-(3/gddU/repUX),t) gddEnPlace);
+%enddef;
+%%% ----------------------------------------------------------------------------
+%%% Grille
+%%% ----------------------------------------------------------------------------
+
+def GrilleRepere =
+ save xmin, xmax, ymin, ymax;
+ xmin = floor(repXmin); xmax = floor(repXmax) ;
+ ymin = floor(repYmin); ymax = floor(repYmax) ;
+ for i:=xmin upto xmax:
+ draw ((i,ymin)--(i,ymax)) gddEnPlace;
+ endfor;
+ for i:=ymin upto ymax:
+ draw ((xmin,i)--(xmax,i)) gddEnPlace;
+ endfor;
+enddef;
+
+%%% ----------------------------------------------------------------------------
+%%% CadreRepere
+%%% ----------------------------------------------------------------------------
+def CadreRepere =
+ (repXmin,repYmin)--(repXmin,repYmax)--(repXmax,repYmax)--(repXmax,repYmin)--cycle
+enddef;
+
+endinput
Property changes on: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-rep.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-svgnames.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-svgnames.mp (rev 0)
+++ trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-svgnames.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,152 @@
+color AliceBlue; AliceBlue = (.94,.972,1);
+color AntiqueWhite; AntiqueWhite = (.98,.92,.844);
+color Aqua; Aqua = (0,1,1);
+color Aquamarine; Aquamarine = (.498,1,.83);
+color Azure; Azure = (.94,1,1);
+color Beige; Beige = (.96,.96,.864);
+color Bisque; Bisque = (1,.894,.77);
+color Black; Black = (0,0,0);
+color BlanchedAlmond; BlanchedAlmond = (1,.92,.804);
+color Blue; Blue = (0,0,1);
+color BlueViolet; BlueViolet = (.54,.17,.888);
+color Brown; Brown = (.648,.165,.165);
+color BurlyWood; BurlyWood = (.87,.72,.53);
+color CadetBlue; CadetBlue = (.372,.62,.628);
+color Chartreuse; Chartreuse = (.498,1,0);
+color Chocolate; Chocolate = (.824,.41,.116);
+color Coral; Coral = (1,.498,.312);
+color CornflowerBlue; CornflowerBlue = (.392,.585,.93);
+color Cornsilk; Cornsilk = (1,.972,.864);
+color Crimson; Crimson = (.864,.08,.235);
+color Cyan; Cyan = (0,1,1);
+color DarkBlue; DarkBlue = (0,0,.545);
+color DarkCyan; DarkCyan = (0,.545,.545);
+color DarkGoldenrod; DarkGoldenrod = (.72,.525,.044);
+color DarkGray; DarkGray = (.664,.664,.664);
+color DarkGreen; DarkGreen = (0,.392,0);
+color DarkGrey; DarkGrey = (.664,.664,.664);
+color DarkKhaki; DarkKhaki = (.74,.716,.42);
+color DarkMagenta; DarkMagenta = (.545,0,.545);
+color DarkOliveGreen; DarkOliveGreen = (.332,.42,.185);
+color DarkOrange; DarkOrange = (1,.55,0);
+color DarkOrchid; DarkOrchid = (.6,.196,.8);
+color DarkRed; DarkRed = (.545,0,0);
+color DarkSalmon; DarkSalmon = (.912,.59,.48);
+color DarkSeaGreen; DarkSeaGreen = (.56,.736,.56);
+color DarkSlateBlue; DarkSlateBlue = (.284,.24,.545);
+color DarkSlateGray; DarkSlateGray = (.185,.31,.31);
+color DarkSlateGrey; DarkSlateGrey = (.185,.31,.31);
+color DarkTurquoise; DarkTurquoise = (0,.808,.82);
+color DarkViolet; DarkViolet = (.58,0,.828);
+color DeepPink; DeepPink = (1,.08,.576);
+color DeepSkyBlue; DeepSkyBlue = (0,.75,1);
+color DimGray; DimGray = (.41,.41,.41);
+color DimGrey; DimGrey = (.41,.41,.41);
+color DodgerBlue; DodgerBlue = (.116,.565,1);
+color FireBrick; FireBrick = (.698,.132,.132);
+color FloralWhite; FloralWhite = (1,.98,.94);
+color ForestGreen; ForestGreen = (.132,.545,.132);
+color Fuchsia; Fuchsia = (1,0,1);
+color Gainsboro; Gainsboro = (.864,.864,.864);
+color GhostWhite; GhostWhite = (.972,.972,1);
+color Gold; Gold = (1,.844,0);
+color Goldenrod; Goldenrod = (.855,.648,.125);
+color Gray; Gray = (.5,.5,.5);
+color Green; Green = (0,.5,0);
+color GreenYellow; GreenYellow = (.68,1,.185);
+color Grey; Grey = (.5,.5,.5);
+color Honeydew; Honeydew = (.94,1,.94);
+color HotPink; HotPink = (1,.41,.705);
+color IndianRed; IndianRed = (.804,.36,.36);
+color Indigo; Indigo = (.294,0,.51);
+color Ivory; Ivory = (1,1,.94);
+color Khaki; Khaki = (.94,.9,.55);
+color Lavender; Lavender = (.9,.9,.98);
+color LavenderBlush; LavenderBlush = (1,.94,.96);
+color LawnGreen; LawnGreen = (.488,.99,0);
+color LemonChiffon; LemonChiffon = (1,.98,.804);
+color LightBlue; LightBlue = (.68,.848,.9);
+color LightCoral; LightCoral = (.94,.5,.5);
+color LightCyan; LightCyan = (.88,1,1);
+color LightGoldenrod; LightGoldenrod = (.933,.867,.51);
+color LightGoldenrodYellow; LightGoldenrodYellow = (.98,.98,.824);
+color LightGray; LightGray = (.828,.828,.828);
+color LightGreen; LightGreen = (.565,.932,.565);
+color LightGrey; LightGrey = (.828,.828,.828);
+color LightPink; LightPink = (1,.712,.756);
+color LightSalmon; LightSalmon = (1,.628,.48);
+color LightSeaGreen; LightSeaGreen = (.125,.698,.668);
+color LightSkyBlue; LightSkyBlue = (.53,.808,.98);
+color LightSlateBlue; LightSlateBlue = (.518,.44,1);
+color LightSlateGray; LightSlateGray = (.468,.532,.6);
+color LightSlateGrey; LightSlateGrey = (.468,.532,.6);
+color LightSteelBlue; LightSteelBlue = (.69,.77,.87);
+color LightYellow; LightYellow = (1,1,.88);
+color Lime; Lime = (0,1,0);
+color LimeGreen; LimeGreen = (.196,.804,.196);
+color Linen; Linen = (.98,.94,.9);
+color Magenta; Magenta = (1,0,1);
+color Maroon; Maroon = (.5,0,0);
+color MediumAquamarine; MediumAquamarine = (.4,.804,.668);
+color MediumBlue; MediumBlue = (0,0,.804);
+color MediumOrchid; MediumOrchid = (.73,.332,.828);
+color MediumPurple; MediumPurple = (.576,.44,.86);
+color MediumSeaGreen; MediumSeaGreen = (.235,.7,.444);
+color MediumSlateBlue; MediumSlateBlue = (.484,.408,.932);
+color MediumSpringGreen; MediumSpringGreen = (0,.98,.604);
+color MediumTurquoise; MediumTurquoise = (.284,.82,.8);
+color MediumVioletRed; MediumVioletRed = (.78,.084,.52);
+color MidnightBlue; MidnightBlue = (.098,.098,.44);
+color MintCream; MintCream = (.96,1,.98);
+color MistyRose; MistyRose = (1,.894,.884);
+color Moccasin; Moccasin = (1,.894,.71);
+color NavajoWhite; NavajoWhite = (1,.87,.68);
+color Navy; Navy = (0,0,.5);
+color NavyBlue; NavyBlue = (0,0,.5);
+color OldLace; OldLace = (.992,.96,.9);
+color Olive; Olive = (.5,.5,0);
+color OliveDrab; OliveDrab = (.42,.556,.136);
+color Orange; Orange = (1,.648,0);
+color OrangeRed; OrangeRed = (1,.27,0);
+color Orchid; Orchid = (.855,.44,.84);
+color PaleGoldenrod; PaleGoldenrod = (.932,.91,.668);
+color PaleGreen; PaleGreen = (.596,.985,.596);
+color PaleTurquoise; PaleTurquoise = (.688,.932,.932);
+color PaleVioletRed; PaleVioletRed = (.86,.44,.576);
+color PapayaWhip; PapayaWhip = (1,.936,.835);
+color PeachPuff; PeachPuff = (1,.855,.725);
+color Peru; Peru = (.804,.52,.248);
+color Pink; Pink = (1,.752,.796);
+color Plum; Plum = (.868,.628,.868);
+color PowderBlue; PowderBlue = (.69,.88,.9);
+color Purple; Purple = (.5,0,.5);
+color Red; Red = (1,0,0);
+color RosyBrown; RosyBrown = (.736,.56,.56);
+color RoyalBlue; RoyalBlue = (.255,.41,.884);
+color SaddleBrown; SaddleBrown = (.545,.27,.075);
+color Salmon; Salmon = (.98,.5,.448);
+color SandyBrown; SandyBrown = (.956,.644,.376);
+color SeaGreen; SeaGreen = (.18,.545,.34);
+color Seashell; Seashell = (1,.96,.932);
+color Sienna; Sienna = (.628,.32,.176);
+color Silver; Silver = (.752,.752,.752);
+color SkyBlue; SkyBlue = (.53,.808,.92);
+color SlateBlue; SlateBlue = (.415,.352,.804);
+color SlateGray; SlateGray = (.44,.5,.565);
+color SlateGrey; SlateGrey = (.44,.5,.565);
+color Snow; Snow = (1,.98,.98);
+color SpringGreen; SpringGreen = (0,1,.498);
+color SteelBlue; SteelBlue = (.275,.51,.705);
+color Tan; Tan = (.824,.705,.55);
+color Teal; Teal = (0,.5,.5);
+color Thistle; Thistle = (.848,.75,.848);
+color Tomato; Tomato = (1,.39,.28);
+color Turquoise; Turquoise = (.25,.88,.815);
+color Violet; Violet = (.932,.51,.932);
+color VioletRed; VioletRed = (.816,.125,.565);
+color Wheat; Wheat = (.96,.87,.7);
+color White; White = (1,1,1);
+color WhiteSmoke; WhiteSmoke = (.96,.96,.96);
+color Yellow; Yellow = (1,1,0);
+color YellowGreen; YellowGreen = (.604,.804,.196);
+endinput
Property changes on: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-svgnames.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-tra.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-tra.mp (rev 0)
+++ trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-tra.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,44 @@
+%% === Pseudo-transparence =====================================================
+%% Code emprunté à Anthony Phan :
+%% http://www-math.univ-poitiers.fr/~phan/metalpha.html
+
+color gdd_tc;
+numeric gdd_ta;
+picture gdd_ap;
+
+def gdd_AlphaFill expr c =
+ gdd_ap := nullpicture;
+ gdd_AlphaPicture(currentpicture,c);
+ addto currentpicture also gdd_ap;
+enddef;
+
+vardef gdd_AlphaPicture(expr p,c) =
+ save p_; picture p_;
+ p_ := nullpicture;
+ addto p_ contour c withcolor gdd_ta[background,gdd_tc];
+ for p__ within p:
+ if (not clipped p__) and (not bounded p__):
+ addto p_ also p__ withcolor
+ gdd_ta[(redpart p__,greenpart p__,bluepart p__), gdd_tc];
+ else:
+ begingroup save gdd_ap;
+ picture gdd_ap; gdd_ap = nullpicture;
+ gdd_AlphaPicture(p__,pathpart p__);
+ addto p_ also gdd_ap;
+ endgroup;
+ fi
+ endfor;
+ clip p_ to c;
+ addto gdd_ap also p_;
+enddef;
+
+vardef colorieAvecTransparence(expr p,c,a) =
+ gdd_tc := c; gdd_ta := a;
+ if path p:
+ gdd_AlphaFill (p gddEnPlace)
+ else:
+ gdd_AlphaFill ((gddTraceObjet p) gddEnPlace)
+ fi
+enddef;
+
+endinput;
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d-tra.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d.mp (rev 0)
+++ trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d.mp 2024-10-14 19:15:06 UTC (rev 72550)
@@ -0,0 +1,14 @@
+%
+if not known mplib: input latexmp fi;
+
+
+input geom2d-arc;
+input geom2d-c2d;
+input geom2d-fct;
+input geom2d-lbl;
+input geom2d-plt;
+input geom2d-rep;
+input geom2d-tra;
+input geom2d-svgnames;
+input geom2d-main;
+input graph;
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/metapost/mp-geom2d/geom2d.mp
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Modified: trunk/Master/tlpkg/bin/tlpkg-ctan-check
===================================================================
--- trunk/Master/tlpkg/bin/tlpkg-ctan-check 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/tlpkg/bin/tlpkg-ctan-check 2024-10-14 19:15:06 UTC (rev 72550)
@@ -587,7 +587,7 @@
moloch mongolian-babel montserrat
monofill montex moodle
moreenum morefloats morehype moremath moresize
- moreverb morewrites morisawa movement-arrows movie15 mp3d
+ moreverb morewrites morisawa movement-arrows movie15 mp-geom2d mp3d
mparhack mparrows mpattern mpchess mpcolornames
mpfonts mpgraphics mpkiviat
mpman-ru mpostinl mptopdf mptrees msc msg mslapa msu-thesis mtgreek
Modified: trunk/Master/tlpkg/libexec/ctan2tds
===================================================================
--- trunk/Master/tlpkg/libexec/ctan2tds 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/tlpkg/libexec/ctan2tds 2024-10-14 19:15:06 UTC (rev 72550)
@@ -1772,6 +1772,7 @@
'frenchle' => '&POST_rmsymlink',
'genealogy-profiles' => '&POST_onelevel',
'gentium-tug' => '&POSTgentium_tug',
+ 'mp-geom2d' => '&POST_onelevel',
'ghsystem' => '&POSTghsystem',
'gitinfo-lua' => '&POST_onelevel',
'glossaries' => '&POST_do_man',
Modified: trunk/Master/tlpkg/tlpsrc/collection-metapost.tlpsrc
===================================================================
--- trunk/Master/tlpkg/tlpsrc/collection-metapost.tlpsrc 2024-10-14 19:13:47 UTC (rev 72549)
+++ trunk/Master/tlpkg/tlpsrc/collection-metapost.tlpsrc 2024-10-14 19:15:06 UTC (rev 72550)
@@ -34,6 +34,7 @@
depend mfpic
depend mfpic4ode
depend minim-hatching
+depend mp-geom2d
depend mp3d
depend mparrows
depend mpattern
Added: trunk/Master/tlpkg/tlpsrc/mp-geom2d.tlpsrc
===================================================================
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