Nouvelles séries d'exemples : courbes en polaires

[mp-gdd.git] / exemples / polaires / pol01.mp

diff --git a/exemples/polaires/pol01.mp b/exemples/polaires/pol01.mp
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+++ b/exemples/polaires/pol01.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 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;
+Crayon(1,OliveDrab);
+label.lrt(TEX("\large Courbe d'équation polaire: " &
+     "\(\displaystyle r=\frac1{\cos\theta-\cos2\theta}\)."),(0,0));
+
+
+endfig;
+
+end
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