%%===============================================
%% GEOMETRIESYR.MP
%% christophe.poulain@melusine.eu.org
%% Création : 19 Février 2003
%% Dernière modification : 26 Août 2004
%%===============================================
%------------------------------------------------
% Appel fichier
%------------------------------------------------
input constantes;
input papiers2;
%------------------------------------------------
% La figure (début et fin) JMS/CP
%------------------------------------------------
path feuillet;
numeric _tfig,_nfig;
pair coinbg,coinbd,coinhd,coinhg;
_nfig:=0;
string typetrace;
typetrace="normal";
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);
%modifié le 29.09.04
z.so=(xpart(coinbg/1cm),ypart(coinbg/1cm));
z.ne=(xpart(coinhd/1cm),ypart(coinhd/1cm));
%fin modification
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 figuremainlevee(expr xa,ya,xb,yb) =
_nfig:=_nfig+1;
typetrace:="mainlevee";
beginfig(_nfig);
feuille(xa,ya,xb,yb);
_tfig:= if (xb-xa)>(yb-ya): xb-xa else: yb-ya fi;
enddef;
def fin =
endfig;
enddef;
def finmainlevee=
endfig;
typetrace:="normal";
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)=
if typetrace="mainlevee":
save $;
picture $;
$=image(
trace aa{dir(angle(bb-aa)+5)}..bb{dir(angle(bb-aa)+5)};
trace cc{dir(angle(bb-cc)+5)}..bb{dir(angle(bb-cc)+5)};
trace aa{dir(angle(cc-aa)+5)}..cc{dir(angle(cc-aa)+5)};
);
else:
save $;
path $;
$=aa--bb--cc--cycle;
fi;
$
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 $;
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;
if typetrace="mainlevee":
picture $;
else:
path $;
fi;
$=polygone(pointchoisi1,pointchoisi2,pointchoisi3);
$
enddef;
vardef polygone(text t)=
pair aaa[];
j:=0;
for p_=t: if pair p_:
j:=j+1;
aaa[j]=p_;
fi;
endfor;
aaa[j+1]:=aaa[1];
if typetrace="mainlevee":
save $;
picture $;
$=image(
for k=1 upto j:
trace segment(aaa[k],aaa[k+1]);
endfor;
);
else:
save $;
path $;
$=aaa1--
for k=2 upto j:
aaa[k]--
endfor
cycle;
fi;
$
enddef;
vardef chemin(text t)=
pair aaa[];
j:=0;
for p_=t: if pair p_:
j:=j+1;
aaa[j]=p_;
fi;
endfor;
if typetrace="mainlevee":
save $;
picture $;
$=image(
for k=1 upto (j-1):
trace segment(aaa[k],aaa[k+1]);
endfor;
);
else:
save $;
path $;
$=aaa1
for k=2 upto j:
--aaa[k]
endfor;
fi;
$
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,nom)=
save s,p,$;
path p;
picture $;
$=image(
trace marqueangle(aa,bb,cc,nb);
label.@#(nom,w);
);
$
enddef;
vardef Marqueangle(expr aa,bb,mark)=%codage d'un angle formé par les demi-droites aa et bb dans le sens direct avec la marque mark
save $;
picture $;
path conf,rr;
pair w,tangent;
numeric t,tt;
conf=fullcircle scaled (2*marque_a) shifted (aa intersectionpoint bb);
numeric te;
te=angle((conf intersectionpoint aa)-(aa intersectionpoint bb));
rr=(conf intersectionpoint aa){dir(90+angle((conf intersectionpoint aa)-(aa intersectionpoint bb)))}..(conf intersectionpoint bb);
t=length rr/2;
w=point(t) of rr;
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 marqueangle(expr aa,bb,cc,mark)=%codage d'un angle de sommet bb dans le sens direct par la marque mark.
save $;
picture $;
path conf,rr;
pair w,tangent;
numeric t;
if typetrace="mainlevee":
conf=fullcircle scaled (2*marque_a) shifted bb;
rr=(conf intersectionpoint demidroite(bb,aa)){dir(90+angle(aa-bb))}..(conf intersectionpoint demidroite(bb,cc));
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;
);
else:
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;
);
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;
vardef milieu(expr AA,BB)=
save $;
pair $;
if typetrace="mainlevee":
$=point((length segment(AA,BB))*(1/2+(-1+uniformdeviate(2))/10)) of segment(AA,BB)
else:
$=iso(AA,BB)
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];
if typetrace="mainlevee":
h:=h shifted((-2+uniformdeviate(4))*unitvector(a-b))
fi;
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)=cercles(iso(aa,bb),bb)
%fullcircle scaled (2*abs(1/2[aa,bb]-bb)) shifted (1/2[aa,bb])
enddef;
%Cercles complets
vardef cercles(text t)=
save $;
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 typetrace="mainlevee":
path $;
path dep;
pair ct;
if n=1 : dep=fullcircle scaled (2*rayon) shifted _t[1];
ct=_t[1];
elseif n=2 : dep=fullcircle scaled (2*abs(_t[1]-_t[2])) shifted _t[1];
ct=_t[1];
elseif n=3 :
dep=fullcircle scaled (2*abs(CentreCercleC(_t[1],_t[2],_t[3])-_t[1])) shifted CentreCercleC(_t[1],_t[2],_t[3]);
ct=CentreCercleC(_t[1],_t[2],_t[3]);
fi
path ess;
ess=pointarc(dep,0){dir(80+uniformdeviate(5))}..pointarc(dep,90){dir(170+uniformdeviate(20))}..pointarc(dep,90){dir(185+uniformdeviate(5))}..pointarc(dep,180){dir(-80-uniformdeviate(20))}..pointarc(dep,180){dir(-100+uniformdeviate(20))}..pointarc(dep,270){dir(-10+uniformdeviate(20))}..pointarc(dep,270){dir(uniformdeviate(10))}..pointarc(dep,360){dir(80+uniformdeviate(20))};
$=ess;
else:
path $;
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
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=fullcircle scaled (2*abs(aa-oo)) shifted 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;
elseif (angle(bb-oo)<0):
arc=subpath(angle(aa-oo)*(length tempo)/360,(length tempo)+angle(bb-oo)*(length tempo)/360) of tempo;
fi;
elseif (angle(aa-oo)<0):
if (angle(bb-oo)=0) or (angle(bb-oo)>0):
arc=subpath(length tempo+angle(aa-oo)*(length tempo)/360,length tempo+angle(bb-oo)*(length tempo)/360) of tempo;
elseif (angle(bb-oo)<0):
if (angle(aa-oo)=angle(bb-oo)) or (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;
fi;
fi;
arc
enddef;
vardef coupdecompas(expr ab,ac,ad)=arccercle(pointarc(cercles(ab,ac),angle(ac-ab)-ad),pointarc(cercles(ab,ac),angle(ac-ab)+ad),ab)
enddef;
%------------------------------------------------
% Droites
%------------------------------------------------
vardef segment(expr aa,bb)=
save $;
path $;
if typetrace="mainlevee":
$=aa{dir(angle(bb-aa)+5)}..bb{dir(angle(bb-aa)+5)}
else:
$=aa--bb
fi;
$
enddef;
vardef droite(expr AA,BB)=
save $;
path $;
if typetrace="mainlevee":
$=(_tfig/abs(AA-BB))[BB,AA]{dir(angle(BB-AA)+10)}..segment(AA,BB)..(_tfig/abs(AA-BB))[AA,BB]{dir(angle(BB-AA)+10)}
else:
$=(_tfig/abs(AA-BB))[BB,AA]--(_tfig/abs(AA-BB))[AA,BB]
fi;
$
enddef;
vardef demidroite(expr AA,BB)=
save $;
path $;
if typetrace="mainlevee":
$=segment(AA,BB)..(_tfig/abs(AA-BB))[AA,BB]{dir(angle(BB-AA)+10)}
else:
$=AA--(_tfig/abs(AA-BB))[AA,BB]
fi;
$
enddef;
vardef bissectrice(expr AA,BB,CC)=
save $;
path $;
if typetrace="mainlevee":
$=rotation(demidroite(BB,CentreCercleI(AA,BB,CC)),BB,-5+uniformdeviate(10))
else:
$=demidroite(BB,CentreCercleI(AA,BB,CC))
fi;
$
enddef;
vardef mediatrice(expr AA,BB)=droite(iso(AA,BB),rotation(BB,iso(AA,BB),90))
enddef;
%main levee : passer par la perpendiculaire passant par le milieu.
vardef perpendiculaire(expr AA,BB,II)=droite(iso(AA,BB),rotation(BB,iso(AA,BB),90)) shifted (II-iso(AA,BB))
enddef;
vardef parallele(expr AA,BB,II)=droite(AA,BB) shifted (II-(projection(II,AA,BB)))
enddef;
%------------------------------------------------
% Transformations
%------------------------------------------------
vardef rotation(expr p,c,a)=
p rotatedaround(c,a)
enddef;
vardef symetrie(expr x)(text t)=
save n;
n:=0;
for p_=t:
n:=n+1;
_t[n]:=p_;
endfor;
if n=1:
rotation(x,_t[1],180)
elseif n=2:
x reflectedabout(_t[1],_t[2])
fi
enddef;
%------------------------------------------------
%Sucres
%------------------------------------------------
vardef hachurage(expr chemin, angle, ecart, trace)=
save $;
picture $;
path support;
support=((u*(-37,0))--(u*(37,0))) rotated angle;
if trace=1:
drawoptions(dashed evenly);
elseif trace=2:
drawoptions(dashed dashpattern(on12bp off6bp on3bp off6bp));
fi;
$ = image(
for j=-200 upto 200:
if ((support shifted (ecart*j*(u,0))) intersectiontimes chemin)<>(-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;
vardef cotationmilrap(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;
draw (1/2[m1,m2]+decalage*unitvector(m1-m2))--9/10[m2,m1];
draw (1/2[m1,m2]-decalage*unitvector(m1-m2))--m2;
label(cote rotated angle(m2-m1),(m1+m2)/2);
);
$
enddef;
endinput
|
geometriesyr15.mp