Une nouvelle série d'exemples : des courbes paramétrées

diff --git a/exemples/courbes/LISTE.txt b/exemples/courbes/LISTE.txt
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+cp01-1.png
+cp02-1.png
+cp03-1.png
+cp04-1.png
+cp05-1.png
+cp06-1.png
+cp07-1.png
+cp08-1.png
+== Les sources
+cp01.mp
+cp02.mp
+cp03.mp
+cp04.mp
+cp05.mp
+cp06.mp
+cp07.mp
+cp08.mp
+== Les PDF
+cp01-1.pdf
+cp02-1.pdf
+cp03-1.pdf
+cp04-1.pdf
+cp05-1.pdf
+cp06-1.pdf
+cp07-1.pdf
+cp08-1.pdf

diff --git a/exemples/courbes/Makefile b/exemples/courbes/Makefile
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+MP  = $(wildcard *.mp)
+PDF = $(patsubst %.mp, %-1.pdf, $(MP))
+
+
+png: $(PDF)
+$(PDF) : %-1.pdf : %.mp
+       ~/bin/mptopdf $< && wpdf -png -rs 50 $@
+
+liste:
+       ls *.png > LISTE.txt
+       echo '== Les sources' >> LISTE.txt
+       ls *.mp >> LISTE.txt
+       echo '== Les PDF' >> LISTE.txt
+       ls *.pdf >> LISTE.txt
\ No newline at end of file

diff --git a/exemples/courbes/cp01-1.pdf b/exemples/courbes/cp01-1.pdf
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diff --git a/exemples/courbes/cp01-1.png b/exemples/courbes/cp01-1.png
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diff --git a/exemples/courbes/cp01.mp b/exemples/courbes/cp01.mp
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+input gdd;
+input gdd-rep;
+input gdd-lbl;
+input gdd-tra;
+input svgnames;
+
+lblPreambule := "\usepackage[frenchb]{babel}"       &
+                "\usepackage[garamond]{mathdesign}" &
+                "\usepackage{amsmath}";
+
+input gdd-fct;
+input gdd-plt;
+
+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;
+
+def avecCrayon(expr t,c) = withpen pencircle scaled t withcolor c 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;
+
+  trace Vecteur((2,0),(1.2,0)) avecCrayon(1,RoyalBlue);
+  trace Vecteur((-2,0),(-1.2,0)) avecCrayon(1,RoyalBlue);
+  trace Vecteur((0,2),(0,1.2)) avecCrayon(1,RoyalBlue);
+  trace Vecteur((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
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diff --git a/exemples/courbes/cp02-1.pdf b/exemples/courbes/cp02-1.pdf
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diff --git a/exemples/courbes/cp02-1.png b/exemples/courbes/cp02-1.png
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diff --git a/exemples/courbes/cp02.mp b/exemples/courbes/cp02.mp
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+input gdd;
+input gdd-rep;
+input gdd-lbl;
+input gdd-tra;
+input svgnames;
+
+lblPreambule := "\usepackage[frenchb]{babel}"       &
+                "\usepackage[garamond]{mathdesign}" &
+                "\usepackage{amsmath}";
+
+input gdd-fct;
+input gdd-plt;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+vardef f(expr t) = sin(2*t+Pi/3) enddef;
+vardef g(expr t) = sin(3*t) enddef;
+
+def avecCrayon(expr t,c) = withpen pencircle scaled t withcolor c 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
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diff --git a/exemples/courbes/cp03-1.pdf b/exemples/courbes/cp03-1.pdf
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diff --git a/exemples/courbes/cp03-1.png b/exemples/courbes/cp03-1.png
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diff --git a/exemples/courbes/cp03.mp b/exemples/courbes/cp03.mp
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+input gdd;
+input gdd-rep;
+input gdd-lbl;
+input gdd-tra;
+input svgnames;
+
+lblPreambule := "\usepackage[frenchb]{babel}"       &
+                "\usepackage[garamond]{mathdesign}" &
+                "\usepackage{amsmath}";
+
+input gdd-fct;
+input gdd-plt;
+
+labeloffset := 6;
+gddU:=1cm;
+
+vardef f(expr t) = t*t enddef;
+vardef g(expr t) = t*t*t enddef;
+
+def avecCrayon(expr t,c) = withpen pencircle scaled t withcolor c enddef;
+
+
+
+beginfig(1);
+
+
+ Repere(8,12,2,6,1,1);
+ Axes; 
+ Debut; 
+  Graduations; Unites(1);
+
+
+  trace Vecteur((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
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diff --git a/exemples/courbes/cp04-1.pdf b/exemples/courbes/cp04-1.pdf
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diff --git a/exemples/courbes/cp04-1.png b/exemples/courbes/cp04-1.png
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diff --git a/exemples/courbes/cp04.mp b/exemples/courbes/cp04.mp
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+input gdd;
+input gdd-rep;
+input gdd-lbl;
+input gdd-tra;
+input svgnames;
+
+lblPreambule := "\usepackage[frenchb]{babel}"       &
+                "\usepackage[garamond]{mathdesign}" &
+                "\usepackage{amsmath}";
+
+input gdd-fct;
+input gdd-plt;
+
+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;
+
+def avecCrayon(expr t,c) = withpen pencircle scaled t withcolor c 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);
+
+  trace Vecteur((3,2),(5,8/3)) avecCrayon(1,DeepPink);
+  trace Vecteur((-1,-2),(-2.8,-2)) avecCrayon(1,DeepPink);
+  trace Vecteur((-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
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diff --git a/exemples/courbes/cp05-1.pdf b/exemples/courbes/cp05-1.pdf
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diff --git a/exemples/courbes/cp05-1.png b/exemples/courbes/cp05-1.png
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diff --git a/exemples/courbes/cp05.mp b/exemples/courbes/cp05.mp
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+input gdd;
+input gdd-rep;
+input gdd-lbl;
+input gdd-tra;
+input svgnames;
+
+lblPreambule := "\usepackage[frenchb]{babel}"       &
+                "\usepackage[garamond]{mathdesign}" &
+                "\usepackage{amsmath}";
+
+input gdd-fct;
+input gdd-plt;
+
+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;
+
+def avecCrayon(expr t,c) = withpen pencircle scaled t withcolor c enddef;
+
+
+
+beginfig(1);
+
+
+ Repere(10,10,2,1,1,1);
+ 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);
+
+  trace Vecteur((-1,2),(-1,2)+(0.5,2)) avecCrayon(1,Crimson);
+  trace Vecteur((3,2),(4,2)) avecCrayon(1,Crimson);
+  trace Vecteur((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
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diff --git a/exemples/courbes/cp06-1.pdf b/exemples/courbes/cp06-1.pdf
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diff --git a/exemples/courbes/cp06-1.png b/exemples/courbes/cp06-1.png
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diff --git a/exemples/courbes/cp06.mp b/exemples/courbes/cp06.mp
new file mode 100644 (file)
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+++ b/exemples/courbes/cp06.mp
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+input gdd;
+input gdd-rep;
+input gdd-lbl;
+input gdd-tra;
+input svgnames;
+
+lblPreambule := "\usepackage[frenchb]{babel}"       &
+                "\usepackage[garamond]{mathdesign}" &
+                "\usepackage{amsmath}";
+
+input gdd-fct;
+input gdd-plt;
+
+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;
+
+def avecCrayon(expr t,c) = withpen pencircle scaled t withcolor c 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
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diff --git a/exemples/courbes/cp07-1.pdf b/exemples/courbes/cp07-1.pdf
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diff --git a/exemples/courbes/cp07-1.png b/exemples/courbes/cp07-1.png
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diff --git a/exemples/courbes/cp07.mp b/exemples/courbes/cp07.mp
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+input gdd;
+input gdd-rep;
+input gdd-lbl;
+input gdd-tra;
+input svgnames;
+
+lblPreambule := "\usepackage[frenchb]{babel}"       &
+                "\usepackage[garamond]{mathdesign}" &
+                "\usepackage{amsmath}";
+
+input gdd-fct;
+input gdd-plt;
+
+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;
+
+def avecCrayon(expr t,c) = withpen pencircle scaled t withcolor c 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
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diff --git a/exemples/courbes/cp08-1.pdf b/exemples/courbes/cp08-1.pdf
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diff --git a/exemples/courbes/cp08-1.png b/exemples/courbes/cp08-1.png
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diff --git a/exemples/courbes/cp08.mp b/exemples/courbes/cp08.mp
new file mode 100644 (file)
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+++ b/exemples/courbes/cp08.mp
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+input gdd;
+input gdd-rep;
+input gdd-lbl;
+input gdd-tra;
+input svgnames;
+
+lblPreambule := "\usepackage[frenchb]{babel}"       &
+                "\usepackage[garamond]{mathdesign}" &
+                "\usepackage{amsmath}";
+
+input gdd-fct;
+input gdd-plt;
+
+labeloffset := 6;
+gddU:=1.2cm;
+
+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 avecCrayon(expr t,c) = withpen pencircle scaled t withcolor c 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);
+  trace Vecteur((2,0),(1.6,0.4)) avecCrayon(1,Crimson);
+  trace Vecteur((-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
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diff --git a/exemples/courbes/index.xml b/exemples/courbes/index.xml
new file mode 100644 (file)
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+++ b/exemples/courbes/index.xml
@@ -0,0 +1,3 @@
+<simple>
+    <titre>mp-gdd &ndash; Courbes paramétrées</titre>
+</simple>

diff --git a/exemples/courbes/vue.xml b/exemples/courbes/vue.xml
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+<page></page>
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