% proflycee-tools-espace.tex % Copyright 2024-2025 Cédric Pierquet % Released under the LaTeX Project Public License v1.3c or later, see http://www.latex-project.org/lppl.txt \RequirePackage{iftex} \ifluatex \RequirePackage{luamplib}% \mplibtextextlabel{enable}% \everymplib[PfLAA]{}\everyendmplib[PfLAA]{}% \everymplib[PfLAB]{}\everyendmplib[PfLAB]{}% \everymplib[PfLAC]{}\everyendmplib[PfLAC]{}% \everymplib[PfLAD]{}\everyendmplib[PfLAD]{}% \everymplib[PfLAE]{}\everyendmplib[PfLAE]{}% \everymplib[PfLAF]{}\everyendmplib[PfLAF]{}% \everymplib[PfLAG]{}\everyendmplib[PfLAG]{}% \everymplib[PfLAH]{}\everyendmplib[PfLAH]{}% \everymplib[PfLAI]{}\everyendmplib[PfLAI]{}% \everymplib[PfLAJ]{}\everyendmplib[PfLAJ]{}% \everymplib[PfLAK]{}\everyendmplib[PfLAK]{}% \everymplib[PfLAL]{}\everyendmplib[PfLAL]{}% \everymplib[PfLAM]{}\everyendmplib[PfLAM]{}% \everymplib[PfLAN]{}\everyendmplib[PfLAN]{}% \everymplib[PfLAO]{}\everyendmplib[PfLAO]{}% \everymplib[PfLAP]{}\everyendmplib[PfLAP]{}% \everymplib[PfLAQ]{}\everyendmplib[PfLAQ]{}% \everymplib[PfLAR]{}\everyendmplib[PfLAR]{}% %\else% % \RequirePackage[shellescape]{gmp}%inclusion de figures metapost "à la volée"% % \gmpoptions{everymp={prologues:=3;}}% \fi% \defKV[posrelatesp]{Echelle=\def\scaleminischemspace{#1},scale=\def\scaleminischemspace{#1}} \setKVdefault[posrelatesp]{Echelle=1,scale=1} \NewDocumentCommand\SchemaEspace{ s O{} m }{% \restoreKV[posrelatesp]% \setKV[posrelatesp]{#2}% \ifluatex% \IfBooleanTF{#1}% {\def\tmplabelespace##1{\mathscr{##1}}}% {\def\tmplabelespace##1{\mathcal{##1}}}% \mplibforcehmode% \IfStrEqCase{#3}{% {plan}{% \begin{mplibcode}[PfLAA] beginfig(56); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; %plan simple pair t,r; transform T,S; pickup pencircle scaled 0.025u; 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; draw z0--z2 ; draw z2--z3 ; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); endfig; \end{mplibcode} }% {interplans}{% \begin{mplibcode}[PfLAB] beginfig(57); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; %intersection de deux plans pair t,r; transform T,S; path p[],q[]; pickup pencircle scaled 0.025u; 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; draw z0--z2; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; 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; draw z5--z6; draw z9--z7; draw z9--z10; draw z10--z6; draw z6--z3; draw z6--z8 dashed evenly; p1 = z2--z6; q1= z9--z10; z11 = p1 intersectionpoint q1; draw z11--z6 dashed evenly; draw z2--z11; p2 = z7--z8; q2= z5--z1; z12 = p2 intersectionpoint q2; draw z12--z8 dashed evenly; draw z7--z12; label.rt(btex $d$ etex scaled echelle, 0.5[z5,z6]); label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); label.rt(btex $\tmplabelespace{Q}$ etex scaled echelle, z9); endfig; \end{mplibcode} }% {plan3points}{% \begin{mplibcode}[PfLAC] beginfig(58); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % representation d'un plan defini par trois points pair t,r; transform T,S; pickup pencircle scaled 0.025u; 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; draw z0--z2; draw z2--z3; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; dotlabel.top(btex $A$ etex scaled echelle, (2.25u,1.5u)); dotlabel.top(btex $B$ etex scaled echelle, (1.25u,.5u)); dotlabel.top(btex $C$ etex scaled echelle, (3.25u,1u)); label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); endfig; \end{mplibcode} }% {plandroitessecantes}{% \begin{mplibcode}[PfLAD] beginfig(59); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % representation d'un plan defini par deux droites secantes pair t,r; transform T,S; pickup pencircle scaled 0.025u; 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; draw z0--z2; draw z2--z3; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; 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 scaled echelle, z5); label.rt(btex $d'$ etex scaled echelle, z7); label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); endfig; \end{mplibcode} }% {plandroitepoint}{% \begin{mplibcode}[PfLAE] beginfig(60); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % representation d'un plan defini par un point et une droite pair t,r; transform T,S; pickup pencircle scaled 0.025u; 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; draw z0--z2; draw z2--z3; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; dotlabel.top(btex $A$ etex scaled echelle, (2.05u,1.35u)); z4 = (1u,.5u); z5 = (3.25u,1.05u); draw z4--z5; label.top(btex $d$ etex scaled echelle, z5); label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); endfig; \end{mplibcode} }% {plandroitespara}{% \begin{mplibcode}[PfLAF] beginfig(61); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % representation d'un plan defini par deux droites parallèles pair t,r; transform T,S; pickup pencircle scaled 0.025u; 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; draw z0--z2; draw z2--z3; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; z4 = (1u,1.15u); z5 =(3u,1.65u); draw z4--z5; z6 = (1.5u,0.2u); z7 = z6 shifted (z5-z4); draw z6--z7; label.rt(btex $d$ etex scaled echelle, z5); label.rt(btex $d'$ etex scaled echelle, z7); label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); endfig; \end{mplibcode} }% {droitesnoncopla}{% \begin{mplibcode}[PfLAG] beginfig(62); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % representation de deux droites non parallelles et sans point commun pair t,r; transform T,S; pickup pencircle scaled 0.025u; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; path p[]; z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; draw z0--z2; draw z2--z3; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; z4 = (0.5u,.5u); z5 = (4u,1u); draw z4--z5; label.top(btex $d$ etex scaled echelle, z5); z6 = (2u,1.5u); z7 = (0.2u,1u); dotlabel.rt(btex $A$ etex scaled echelle, z6); z9 = z6 shifted z7; z10 = z6 shifted -2z7; p1 = z6--z10; p2 = z0--z1; z11 = p1 intersectionpoint p2; draw z6--z11 dashed evenly; draw z11--z10; draw z6--z9; label.rt(btex $d'$ etex scaled echelle, z10); label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); endfig; \end{mplibcode} }% {incidence}{% \begin{mplibcode}[PfLAH] beginfig(63); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % representation d'un plan pair t,r; transform T,S; path p[],q[]; pickup pencircle scaled 0.025u; 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; draw z0--z2; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; z4=(0u,-2.2u); z5 = z4 transformed T; z6 = z4 transformed S; z7 = z4 transformed T transformed S; draw z4--z6; draw z4--z5 withpen pencircle scaled 0.05u; draw z5--z7 withpen pencircle scaled 0.05u; z8=1/5[z0,z1]+1/2[z0,z2]; z9=3/5[z4,z5]+1/2[z6,z4]; draw z8--z9; z10 = z8 transformed S; draw z8--z10; 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; draw z10--z12; draw z12--z13 dashed evenly; draw z13--z14; draw z14--z11 dashed evenly; p2 = z8--z10; z15 = p2 intersectionpoint q1; draw z2--z15; draw z15--z12 dashed evenly; draw z12--z3; p3 = z8--z9; z16 = p3 intersectionpoint q2; z17 = p3 intersectionpoint q3; q4 = z4--z5; z18 = p3 intersectionpoint q4; draw z16--z12; draw z6--z17; draw z17--z14 dashed evenly; draw z14--z7; draw z18--z14; p4 = z9--z11; z19 = p4 intersectionpoint q4; draw z9--z19;draw z19--z11 dashed evenly; label.rt(btex $d$ etex scaled echelle, 0.5[z12,z16]); label.rt(btex $d'$ etex scaled echelle, 0.5[z18,z14]); label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); label.urt(btex $\tmplabelespace{Q}$ etex scaled echelle, z4+(0.1u,0u)); endfig; \end{mplibcode} }% {droiteparaplans}{% \begin{mplibcode}[PfLAI] beginfig(64); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % droite parallele a deux plans secants pair t,r; transform T,S; path p[]; pickup pencircle scaled 0.025u; t=(4u,1u); r=(0u,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; draw z0--z2; draw z2--z3; draw z1--z3; z4=0.5[z0,z1]; z5 = z4 transformed S; draw z4--z5; label.lft(btex $\Delta$ etex scaled echelle,0.5[z4,z5]); z6 = z4 shifted (1.5u,-1u); z4=0.5[z6,z7]; z8 = z6 transformed S; z9 = z7 transformed S; draw z0--z4; draw z4--z6; draw z6--z8; draw z8--z9; draw z4--z7 dashed evenly; p1= z4--z1; p2 = z6--z8; z10 = p1 intersectionpoint p2; draw z4--z10 dashed evenly;draw z10--z1; p3 = z2--z3; p4 = z9--z7; z11 = p3 intersectionpoint p4; draw z11--z9; draw z11--z7 dashed evenly; draw z7--z4 dashed evenly; z12 = (-1u,0u); z13 = z12 shifted (0u,3u); draw z13--z12; label.lft(btex $d$ etex scaled echelle, z12); label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0u,0.025u)); label.lft(btex $\tmplabelespace{Q}$ etex scaled echelle, z6+(0u,0.5u)); endfig; \end{mplibcode} }% {toit}{% \begin{mplibcode}[PfLAJ] beginfig(65); numeric u,echelle; u=\scaleminischemspace*1cm; echelle=\scaleminischemspace; % theoreme du toit pair t,r,v; transform T,S,V; path p[]; pickup pencircle scaled 0.025u; 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; draw z0--z1; draw z2--z3; 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; draw z101--z23; draw z10--z32; draw z23--z45; draw z32--z54 dashed evenly; p1 = z101--z23; p2 = z4--z5; z11 = p1 intersectionpoint p2; draw z4--z11; draw z11--z5 dashed evenly; label.lft(btex $d$ etex scaled echelle, z0); label.lft(btex $d'$ etex scaled echelle, z4); label.top(btex $\Delta$ etex scaled echelle, z2); endfig; \end{mplibcode} }% {planspara}{% \begin{mplibcode}[PfLAK] beginfig(66); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % plans paralleles a l'aide de droites secantes pair t,r; transform T,S; pickup pencircle scaled 0.025u; 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; draw z0--z2; draw z2--z3; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; 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 scaled echelle, z5); label.rt(btex $d'$ etex scaled echelle, z7); z10=(0u,-2.5u); z11 = z10 transformed T; z12 = z10 transformed S; z13 = z10 transformed T transformed S; draw z10--z12; draw z12--z13; draw z10--z11 withpen pencircle scaled 0.05u; draw z11--z13 withpen pencircle scaled 0.05u; 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 scaled echelle, z15); label.rt(btex $d'_{1}$ etex scaled echelle, z17); label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); label.urt(btex $\tmplabelespace{Q}$ etex scaled echelle, z10+(0.1u,0u)); endfig; \end{mplibcode} }% {droiteplanpara}{% \begin{mplibcode}[PfLAL] beginfig(67); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % parallelisme plan et droite pair t,r; transform T,S; pickup pencircle scaled 0.025u; 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; draw z0--z2; draw z2--z3; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; z4 = (1u,.5u); z5 = (4u,1u); draw z4--z5; label.top(btex $d'$ etex scaled echelle, z4); z6 = (1u,2.5u); z7 = z6 shifted z5-z4; draw z6--z7; label.top(btex $d$ etex scaled echelle, z6); label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); endfig; \end{mplibcode} }% {droitesortho}{% \begin{mplibcode}[PfLAM] beginfig(68); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % droites orthogonales pair t,r; transform T,S; pickup pencircle scaled 0.025u; t=(2u,3u); r=(0u,2u); T = identity shifted t; S = identity shifted r; z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; draw z0--z1; draw z0--z2; label.bot(btex $I$ etex scaled echelle, z0); z3=0.1[z0,z1]; z4=0.1[z0,z2]; z5=z3 shifted z4-z0; draw z3--z5; draw z4--z5; z6=(0u,-1u); z7 = z6 transformed T; draw z7--z6; label.bot(btex $\Delta$ etex scaled echelle, z7); z8=(-1u,-1u); z9= z8 transformed S; label.lft(btex $d$ etex scaled echelle, z9); draw z9--z8; endfig; \end{mplibcode} }% {droiteorthoplan}{% \begin{mplibcode}[PfLAN] beginfig(69); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % droite orthogonale a un plan pair t,r; transform T,S; path p[]; pickup pencircle scaled 0.025u; 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; draw z0--z2; draw z2--z3; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; 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 scaled echelle, z5); label.rt(btex $d'$ etex scaled echelle, z7); p1 = z4--z5;p2 = z6--z7; z8 = p1 intersectionpoint p2; z9 = z8 shifted (0u,2u); label.rt(btex $\Delta$ etex scaled echelle, 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; 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; label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); endfig; \end{mplibcode} }% {plansparadroiteortho}{% \begin{mplibcode}[PfLAO] beginfig(7); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % plans paralleles et droite orthogonale pair t,r; transform T,S; pickup pencircle scaled 0.025u; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; path p[]; z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; draw z0--z2; draw z2--z3; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; 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 scaled echelle, z5); label.rt(btex $d'$ etex scaled echelle, z7); z10=(0u,-2.5u); z11 = z10 transformed T; z12 = z10 transformed S; z13 = z10 transformed T transformed S; draw z10--z12; draw z12--z13; draw z10--z11 withpen pencircle scaled 0.05u; draw z11--z13 withpen pencircle scaled 0.05u; 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 scaled echelle, z15); label.rt(btex $d'_{1}$ etex scaled echelle, z17); 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 scaled echelle, z24); 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; label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); label.urt(btex $\tmplabelespace{Q}$ etex scaled echelle, z10+(0.1u,0u)); endfig; \end{mplibcode} }% {plansparadroitesortho}{% \begin{mplibcode}[PfLAP] beginfig(71); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % droites orthogonales a deux plans paralleles pair t,r; transform T,S; pickup pencircle scaled 0.025u; t=(4u,0u); r=(1u,2u); T = identity shifted t; S = identity shifted r; path p[]; z0=(0u,0u); z1 = z0 transformed T; z2 = z0 transformed S; z3 = z0 transformed T transformed S; draw z0--z2; draw z2--z3; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; z10=(0u,-2.5u); z11 = z10 transformed T; z12 = z10 transformed S; z13 = z10 transformed T transformed S; draw z10--z12; draw z12--z13; draw z10--z11 withpen pencircle scaled 0.05u; draw z11--z13 withpen pencircle scaled 0.05u; 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; 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; 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; label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); label.urt(btex $\tmplabelespace{Q}$ etex scaled echelle, z10+(0.1u,0u)); endfig; \end{mplibcode} }% {plansperp}{% \begin{mplibcode}[PfLAQ] beginfig(72); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % intersection de deux plans perpendiculaires pair t,r; transform T,S; path p[],q[]; pickup pencircle scaled 0.025u; 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; draw z0--z2; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; 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; draw z5--z6; draw z9--z7; draw z9--z10; draw z10--z6; draw z6--z3; draw z7--z8; p1 = z2--z6; q1= z5--z9; z11 = p1 intersectionpoint q1; draw z11--z6 dashed evenly; draw z2--z11; p2 = z6--z8; q2= z5--z1; z12 = p2 intersectionpoint q2; draw z12--z6 dashed evenly; draw z8--z12; label.rt(btex $d$ etex scaled echelle, 0.6[z5,z6]); 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; 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; z30=0.1[z13,z18];z31=0.1[z13,z14]; z32 = z31 shifted z30-z13; draw z32--z30; draw z32--z31; label.urt(btex $\tmplabelespace{P}$ etex scaled echelle, z0+(0.1u,0.025u)); label.rt(btex $\tmplabelespace{Q}$ etex scaled echelle, z9); endfig; \end{mplibcode} }% {plansperpplan}{% \begin{mplibcode}[PfLAR] beginfig(73); numeric u,echelle; u=\scaleminischemspace*1cm;echelle=\scaleminischemspace; % plans perpendiculaires a un meme plan pair t,r; transform T,S; path p[],q[]; pickup pencircle scaled 0.025u; t=(5u,0u); r=(1u,2.3u); 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; draw z0--z2; draw z0--z1 withpen pencircle scaled 0.05u; draw z1--z3 withpen pencircle scaled 0.05u; z4= 1/4[z0,z1]; z5= 3/4[z0,z1]; z6= 1/2[z4,z5]; z7 = z6 shifted (0u,1u); draw z4--z7; draw z5--z7; 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]; 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; p1 = z2--z3; q1 = z8--z10; q2=z9--z10; z14= p1 intersectionpoint q1; z15= p1 intersectionpoint q2; draw z2--z14; draw z14--z15 dashed evenly; draw z15--z3; 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.urt(btex $\tmplabelespace{Q}$ etex scaled echelle, z0+(0.1u,0.025u)); label.bot(btex $\tmplabelespace{P}$ etex scaled echelle, z11+(0.2u,0.6u)); label.bot(btex $\tmplabelespace{P}'$ etex scaled echelle, z12+(-0.2u,0.8u)); endfig; \end{mplibcode} }% }% \else% La commande nécessite \hologo{LuaLaTeX} !% % \else% % \IfStrEqCase{#3}{% % {plan}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repplansimple ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % \end{mpost} % }% % {interplans}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repinterplan ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % label.rt(btex $Q$ etex scaled echelle, z9); % \end{mpost} % }% % {plan3points}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repplantroispoints ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % \end{mpost} % }% % {plandroitessecantes}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repplandeuxdroites ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % \end{mpost} % }% % {plandroitepoint}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repplandroite ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % \end{mpost} % }% % {plandroitespara}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repplandtespara ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % \end{mpost} % }% % {droitesnoncopla}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % droitesnoncoplan ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % \end{mpost} % }% % {incidence}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repincidence ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % label.urt(btex $Q$ etex scaled echelle, z4+(0.1u,0u)); % \end{mpost} % }% % {droiteparaplans}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repdroiteparaplans ; % label.urt(btex $P$ etex scaled echelle, z0+(0u,0.025u)); % label.lft(btex $Q$ etex scaled echelle, z6+(0u,0.5u)); % \end{mpost} % }% % {toit}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % reptoit ; % \end{mpost} % }% % {planspara}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repplanspara ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % label.urt(btex $Q$ etex scaled echelle, z10+(0.1u,0u)); % \end{mpost} % }% % {droiteplanpara}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repdteplanpara ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % \end{mpost} % }% % {droitesortho}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repdtesortho ; % \end{mpost} % }% % {droiteorthoplan}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repdroiteorthoplan ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % \end{mpost} % }% % {plansparadroiteortho}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repplansparadroiteortho ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % label.urt(btex $Q$ etex scaled echelle, z10+(0.1u,0u)); % \end{mpost} % }% % {plansparadroitesortho}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repdrtoitesorthoplanspara ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % label.urt(btex $Q$ etex scaled echelle, z10+(0.1u,0u)); % \end{mpost} % }% % {plansperp}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repplansperp ; % label.urt(btex $P$ etex scaled echelle, z0+(0.1u,0.025u)); % label.rt(btex $Q$ etex scaled echelle, z9); % \end{mpost} % }% % {plansperpplan}{% % \begin{mpost}[mpsettings={u=\scaleminischemspace*1cm;echelle=\scaleminischemspace;}] % input PfLEspace; % repplansperpplan ; % label.urt(btex $Q$ etex scaled echelle, z0+(0.1u,0.025u)); % label.bot(btex $P$ etex scaled echelle, z11+(0.2u,0.6u)); % label.bot(btex $P'$ etex scaled echelle, z12+(-0.2u,0.8u)); % \end{mpost} % }% % }% \fi% } \NewCommandCopy\pflschemesp\SchemaEspace \endinput