%%[slideshow] \input slideshow; author("Christophe Poulain & Régis Leclercq"); title("Construction de la parallèle à une droite passant par un point"); %%[navigation] \input navigation; couleurboutons:=(1,1,0.3); couleurfond:=(0,0,0.7); %% Choix de LaTeX verbatimtex %&latex \documentclass[a4paper]{article} \usepackage[latin1]{inputenc} \usepackage[frenchb]{babel} \begin{document} etex %%[geometrie] input geometrie2; %%[Image] picture cp; cp=thelabel(btex \sf C.POULAIN -- 2002 etex scaled 0.5,(0.90lawidth,0.03laheight)); footer(image(draw cp withcolor blue;)); %% -- navigation PDF & logos def navPDFlogos = init_navigation; navigation; internavigation; enddef; extra_endfig := extra_endfig & "navPDFlogos;"; % gs will need this prologues:=2; %fond d'écran noslides := 11; def doback = background := image(drawgradient((charcode/noslides)[white,white], (charcode/noslides)[white,white]);); enddef; doback; %%cadre path cadre; cadre=(0.05lawidth,0.9laheight)--(0.95lawidth,0.9laheight)--(0.95lawidth,0.98laheight)--(0.05lawidth,0.98laheight)--cycle; draw cadre; %% -- instructions color C[]; C6=0.8white; vardef instruction(expr s) = fill cadre withcolor C6; label.rt(s,p100); enddef; %[Points] pair c[],largeur,hauteur,p[],i[],q[],r[]; c0=(0.578125lawidth,0.5laheight); largeur=(0.15625lawidth,0); hauteur=(0,0.20833laheight);%5/24 c1=c0 shifted hauteur; c2=c0 shifted (hauteur-largeur); c3=c0 shifted (-largeur); c4=c0 shifted ((3/5)*(-hauteur-largeur)); c5=c4 shifted hauteur; c6=c4 shifted (hauteur-largeur); c7=c4 shifted (-largeur); c8=(c0--c3) intersectionpoint (c4--c5); c9=(c2--c3) intersectionpoint (c6--c5); p4=c0 shifted largeur; p5=c1 shifted largeur; p6=c2 shifted (-largeur); p7=c3 shifted (-largeur); p0=c0 shifted (-2*hauteur); p3=c3 shifted (-2*hauteur); q5=c1 shifted hauteur; q6=c2 shifted hauteur; r5=c4 shifted ((3/5)*(-largeur-hauteur)); r6=c7 shifted ((3/5)*(-largeur-hauteur)); vues=5; path fleche[]; fleche1=c5{dir0}..p5{dir90}; fleche2=c5{dir90}..q5{dir0}; fleche3=c5{dir180}..r5{dir-90}; fleche4=c7{dir180}..p7{dir90}; fleche5=r5{dir-90}..p0{dir0}; nextfig; draw c5--c6--c7--c4--cycle; draw c0--c1--c5--c4--cycle; draw c1--c2--c6; draw c2--c3--c0 dashed evenly; draw c3--c7 dashed evenly; endfig; for vue=0 upto vues : nextfig; if vue=0 : draw c5--c6--c7--c4--cycle; draw c0--c1--c5--c4--cycle; draw c1--c2--c6; draw c2--c3--c0 dashed evenly; draw c3--c7 dashed evenly; drawarrow subpath(0,vue*(length fleche1)/vues) of fleche1 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche1)/vues) of fleche1 shifted (-hauteur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c0--c1--(point(vue*(length fleche1)/vues) of fleche1)--(point(vue*(length fleche1)/vues) of fleche1 shifted (-hauteur))--cycle withcolor red; fi if vue=1 : i1=(c3--c0) intersectionpoint ((point(vue*(length fleche1)/vues) of fleche1)--(point(vue*(length fleche1)/vues) of fleche1 shifted (-hauteur))); draw c2--c3--c8 dashed evenly; draw c8--i1; draw i1--c0 dashed evenly; draw c5--c6--c7--c4--cycle; draw c0--c1--c5--c4--cycle; draw c1--c2--c6; draw c2--c3--c0 dashed evenly; draw c3--c7 dashed evenly; drawarrow subpath(0,vue*(length fleche1)/vues) of fleche1 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche1)/vues) of fleche1 shifted (-hauteur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c0--c1--(point(vue*(length fleche1)/vues) of fleche1)--(point(vue*(length fleche1)/vues) of fleche1 shifted (-hauteur))--cycle withcolor red; fi if vue>1 : draw c5--c6--c7--c4--cycle; draw c0--c1--c5--c4--cycle; draw c1--c2--c6; draw c8--c0; draw c2--c3--c8 dashed evenly; draw c3--c7 dashed evenly; drawarrow subpath(0,vue*(length fleche1)/vues) of fleche1 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche1)/vues) of fleche1 shifted (-hauteur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c0--c1--(point(vue*(length fleche1)/vues) of fleche1)--(point(vue*(length fleche1)/vues) of fleche1 shifted (-hauteur))--cycle withcolor red; fi endfig; discontinue; endfor nextfig; draw p4--p5--c2--c6--c7--c4--c0--cycle; draw c6--c5--c1--c0; draw c5--c4; draw c2--c3--c7 dashed evenly; draw c3--c8 dashed evenly; draw c8--c0; endfig; for vue=0 upto vues : nextfig; if vue=0 : draw p4--p5--c2--c6--c7--c4--c0--cycle; draw c6--c5--c4; draw c1--c0; draw c2--c3--c7 dashed evenly; draw c3--c8 dashed evenly; draw c8--c0; drawarrow subpath(0,vue*(length fleche2)/vues) of fleche2 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche2)/vues) of fleche2 shifted (-largeur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c1--c2--(point(vue*(length fleche2)/vues) of fleche2 shifted (-largeur))--(point(vue*(length fleche2)/vues) of fleche2)--cycle withcolor red; fi if vue=1 : i2=(c3--c2) intersectionpoint ((point(vue*(length fleche2)/vues) of fleche2)--(point(vue*(length fleche2)/vues) of fleche2 shifted (-largeur))); i3=(c6--c2) intersectionpoint ((point(vue*(length fleche2)/vues) of fleche2)--(point(vue*(length fleche2)/vues) of fleche2 shifted (-largeur))); draw c0--p4--p5--c1--c0--c4--c5--c6--c7--c4; draw c2--i3 dashed evenly; draw i3--c6; draw c6--c5--c4; draw c1--c0; draw c2--i2 dashed evenly; draw i2--c9; draw c9--c3--c7 dashed evenly; draw c3--c8 dashed evenly; draw c8--c0; drawarrow subpath(0,vue*(length fleche2)/vues) of fleche2 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche2)/vues) of fleche2 shifted (-largeur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c1--c2--(point(vue*(length fleche2)/vues) of fleche2 shifted (-largeur))--(point(vue*(length fleche2)/vues) of fleche2)--cycle withcolor red; fi if vue>1 : draw c0--p4--p5--c1--c0--c4--c5--c6--c7--c4; draw c2--c6--c5--c4; draw c1--c0; draw c2--c9; draw c9--c3--c7 dashed evenly; draw c3--c8 dashed evenly; draw c8--c0; drawarrow subpath(0,vue*(length fleche2)/vues) of fleche2 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche2)/vues) of fleche2 shifted (-largeur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c1--c2--(point(vue*(length fleche2)/vues) of fleche2 shifted (-largeur))--(point(vue*(length fleche2)/vues) of fleche2)--cycle withcolor red; fi endfig; discontinue; endfor nextfig; draw c0--p4--p5--c1--c0--c4--c5--c6--c7--c4; draw c2--c6--c5--c4; draw c1--c0; draw c2--c9; draw c9--c3--c7 dashed evenly; draw c3--c8 dashed evenly; draw c8--c0; draw c1--c2--point(length fleche2) of fleche2 shifted (-largeur)--point(length fleche2) of fleche2--cycle; endfig; for vue=0 upto vues : nextfig; if vue=0 : draw c0--p4--p5--c1--c0--c4--c5--c6--c7--c4; draw c2--c6--c5--c4; draw c1--c0; draw c2--c9; draw c9--c3--c7 dashed evenly; draw c3--c8 dashed evenly; draw c8--c0; draw c1--c2--point(length fleche2) of fleche2 shifted (-largeur)--point(length fleche2) of fleche2--cycle; drawarrow subpath(0,vue*(length fleche3)/vues) of fleche3 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche3)/vues) of fleche3 shifted (-largeur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c4--c7--(point(vue*(length fleche3)/vues) of fleche3 shifted (-largeur))--(point(vue*(length fleche3)/vues) of fleche3)--cycle withcolor red; fi if vue=1 : draw c6--c2--q6--q5--c1--p5--p4--c0--c4; draw c2--c1--c0; draw c2--c9; i4=((point(vue*(length fleche3)/vues) of fleche3 shifted (-largeur))--(point(vue*(length fleche3)/vues) of fleche3)) intersectionpoint (c2--c3); draw c2--i4; draw i4--c3 dashed evenly; i5=((point(vue*(length fleche3)/vues) of fleche3 shifted (-largeur))--(point(vue*(length fleche3)/vues) of fleche3)) intersectionpoint (c6--c7); draw c6--i5; draw i5--c7 dashed evenly; i6=(c4--(point(vue*(length fleche3)/vues) of fleche3)) intersectionpoint (c3--c0); draw c9--c3--c7 dashed evenly; draw c3--i6 dashed evenly; draw i6--c0; drawarrow subpath(0,vue*(length fleche3)/vues) of fleche3 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche3)/vues) of fleche3 shifted (-largeur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c4--c7--(point(vue*(length fleche3)/vues) of fleche3 shifted (-largeur))--(point(vue*(length fleche3)/vues) of fleche3)--cycle withcolor red; fi if vue=2 : draw c6--c2--q6--q5--c1--p5--p4--c0--c4; draw c2--c1--c0; draw c2--c9; draw c2--c3; i7=((point(vue*(length fleche3)/vues) of fleche3 shifted (-largeur))--(point(vue*(length fleche3)/vues) of fleche3)) intersectionpoint (c6--c7); draw c6--i7; draw i7--c7 dashed evenly; draw c3--c0; i8=(c4--(point(vue*(length fleche3)/vues) of fleche3)) intersectionpoint (c3--c7); draw i8--c7 dashed evenly; draw c3--i8; drawarrow subpath(0,vue*(length fleche3)/vues) of fleche3 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche3)/vues) of fleche3 shifted (-largeur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c4--c7--(point(vue*(length fleche3)/vues) of fleche3 shifted (-largeur))--(point(vue*(length fleche3)/vues) of fleche3)--cycle withcolor red; fi if vue=3 : draw c6--c2--q6--q5--c1--p5--p4--c0--c4; draw c2--c1--c0; draw c2--c9; draw c2--c3; i9=((point(vue*(length fleche3)/vues) of fleche3 shifted (-largeur))--(point(vue*(length fleche3)/vues) of fleche3)) intersectionpoint (c6--c7); draw c6--i9; draw i9--c7 dashed evenly; draw c3--c0; i10=((point(vue*(length fleche3)/vues) of fleche3 shifted (-largeur))--(point(vue*(length fleche3)/vues) of fleche3)) intersectionpoint (c3--c7); draw i10--c7 dashed evenly; draw c3--i10; drawarrow subpath(0,vue*(length fleche3)/vues) of fleche3 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche3)/vues) of fleche3 shifted (-largeur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c4--c7--(point(vue*(length fleche3)/vues) of fleche3 shifted (-largeur))--(point(vue*(length fleche3)/vues) of fleche3)--cycle withcolor red; fi if vue>3 : draw c6--c2--q6--q5--c1--p5--p4--c0--c4; draw c2--c1--c0; draw c2--c9; draw c2--c3; draw c6--c7; draw c3--c0; draw c3--c7; drawarrow subpath(0,vue*(length fleche3)/vues) of fleche3 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche3)/vues) of fleche3 shifted (-largeur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c4--c7--(point(vue*(length fleche3)/vues) of fleche3 shifted (-largeur))--(point(vue*(length fleche3)/vues) of fleche3)--cycle withcolor red; fi endfig; discontinue; endfor; nextfig; draw c6--c2--q6--q5--c1--p5--p4--c0--c4; draw c2--c1--c0; draw c2--c9; draw c2--c3; draw c6--c7; draw c3--c0; draw c3--c7; draw c4--c7--point(length fleche3) of fleche3 shifted (-largeur)--point(length fleche3) of fleche3--cycle; endfig; for vue=0 upto 5 : nextfig; draw r6--c3--q6--q5--c1--p5--p4--c0--r5--cycle; draw c2--c1--c0--c3; draw c7--c4; drawarrow subpath(0,vue*(length fleche4)/vues) of fleche4 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche4)/vues) of fleche4 shifted (hauteur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c3--c2--(point(vue*(length fleche4)/vues) of fleche4 shifted (hauteur))--(point(vue*(length fleche4)/vues) of fleche4)--cycle withcolor red; endfig; discontinue; endfor nextfig; draw r6--c3--q6--q5--c1--p5--p4--c0--r5--cycle; draw c2--c1--c0--c3; draw c7--c4; draw c3--p7--p6--c2; endfig; for vue=0 upto vues : nextfig; pair mi[],mil[]; if vue=0 : draw r6--c3--q6--q5--c1--p5--p4--c0--r5--cycle; draw c2--c1--c0--c3; draw c7--c4; draw c3--p7--p6--c2; mi[vue]=milieu(c3,(point(vue*(length fleche5)/vues) of fleche5 shifted (-largeur))); mil[vue]=mi[vue] shifted (largeur); draw mi[vue]--mil[vue] withcolor red; drawarrow subpath(0,vue*(length fleche5)/vues) of fleche5 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche5)/vues) of fleche5 shifted (-largeur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c0--c3--(point(vue*(length fleche5)/vues) of fleche5 shifted (-largeur))--(point(vue*(length fleche5)/vues) of fleche5)--cycle withcolor red; fi if vue>0 : draw c3--q6--q5--c1--p5--p4--c0--cycle; draw c2--c1--c0--c3; draw c3--p7--p6--c2; mi[vue]=milieu(c3,(point(vue*(length fleche5)/vues) of fleche5 shifted (-largeur))); mil[vue]=mi[vue] shifted (largeur); draw mi[vue]--mil[vue] withcolor red; drawarrow subpath(0,vue*(length fleche5)/vues) of fleche5 dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); drawarrow subpath(0,vue*(length fleche5)/vues) of fleche5 shifted (-largeur) dashed dashpattern(on 12bp off 6bp on 3bp off 6bp); draw c0--c3--(point(vue*(length fleche5)/vues) of fleche5 shifted (-largeur))--(point(vue*(length fleche5)/vues) of fleche5)--cycle withcolor red; fi endfig; discontinue; endfor nextfig; draw c3--q6--q5--c1--p5--p4--c0--cycle; draw c2--c1--c0--c3; draw c3--p7--p6--c2; %mi[]=milieu(c3,(point(vue*(length fleche5)/vues) of fleche5 shifted (-largeur))); %mil[vue]=mi[vue] shifted (largeur); draw mi[5]--mil[5]; draw c0--c3--point(length fleche5) of fleche5 shifted (-largeur)--point(length fleche5) of fleche5--cycle; endfig; end