Geometriesyr16 - Exemple 9

 verbatimtex
 %&latex
 \documentclass{article}
 \usepackage{mathrsfs}
 \begin{document}
 etex
 
 input geometriesyr16;
 
 vardef ProjectionsurDroite(expr aa,bb,cc)=%de aa sur (bbcc)
   save vc;
   color vd;
   numeric vc,vcc;
   vc=Module(Normal(bb,aa,cc))/Module(cc-bb);
   vcc=Module(bb-aa);
   vd=bb+sqrt(vcc**2-vc**2)*(cc-bb);
   vd
 enddef;
   
 

 figureespace(-10u,-10u,10u,10u);
 Initialisation(5,26,20,650);
 color E,F,G,J,I,K,A,B,C,S,R,T,O,Fp,F';
 F=(1.25,0,0);
 E-F=(0,1.25,0);
 G-F=(-1.5,0,0);
 J=3/5[E,F];
 I-J=G-F;
 K-J=(0,0,1);
 A=1/3[G,F]+(0.2,0,1);
 B-A=E-F+(0.4,0,0);
 C=1/3[G,F]+B-A;
 S-A=1.5/5[G,F]-G;
 R-S=C-B;
 T=IntersectionDroite(A,B,K,K+I-J)+S-A;
 O=0.55[C,B];
 Fp=ProjectionsurPlan(O,I,J,K);
 F'=ProjectionsurDroite(O,A+T-S,A+T-S+C-B);
 path dhh;
 dhh=IntersectionPlanPlan(I,J,K,A,B,C);
 path dh;
 dh=droite(Fp,I+Fp-J);
 %tracé
 fillcolor:=0.75[orange,blanc];
 transparence polygone(A+T-S,A,A+C-B,A+T-S+C-B);
 fillcolor:=0.75[jaune,blanc];
 transparence polygone(I,J,K,K+I-J);
 fillcolor:=0.75[orange,blanc];
 transparence polygone(A+T-S,B,C,A+T-S+C-B);
 trace segment(O,Fp);
 trace dhh cutbefore droite(K,K+I-J) cutafter droite(I,J) withcolor gris;
 trace dh cutbefore droite(K,J) cutafter dhh;
 trace dh cutbefore dhh cutafter droite(K+I-J,I) dashed evenly;
 trace segment(O,F') dashed evenly;
 %plan (RST)->ok
 trace chemin(T,S,R,R+T-S) cutafter segment(K,J); 
 trace chemin(T,S,R,R+T-S) cutbefore segment(K,J) dashed evenly;
 trace segment(T,T+R-S) withcolor gris;
 %plan (EFG)
 trace chemin(E,F,G) cutafter droite(K,J);
 trace chemin(F,G,G+E-F) cutbefore droite(K,J) cutafter droite(B,C) dashed evenly;
 trace chemin(G,G+E-F,E) cutbefore droite(B,C);
 %Plan (IJK)->ok
 trace segment(J,I) cutbefore droite(C,C+A-B) dashed evenly;
 trace segment(J,I) cutafter droite(C,C+A-B);
 trace chemin(J,K,K+I-J,I) cutafter droite(A,B);
 trace chemin(J,K,K+I-J,I) cutbefore droite(A,B) dashed evenly;
 %Plan (ABC)->ok
 trace segment(C,C+A-B) cutbefore droite(I,J) dashed evenly;
 trace segment(C,C+A-B) cutafter droite(I,J);
 trace chemin(C,B,A,A+C-B) cutafter droite(T,S);
 trace chemin(C,B,A,A+C-B) cutbefore droite(T,S) dashed evenly;
 %sucre :)
 trace appelation(J,1/3[J,I],2mm,btex \small Tableau etex);
 trace codeperp(O,Fp,0.55[J,K],8);
 trace codeperp(O,F',A+T-S,8);
 label.rt(btex $O$ etex,Projette(O));
 dotlabel.ulft(btex $F'$ etex,Projette(F'));
 dotlabel.ulft(btex $F_p$ etex,Projette(Fp));
 labeloffset:=labeloffset*2;
 label.lrt(btex $\mathscr{P'}$ etex,Projette(A));
 label.lrt(btex $\mathscr{P}$ etex,Projette(S));
 labeloffset:=labeloffset/2;
 label.rt(btex $(h')$ etex,Projette(iso(A+T-S,F')));
 trace appelation(F',O,2mm, btex $d'$ etex);
 trace appelation(Fp,O,-2mm,btex $d$ etex);
 trace appelation(1.4[Fp+I-J,Fp],Fp,2mm,btex $(h)$ etex);
 finespace;
 end