%%=============================================== %% GEOMETRIESYR.MP %% christophe.poulain@melusine.eu.org %% Création : 19 Février 2003 %% Dernière modification : 04 Mars 2004 %%=============================================== %------------------------------------------------ % Appel fichier %------------------------------------------------ input constantes; input papiers1; %------------------------------------------------ % La figure (début et fin) JMS/CP %------------------------------------------------ path feuillet; numeric _tfig,_nfig; pair coinbg,coinbd,coinhd,coinhg; _nfig:=0; def feuille(expr xa,ya,xb,yb) = feuillet := (xa,ya)--(xa,yb)--(xb,yb)--(xb,ya)--cycle; coinbg := (xa,ya); coinbd := (xb,ya); coinhd := (xb,yb); coinhg := (xa,yb); z.so=coinbg; z.ne=coinhd; extra_endfig := "clip currentpicture to feuillet;" & extra_endfig; enddef; def figure(expr xa,ya,xb,yb) = _nfig:=_nfig+1; beginfig(_nfig); feuille(xa,ya,xb,yb); _tfig:= if (xb-xa)>(yb-ya): xb-xa else: yb-ya fi; enddef; def fin = endfig; enddef; %%----------------------------------------------- %% Les marques (JMS) %%----------------------------------------------- string marque_p; marque_p := "non"; marque_r := 20; marque_a := 20; %------------------------------------------------ % Les tables %------------------------------------------------ numeric _tn; _tn:=0; pair _t[]; %%----------------------------------------------- %% Procédures d'affichage %%----------------------------------------------- def MarquePoint(expr p)= %JMS if marque_p = "plein": fill fullcircle scaled (marque_r/5) shifted p; elseif marque_p = "creux": fill fullcircle scaled (marque_r/5) shifted p withcolor white; draw fullcircle scaled (marque_r/5) shifted p; %fin JMS elseif marque_p = "croix": draw (p shifted (-u/10,u/10))--(p shifted (u/10,-u/10)); draw (p shifted (-u/10,-u/10))--(p shifted (u/10,u/10)); fi enddef; %JMS vardef pointe(text t) = for p_ = t: if pair p_: MarquePoint(p_); fi endfor; enddef; vardef nomme@#(suffix p)= MarquePoint(p); label.@#(str p,p); enddef; def trace expr o = if path o: draw o else: draw o fi enddef; def remplis expr o = if path o: fill o else: fill o fi enddef; vardef triangle(expr aa,bb,cc)=aa--bb--cc--cycle enddef; %fin JMS vardef bary(expr a,b,c,d)= save $; pair $; numeric t[]; t1=uniformdeviate(1); t2=uniformdeviate(1); t3=uniformdeviate(1); t4=uniformdeviate(1); $=(1/(t1+t2+t3+t4))*(t1*a+t2*b+t3*c+t4*d); $ enddef; vardef triangleqcq(text t)= save $; path $; pair pointchoisi[]; pointchoisi1:=bary(coinbg,1/4[coinbg,coinbd],iso(coinbg,iso(coinhg,coinhd)),iso(coinhg,coinbg)); pointchoisi2:=bary(coinbd,3/4[coinbg,coinbd],iso(coinbd,iso(coinhg,coinhd)),iso(coinhd,coinbd)); test:=uniformdeviate(1); choix:=43+uniformdeviate(4); ecart:=abs(45-choix); relation:=60-(ecart/2)+uniformdeviate(ecart); if test<0.5 : pointchoisi3:=droite(pointchoisi1,rotation(pointchoisi2,pointchoisi1,choix)) intersectionpoint droite(pointchoisi2,rotation(pointchoisi1,pointchoisi2,-relation)); else : pointchoisi3:=droite(pointchoisi2,rotation(pointchoisi1,pointchoisi2,-choix)) intersectionpoint droite(pointchoisi1,rotation(pointchoisi2,pointchoisi1,relation)); fi j:=1; for p_=t: p_=pointchoisi[j]; j:=j+1; endfor; $=pointchoisi1--pointchoisi2--pointchoisi3--cycle; $ enddef; %------------------------------------------------ % Procédures de codage %------------------------------------------------ %Codage de l'angle droit de sommet B vardef codeperp(expr aa,bb,cc,m)=%normalement m=5 (bb+m*unitvector(aa-bb))--(bb+m*unitvector(aa-bb)+m*unitvector(cc-bb))--(bb+m*unitvector(cc-bb)) enddef; %Codage d'un milieu vardef codemil(expr AA,BB, n) =%extrêmités-angle de codage save $,a,b,c,d; path $; pair a,b,c,d; a=1/2[AA,BB]; b=(a+2*unitvector(BB-AA))-(a-2*unitvector(BB-AA)); c=b rotated n shifted a; d=2[c,a]; $=c--d; $ enddef; %Codage de deux segments égaux vardef codesegments(expr AA,BB,CC,DD,n)=%extrémités des segments(4)-type de codage save $,v,w; picture $; $=image( if n=5 : draw fullcircle scaled 0.1cm shifted (1/2[AA,BB]); draw fullcircle scaled 0.1cm shifted (1/2[CC,DD]); elseif n=4 : pair v,w; v=1/2[AA,BB]; w=1/2[CC,DD]; draw codemil(AA,BB,60); draw codemil(AA,BB,120); draw codemil(CC,DD,60); draw codemil(CC,DD,120); elseif n=3 : draw codemil(AA,BB,60); draw codemil(AA,BB,60) shifted (2*unitvector(AA-BB)); draw codemil(AA,BB,60) shifted (2*unitvector(BB-AA)); draw codemil(CC,DD,60); draw codemil(CC,DD,60) shifted (2*unitvector(CC-DD)); draw codemil(CC,DD,60) shifted (2*unitvector(DD-CC)); elseif n=2 : draw codemil(AA,BB,60) shifted unitvector(AA-BB); draw codemil(AA,BB,60) shifted unitvector(BB-AA); draw codemil(CC,DD,60) shifted unitvector(CC-DD); draw codemil(CC,DD,60) shifted unitvector(DD-CC); elseif n=1 : draw codemil(AA,BB,60); draw codemil(CC,DD,60); fi; ); $ enddef; %Codage de l'angle abc non orienté (mais donné dans le sens direct) n fois avec des mesures différentes vardef codeangle@#(expr aa,bb,cc,nb,ecart,nom)= save s,p,$; path p; picture $; $=image( pickup pencircle scaled 0.25bp; for j=0 upto (nb-1) : draw arccercle(((ecart+j*mm)*unitvector(aa-bb) shifted bb),((ecart+j*mm)*unitvector(cc-bb) shifted bb),bb); endfor; label.@#(nom,iso((ecart+nb*mm)*unitvector(aa-bb) shifted bb,(ecart+nb*mm)*unitvector(cc-bb) shifted bb)); ); $ enddef; vardef marqueangle(expr aa,bb,cc,mark)=%codage d'un angle de sommet bb dans le sens direct par la marque mark. save $; picture $; path rr; pair w; pair tangent; numeric t; rr=arccercle(bb+marque_a*unitvector(aa-bb),bb+marque_a*unitvector(cc-bb),bb); w=rr intersectionpoint droite(bb,CentreCercleI(aa,bb,cc)); t=length rr/2; tangent=unitvector(direction t of rr); $=image( trace rr; if mark=1: trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90); elseif mark=2: trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90) shifted tangent; trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90) shifted(-tangent); elseif mark=3: trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90); trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90) shifted(1.5*tangent); trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90) shifted(-1.5*tangent); elseif mark=4: trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,45); trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,-45); fi; ); $ enddef; vardef coloreangle(expr aa,bb,cc)=arccercle(bb+marque_a*unitvector(aa-bb),bb+marque_a*unitvector(cc-bb),bb)--bb--cycle enddef; vardef marque_para(expr dd,ee,pa)= save im; picture im; pair kk,ll,mn,mo; kk=point(pa*length dd) of dd; ll=projection(kk,point(0.25*length ee) of ee,point(0.5*length ee) of ee); mn=iso(kk,ll); mo=(mn--kk) intersectionpoint cercles(mn,3mm); im=image( drawarrow mo--kk; drawarrow symetrie(mo,mn)--ll; label(btex $//$ etex,mn); ); im enddef; %------------------------------------------------ % Points %------------------------------------------------ %JMS vardef iso(text t) = save s,n; numeric n; pair s; s := (0,0) ; n := 0; for p_ = t: s := s + p_; n := n + 1 ; endfor; if n>0: (1/n)*s fi enddef; % -- projection de m sur (a,b) vardef projection(expr m,a,b) = save h; pair h; h - m = whatever * (b-a) rotated 90; h = whatever [a,b]; h enddef; % -- centre du cercle circonscrit vardef CentreCercleC(expr a, b ,c) = save o; pair o; o - .5[a,b] = whatever * (b-a) rotated 90; o - .5[b,c] = whatever * (c-b) rotated 90; o enddef; % -- orthocentre vardef Orthocentre(expr a, b, c) = save h; pair h; h - a = whatever * (c-b) rotated 90; h - b = whatever * (a-c) rotated 90; h enddef; %fin JMS vardef CentreCercleI(expr aa,bb,cc)= save $,a,c; pair $; numeric a,c; a=(angle(aa-cc)-angle(bb-cc))/2; c=(angle(cc-bb)-angle(aa-bb))/2; ($-cc) rotated a shifted cc=whatever[aa,cc]; ($-bb) rotated c shifted bb=whatever[bb,cc]; $ enddef; %------------------------------------------------ % Cercles %------------------------------------------------ %Cercle connaissant le centre A et le rayon q vardef cercle(expr aa, q)=fullcircle scaled (2*q) shifted aa enddef; %Cercle de centre A et passant par B vardef cerclepoint(expr aa,bb)=fullcircle scaled (2*abs(aa-bb)) shifted aa enddef; %Cercle connaissant le diamètre [AB] vardef cercledia(expr aa,bb)= fullcircle scaled (2*abs(1/2[aa,bb]-bb)) shifted (1/2[aa,bb]) enddef; %Cercles complets vardef cercles(text t)= save $; path $; save n; n:=0; for p_=t: if pair p_: n:=n+1; _t[n]:=p_; fi if numeric p_: rayon:=p_; fi; endfor; if n=1 : $=fullcircle scaled (2*rayon) shifted _t[1]; elseif n=2 : $=fullcircle scaled (2*abs(_t[1]-_t[2])) shifted _t[1]; elseif n=3 : $=cercles(CentreCercleC(_t[1],_t[2],_t[3]),_t[1]); fi $ enddef; %Point particulier sur le cercle vardef pointarc(expr cercla,angle)= point(arctime((angle/360)*arclength cercla) of cercla) of cercla enddef; %Arc de cercle AB de centre 0(dans le sens direct) : les points A et B doivent être sur le cercle. vardef arccercle(expr aa,bb,oo)= path tempo; path arc; tempo=cercle(oo,abs(aa-oo)); if (angle(aa-oo)=0) or (angle(aa-oo)>0) : if (angle(bb-oo)=0) or (angle(bb-oo)>0): if (angle(aa-oo)<=angle(bb-oo)): arc=subpath(angle(aa-oo)*(length tempo)/360,angle(bb-oo)*(length tempo)/360) of tempo; else: arc=subpath(angle(aa-oo)*(length tempo)/360,(length tempo)+angle(bb-oo)*(length tempo)/360) of tempo; fi; else : if (angle(aa-oo)=angle(bb-oo)) or (angle(aa-oo)>angle(bb-oo)): arc=subpath(angle(aa-oo)*(length tempo)/360,(length tempo)+angle(bb-oo)*(length tempo)/360) of tempo; fi; fi; else: if (angle(bb-oo)<0): if (angle(aa-oo)<=angle(bb-oo)): arc=subpath((length tempo)+angle(aa-oo)*(length tempo)/360,(length tempo)+angle(bb-oo)*(length tempo)/360) of tempo; else: arc=subpath((length tempo)+angle(aa-oo)*(length tempo)/360,2*(length tempo)+angle(bb-oo)*(length tempo)/360) of tempo; fi; else : if (angle(aa-oo)=angle(bb-oo)) or (angle(aa-oo)(-1,-1): draw support shifted (ecart*j*(u,0)); fi endfor; ); clip $ to chemin; drawoptions(); $ enddef; %flèche pour coter un segment [AB] (Jacques Marot) vardef cotation(expr aa,bb,ecart,decalage,cote)= pair m[] ; save $; picture $; m3=unitvector(bb-aa) rotated 90; m1=aa+ecart*m3; m2=bb+ecart*m3; $=image( pickup pencircle scaled 0.2bp; drawdblarrow m1--m2 ; draw aa--m1 dashed evenly; draw bb--m2 dashed evenly; label(cote rotated angle(m2-m1),(m1+m2)/2+decalage*m3); ); $ enddef; vardef appelation(expr aa,bb,decalage,cote)= save $; picture $; pair m[]; m3=unitvector(bb-aa) rotated 90; $=image( label(cote rotated angle(bb-aa),(bb+aa)/2+decalage*m3); ); $ enddef; vardef cotationmil(expr aa,bb,ecart,decalage,cote)= %Christophe pair m[] ; save $; picture $; m3=unitvector(bb-aa) rotated 90; m1=aa+ecart*m3; m2=bb+ecart*m3; $=image( pickup pencircle scaled 0.2bp; drawarrow (1/2[m1,m2]+decalage*unitvector(m1-m2))--m1; drawarrow (1/2[m1,m2]-decalage*unitvector(m1-m2))--m2; draw aa--m1 dashed evenly; draw bb--m2 dashed evenly; label(cote rotated angle(m2-m1),(m1+m2)/2); ); $ enddef; endinput