input couleur; verbatimtex %&latex \documentclass{article} \usepackage[upright]{fourier} \usepackage{preambule} \begin{document} etex
\ve{}
par exemple pour les vecteurs.
Il faut bien sûr avoir sous la main une version de couleur
Ces figures ont été créées par David
NIVAUD.
Je les ai juste un peu améliorées esthétiquement et en ai créées
d'autres sur le même modèle.
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beginfig(1); %representation d'un plan numeric u; pair t,r; transform T,S; path p; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; %on place les points du parallèlogramme représentant le plan z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; %on trace le parallèlogramme draw z0--z2; draw z2--z3; %on donne un effet d'epaisseur en changeant l'epaisseur du stylo pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; %on rechange l'epaisseur du stylo pickup pencircle scaled 0.5pt; %on indique le nom du plan label.urt(btex $P$ etex, z0+(0.1u,0u)); endfig;
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beginfig(2); %intersection de deux plans numeric u; pair t,r; transform T,S; path p[],q[]; u= 1cm; %Tracé de P t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %Tracé de Q z5 = 0.5[z0,z1]; z6 = z5 transformed S; z7 = (2.5u,-1u); z8 = z7 transformed S; z5 = 0.5[z9,z7]; z10= z9 transformed S; p1 = z2--z6; q1= z9--z10; z11 = p1 intersectionpoint q1; p2 = z7--z8; q2= z5--z1; z12 = p2 intersectionpoint q2; path pp; pp=z7--z8--z10--z9--cycle; fill pp withcolor green; %fillcolor:=green; %transparence pp; path ppp; ppp:=z5--z6--z11--z9--cycle; fill ppp withcolor (green+.55*bleu_ciel); path Pp; Pp:=z5--z12--z8--z6--cycle; fill Pp withcolor (green +.75*bleu_ciel); draw z5--z6 withcolor bleu; %ici on trace la droite d'intersection draw z9--z7; draw z9--z10; draw z10--z6; draw z6--z3; draw z6--z8 dashed evenly; draw z11--z6 dashed evenly; draw z2--z11; draw z5--z12 withpen pencircle scaled 2pt; draw z12--z8 dashed evenly; draw z7--z12; label.rt(btex $Q$ etex, z9); %nom de la droite d'intersection label.rt(btex $d$ etex, 0.5[z5,z6])withcolor bleu; endfig;
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beginfig(3); %representation d'un plan defini par trois points numeric u; pair t,r; transform T,S; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; %tracé du plan z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %tracé des points dotlabel.top(btex $A$ etex, (2u,1.5u)); dotlabel.top(btex $B$ etex, (1u,.5u)); dotlabel.top(btex $C$ etex, (3u,1u)); endfig;
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beginfig(4); %representation d'un plan defini par deux droites secantes numeric u; pair t,r; transform T,S; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; %tracé du plan z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %tracé des droites z4 = (0.8u,1u); z5 =(4u,1.5u);draw z4--z5; z6 = (1u,1.6u);z7=(3.6u,0.4u);draw z6--z7; label.rt(btex $d$ etex, z5); label.rt(btex $d'$ etex, z7); endfig;
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beginfig(5); %representation d'un plan defini par un point et une droite numeric u; pair t,r; transform T,S; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; %tracé du plan z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %le point et la droite dotlabel.top(btex $A$ etex, (2u,1.5u)); z4 = (1u,.5u); z5 = (3u,1u); draw z4--z5; label.top(btex $d$ etex, z5); endfig;
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beginfig(6); %representation d'un plan defini par deux droites parallèles numeric u; pair t,r; transform T,S; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; %tracé du plan z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %les deux droites z4 = (1u,1.3u); z5 =(3u,1.8u);draw z4--z5; z6 = (1.5u,0.2u);z7 = z6 shifted (z5-z4);draw z6--z7; label.rt(btex $d$ etex, z5); label.rt(btex $d'$ etex, z7); endfig;
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beginfig(7); %representation de deux droites non parallelles et sans point commun numeric u; pair t,r; transform T,S; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; path p[]; %tracé du plan z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %tracé de la droite z4 = (0.5u,.5u); z5 = (4u,1u); draw z4--z5; label.top(btex $d$ etex, z5); %tracé du point z6 = (2u,1.5u); z7 = (0.2u,1u); dotlabel.rt(btex $A$ etex, z6); %on met en place les pointillés z9 = z6 shifted 2z7; z10 = z6 shifted -3z7; p1 = z6--z10; p2 = z0--z1; z11 = p1 intersectionpoint p2; draw z6--z11 dashed evenly; draw z11--z10; draw z6--z9; %le nom de la droite label.rt(btex $d'$ etex, z10); endfig;
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beginfig(8); %representation d'un plan numeric u; pair t,r; transform T,S; path p[],q[]; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; %Trace de P z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %Trace de Q z4=(0u,-2.2u); z5 = z4 transformed T; z6 = z4 transformed S; z7 = z4 transformed T transformed S; path pp; pp:=z4--z5--z7--z6--cycle; fill pp withcolor 1.2*green; draw z4--z6; pickup pencircle scaled 2pt; draw z4--z5; draw z5--z7; pickup pencircle scaled 0.5pt; label.urt(btex $Q$ etex, z4+(0.1u,0u)); %Plan d'intersection z8=1/5[z0,z1]+1/2[z0,z2]; z9=3/5[z4,z5]+1/2[z6,z4]; z10 = z8 transformed S; z11 = z9 transformed S; p1 = z10--z11; q1 = z2--z3; q2 = z0--z1; q3 = z6--z7; z12 = p1 intersectionpoint q1; z13 = p1 intersectionpoint q2; z14 = p1 intersectionpoint q3; p2 = z8--z10; z15 = p2 intersectionpoint q1; p3 = z8--z9; z16 = p3 intersectionpoint q2; z17 = p3 intersectionpoint q3; q4 = z4--z5; z18 = p3 intersectionpoint q4; p4 = z9--z11; z19 = p4 intersectionpoint q4; path k[]; k[1]:=z8--z10--z11--z9--cycle; fill k[1] withcolor rose; k[2]:=z8--z15--z12--z16--cycle; fill k[2] withcolor (.75rose+.15bleu_ciel); k[3]:=z16--z13--z12--cycle; fill k[3] withcolor (.75rose+.35bleu_ciel); k[4]:=z18--z17--z14--z19--cycle; fill k[4] withcolor (.75rose+.25green); k[5]:=z18--z19--z11--z14--cycle; fill k[5] withcolor (.45rose+.45green); draw z9--z19;draw z19--z11 dashed evenly; draw z8--z9; draw z8--z10; draw z10--z12; draw z12--z13 dashed evenly;draw z13--z14;draw z14--z11 dashed evenly; draw z2--z15; draw z15--z12 dashed evenly;draw z12--z3; draw z16--z12; draw z6--z17;draw z17--z14 dashed evenly;draw z14--z7; draw z18--z14; pickup pencircle scaled 2pt; draw z4--z5; draw z0--z1; %nom des droites d'intersection label.rt(btex $d$ etex, 0.5[z12,z16]); label.rt(btex $d'$ etex, 0.5[z18,z14]); endfig;
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beginfig(9); %droite parallele a deux plans secants numeric u; pair t,r; transform T,S; path p[]; u= 1cm; t=(4u,1u); r=(0u,2u); T = identity shifted t; S = identity shifted r; %Plan P z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %Plan Q z4=0.5[z0,z1]; z5 = z4 transformed S; z6 = z4 shifted (1.5u,-1u); z4=0.5[z6,z7]; z8 = z6 transformed S; z9 = z7 transformed S; p1= z4--z1; p2 = z6--z8; z10 = p1 intersectionpoint p2; p3 = z2--z3; p4 = z9--z7; z11 = p3 intersectionpoint p4; path k[]; k[1]:=z8--z9--z7--z6--cycle; fill k[1] withcolor green; k[2]:=z11--z5--z4--z7--cycle; fill k[2] withcolor (.75bleu_ciel+green); k[3]:=z5--z8--z10--z4--cycle; fill k[3] withcolor (green+.55bleu_ciel); draw z5--z11; draw z11--z9;draw z11--z7 dashed evenly; draw z7--z4 dashed evenly; label.lft(btex $Q$ etex, z6+(0u,0.5u)); draw z4--z5 withcolor red; label.lft(btex $\Delta$ etex,0.5[z4,z5])withcolor red; draw z0--z4;draw z4--z6;draw z6--z8;draw z8--z9;draw z4--z7 dashed evenly; draw z4--z10 dashed evenly;draw z10--z1; %droite parallele aux deux plans z12 = (-1u,0u); z13 = z12 shifted (0u,3u); draw z13--z12 withcolor red; label.lft(btex $d$ etex, z12)withcolor red; endfig;
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beginfig(10); %theoreme du toit numeric u; pair t,r,v; transform T,S,V; path p[]; u= 1cm; t=(3u,2u); r=(-2u,1.5u);v=(-3u,0u); T = identity shifted t; S = identity shifted r; V = identity shifted v; z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed S transformed T; z4 = z0 transformed V; z5 = z0 transformed V transformed T; z101=0.1[z0,z1]; z10=0.9[z0,z1]; z23 = z101 transformed S; z32=z10 transformed S; z45 = z101 transformed V; z54=z10 transformed V; p1 = z101--z23; p2 = z4--z5; z11 = p1 intersectionpoint p2; path k[]; k[1]:=z45--z54--z32--z23--cycle; fill k[1] withcolor green; k[3]:=z23--z101--z10--z32--cycle; fill k[3] withcolor bleu_ciel; k[2]:=z23--z32--z54--z11--cycle; fill k[2] withcolor (.75bleu_ciel+green); draw z0--z1 ; draw z2--z3 withcolor red; %pour un exemple de mise en couleur draw z101--z23 ; draw z10--z32 ; draw z23--z45 ; draw z32--z54 dashed evenly ; draw z4--z11 ; draw z11--z5 dashed evenly ; label.rt(btex $d$ etex, z0); label.rt(btex $d'$ etex, z4); label.top(btex $\Delta$ etex, z2); endfig;
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beginfig(11); % plans paralleles a l'aide de droites secantes numeric u; pair t,r; transform T,S; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; %premier plan P z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %droites secantes z4 = (0.8u,1u); z5 =(4u,1.5u);draw z4--z5; z6 = (1u,1.6u);z7=(3.6u,0.4u);draw z6--z7; label.rt(btex $d$ etex, z5); label.rt(btex $d'$ etex, z7); %deuxieme plan Q z10=(0u,-2.5u); z11 = z10 transformed T; z12 = z10 transformed S; z13 = z10 transformed T transformed S; path pP; pP:=z10--z11--z13--z12--cycle; fill pP withcolor green; draw z10--z12; draw z12--z13; pickup pencircle scaled 2pt; draw z10--z11; draw z11--z13; pickup pencircle scaled 0.5pt; label.urt(btex $Q$ etex, z10+(0.1u,0u)); %droites secantes z14 = (0.8u,-1.5u); z15 =(4u,-1u);draw z14--z15; z16 = (1u,-0.9u);z17=(3.6u,-2.1u);draw z16--z17; label.rt(btex $d_{1}$ etex, z15); label.rt(btex $d'_{1}$ etex, z17); endfig;
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beginfig(12); % parallelisme plan et droite numeric u; pair t,r; transform T,S; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; %plan z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %droite dans le plan z4 = (1u,.5u); z5 = (4u,1u); draw z4--z5; label.top(btex $d'$ etex, z4); %la droite en dehors du plan z6 = (1u,2.5u); z7 = z6 shifted z5-z4; draw z6--z7; label.top(btex $d$ etex, z6); endfig;
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beginfig(13); %droites orthogonales numeric u; pair t,r; transform T,S; u= 1cm; t=(2u,3u); r=(0u,2u); T = identity shifted t; S = identity shifted r; %les droites perpendiculaires en I z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; draw z0--z1; draw z0--z2; label.bot(btex $I$ etex, z0); %marquage de l'angle droit z3=0.1[z0,z1];z4=0.1[z0,z2]; z5=z3 shifted z4-z0; draw z3--z5; draw z4--z5; %droites d et delta z6=(0u,-1u); z7 = z6 transformed T; draw z7--z6; label.bot(btex $\Delta$ etex, z7); z8=(-1u,-1u); z9= z8 transformed S; label.lft(btex $d$ etex, z9); draw z9--z8; endfig;
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beginfig(14); %droite orthogonale a un plan numeric u; pair t,r; transform T,S; path p[]; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; %plan P z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %droites secantes z4 = (0.8u,1u); z5 =(4u,1.5u);draw z4--z5; z6 = (1u,1.6u);z7=(3.6u,0.4u);draw z6--z7; label.rt(btex $d$ etex, z5); label.rt(btex $d'$ etex, z7); p1 = z4--z5;p2 = z6--z7; %droite orthogonale z8 = p1 intersectionpoint p2; z9 = z8 shifted (0u,2u); label.rt(btex $\Delta$ etex, z9); draw z8--z9; z10 = z8 shifted (0u,-2u); p3 = z9--z10;p4 = z0--z1; z11 = p3 intersectionpoint p4; draw z8--z11 dashed evenly;draw z11--z10; %marquage des angles droits z12=0.1[z8,z7];z13=0.1[z8,z9]; z14= z13 shifted z12-z8; draw z12--z14; draw z13--z14; z15=0.2[z8,z4];z16=0.1[z8,z9]; z17= z16 shifted z15-z8; draw z15--z17; draw z16--z17; endfig;
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beginfig(15); %plans paralleles et droite orthogonale numeric u; pair t,r; transform T,S; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; path p[]; %premier plan et droites z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %droites secantes z4 = (0.8u,1u); z5 =(4u,1.5u);draw z4--z5; z6 = (1u,1.6u);z7=(3.6u,0.4u);draw z6--z7; label.rt(btex $d$ etex, z5); label.rt(btex $d'$ etex, z7); %deuxieme plan et droites z10=(0u,-2.5u); z11 = z10 transformed T; z12 = z10 transformed S; z13 = z10 transformed T transformed S; path Pp; Pp:=z10--z11--z13--z12--cycle; fill Pp withcolor green; draw z10--z12; draw z12--z13; pickup pencircle scaled 2pt; draw z10--z11; draw z11--z13; pickup pencircle scaled 0.5pt; label.urt(btex $Q$ etex, z10+(0.1u,0u)); %droites secantes z14 = (0.8u,-1.5u); z15 =(4u,-1u);draw z14--z15; z16 = (1u,-0.9u);z17=(3.6u,-2.1u);draw z16--z17; label.rt(btex $d_{1}$ etex, z15); label.rt(btex $d'_{1}$ etex, z17); %droite orthogonale p1=z4--z5;p2=z6--z7; p3=z14--z15;p4=z16--z17; p5=z0--z1;p6=z10--z11; z20 = p1 intersectionpoint p2; z21 = p3 intersectionpoint p4; p7 = z20--z21; z22 = p7 intersectionpoint p5; z24 = z20 shifted (0u,1.5u); z25 = z21 shifted (0u,-1.5u); p8 = z21--z25; z23 = p8 intersectionpoint p6; draw z24--z20;draw z20--z22 dashed evenly; draw z22--z21; draw z21--z23 dashed evenly; draw z23--z25; label.rt(btex $\Delta$ etex, z24); %marquage des angles droits z30=0.2[z20,z4];z31=0.1[z20,z24]; z32 = z31 shifted z30-z20; draw z32--z30; draw z32--z31; z40=0.2[z21,z14];z41=0.1[z21,z22]; z42 = z41 shifted z40-z21; draw z42--z40; draw z42--z41; z50=0.1[z20,z7];z51=0.1[z20,z24]; z52 = z51 shifted z50-z20; draw z52--z50; draw z52--z51; z60=0.1[z21,z17];z61=0.1[z21,z22]; z62 = z61 shifted z60-z21; draw z62--z60; draw z62--z61; endfig;
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beginfig(16); %droites orthogonales a deux plans paralleles numeric u; pair t,r; transform T,S; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; path p[]; %premier plan z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; path p; p:=z0--z1--z3--z2--cycle; fill p withcolor bleu_ciel; draw z0--z2; draw z2--z3; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); %deuxieme plan z10=(0u,-2.5u); z11 = z10 transformed T; z12 = z10 transformed S; z13 = z10 transformed T transformed S; path pP; pP:=z10--z11--z13--z12--cycle; fill pP withcolor green; draw z10--z12; draw z12--z13; pickup pencircle scaled 2pt; draw z10--z11; draw z11--z13; pickup pencircle scaled 0.5pt; label.urt(btex $Q$ etex, z10+(0.1u,0u)); %premiere droite z20 = (2u,1u);z26 = z20 shifted (0u,-2.5u); z21 = z20 shifted (0u,2u); z22 = z20 shifted (0u,-4.5u); p1 = z21--z22; p2 = z0--z1; p3 = z10--z11; z24 = p1 intersectionpoint p2; z25 = p1 intersectionpoint p3; draw z21--z20;draw z20--z24 dashed evenly;draw z24--z26;draw z26--z25 dashed evenly; draw z25--z22; %deuxieme droite z30 = (3u,1.5u);z36 = z30 shifted (0u,-2.5u); z31 = z30 shifted (0u,2u); z32 = z30 shifted (0u,-4.5u); p11 = z31--z32; p12 = z0--z1; p13 = z10--z11; z34 = p11 intersectionpoint p12; z35 = p11 intersectionpoint p13; draw z31--z30;draw z30--z34 dashed evenly;draw z34--z36;draw z36--z35 dashed evenly; draw z35--z32; %marquage des angles droits z40=0.1[z20,z30];z41=0.1[z20,z21]; z42 = z41 shifted z40-z20; draw z42--z40; draw z42--z41; z50=0.1[z30,z20];z51=0.1[z30,z31]; z52 = z51 shifted z50-z30; draw z52--z50; draw z52--z51; z60=0.1[z26,z36];z61=0.1[z26,z24]; z62 = z61 shifted z60-z26; draw z62--z60; draw z62--z61; z70=0.1[z36,z26];z71=0.2[z36,z34]; z72 = z71 shifted z70-z36; draw z72--z70; draw z72--z71; draw z20--z30; draw z26--z36; endfig;
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beginfig(17); %intersection de deux plans perpendiculaires numeric u; pair t,r; transform T,S; path p[],q[]; u= 1cm; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; %Tracé de P z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; draw z0--z2; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; %Tracé de Q z5 = 0.5[z0,z1]; z6 = z5 transformed S; z7 = z5 shifted (0u,-2.5u); z8 = z7 transformed S; z5 = 0.5[z9,z7]; z10= z9 transformed S; p1 = z2--z6; q1= z5--z9; z11 = p1 intersectionpoint q1; p2 = z6--z8; q2= z5--z1; z12 = p2 intersectionpoint q2; path k[]; k[1]:=z7--z8--z10--z9--cycle; fill k[1] withcolor green; k[3]:=z0--z1--z3--z2--cycle; fill k[3] withcolor bleu_ciel; k[2]:=z11--z6--z5--cycle; fill k[2] withcolor (.55bleu_ciel+green); k[4]:=z5--z12--z6--cycle; fill k[4] withcolor (.75bleu_ciel+green); draw z0--z1--z3 withpen pencircle scaled 2pt; label.urt(btex $P$ etex, z0+(0.1u,0u)); draw z5--z6 withcolor red; draw z9--z7; draw z9--z10; draw z10--z6; draw z6--z3; draw z7--z8; draw z11--z6 dashed evenly; draw z2--z11; draw z12--z6 dashed evenly; draw z8--z12; label.rt(btex $Q$ etex, z9); %nom de la droite d'intersection label.rt(btex $d$ etex, 0.6[z5,z6])withcolor red; %droites orthogonales z13=0.5[z5,z6]; z14 = z13 shifted (0u,2u); z15 = z13 shifted (0u,-2u); p3 = z0--z1; q3 = z13--z15; z16 = p3 intersectionpoint q3; draw z14--z13; draw z13--z16 dashed evenly; draw z16--z15; %marquage de l'angle droit z20=0.2[z13,z6];z21=0.2[z13,z14]; z22 = z21 shifted z20-z13; draw z22--z20; draw z22--z21; z17 = z13 shifted 0.8(z1-z5); z18 = z13 shifted 0.8(z0-z5); p4 = z13--z18; z19 = q1 intersectionpoint p4; draw z18--z19; draw z19--z13 dashed evenly; draw z13--z17; %marquage de l'angle droit z30=0.1[z13,z18];z31=0.1[z13,z14]; z32 = z31 shifted z30-z13; draw z32--z30; draw z32--z31; endfig;
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beginfig(18); %plans perpendiculaires a un meme plan numeric u; pair t,r; transform T,S; path p[],q[]; u= 1cm; t=(5u,0u); r=(1u,2.3u); T = identity shifted t; S = identity shifted r; %plan Q z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; %les plans perpendiculaires z4= 1/4[z0,z1]; z5= 3/4[z0,z1]; z6= 1/2[z4,z5]; z7 = z6 shifted (0u,1u); z8 = z4 shifted (0u,2u); z9 = z5 shifted (0u,2u); z10 = z7 shifted (0u,2u); z4=0.5[z8,z11];z5=0.5[z12,z9];z7=0.5[z13,z10]; p1 = z2--z3; q1 = z8--z10;q2=z9--z10; z14= p1 intersectionpoint q1; z15= p1 intersectionpoint q2; z16=1/2[z14,z15]; path k[]; k[1]:=z0--z1--z3--z2--cycle; fill k[1] withcolor green; k[3]:=z8--z11--z13--z10--cycle; fill k[3] withcolor bleu_ciel; k[2]:=z10--z13--z12--z9--cycle; fill k[2] withcolor rose; k[4]:=z8--z14--z16--z7--z4--cycle; fill k[4] withcolor(green +.75bleu_ciel); k[5]:=z4--z7--z6--cycle; fill k[5] withcolor(green+.55bleu_ciel); k[6]:=z5--z7--z16--z15--z9--cycle; fill k[6] withcolor(.25green +.75rose); k[7]:=z5--z7--z6--cycle; fill k[7] withcolor(.45green+.45rose); draw z0--z2; pickup pencircle scaled 2pt; draw z0--z1; draw z1--z3; pickup pencircle scaled 0.5pt; label.urt(btex $Q$ etex, z0+(0.1u,0u)); draw z4--z7; draw z5--z7; draw z8--z11;draw z8--z10; draw z12--z9;draw z9--z10; draw z7--z10; draw z7--z6 dashed evenly; draw z6--z13; draw z11--z13; draw z13--z12; draw z2--z14;draw z14--z15 dashed evenly; draw z15--z3; %marquage des angles droits; z20=0.1[z7,z10];z21=0.2[z7,z4]; z22 = z21 shifted z20-z7; draw z22--z20; draw z22--z21; z30=0.1[z7,z10];z31=0.2[z7,z5]; z32 = z31 shifted z30-z7; draw z32--z30; draw z32--z31; label.bot(btex $P$ etex, z11+(0.2u,0.6u)); label.bot(btex $P'$ etex, z12+(-0.2u,0.8u)); endfig;