warningcheck:=0;

warningcheck:=0;

input rboxes;
input sarith;
input graph;

verbatimtex
\documentclass[a4paper,12pt]{article}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\begin{document}
etex

vardef TEX primary s =
write "verbatimtex" to "mptextmp.mp";
write "\documentclass[12pt]{article}" to "mptextmp.mp";
write "\usepackage[T1]{fontenc}" to "mptextmp.mp";
write "\usepackage{amsmath,amssymb}" to "mptextmp.mp";
write "\begin{document}" to "mptextmp.mp";
write "etex" to "mptextmp.mp";
write "btex "&s&" etex" to "mptextmp.mp";
write EOF to "mptextmp.mp";
scantokens "input mptextmp"
enddef;

vardef longueur(expr p) =
save l,i;
numeric l;
l:=0;
for i=0 step .01 until length(p):
l:=l+abs( (point i of p) - (point(i+.01) of p) );
endfor;
l % Pas de point-virgule
enddef;

vardef milieu(expr p) =
save l,i,tot,A,B;
numeric l,tot,i;
pair A,B;
tot := longueur(p);
l:=0;
B := point 0 of p;
for i:=0 step .01 until length(p):
A := B;
B := point i of p;
l := l+abs(B-A);
exitif l > 1/2 tot;
endfor;
show l; show tot;
1/2[A,B]
enddef;

vardef milieu_time(expr p) =
save l,i,tot,A,B,t;
numeric l,tot,i,t;
pair A,B;
tot := longueur(p);
l:=0;
B := point 0 of p;
for i:=0 step .01 until length(p):
t:=i;
A := B;
B := point i of p;
l := l+abs(B-A);
exitif l > 1/2 tot;
endfor;
t
enddef;

beginfig(1)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C;

endfig;
beginfig(2)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle;

endfig;
beginfig(3)
pair A[];
A[0]:=(-1cm, -1cm);
A[1]:=( 1cm, -1cm);
A[2]:=( 1cm, 1cm);
A[3]:=(-1cm, 1cm);
draw A[0]--A[1]--A[2]--A[3]--cycle;
draw A[0]--A[2];
draw A[1]--A[3];
endfig;
beginfig(4)
pair A;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A withpen pencircle scaled 4bp;

endfig;
beginfig(5)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle;
draw A withpen pencircle scaled 4bp;
draw B withpen pencircle scaled 4bp;
draw C withpen pencircle scaled 4bp;
endfig;
beginfig(6)
pair A, B, C, D;
A:=(0,0); B:=(1cm,0);
C:=(1cm,1cm); D:=(0,1cm);
draw A--B--C--D--cycle;
draw A--C;
draw B--D;
draw A withpen pencircle scaled 4bp;
draw B withpen pencircle scaled 4bp;
draw C withpen pencircle scaled 4bp;
draw D withpen pencircle scaled 4bp;
endfig;
beginfig(7)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle;
draw 1/2[A,B] -- C;
draw 1/2[B,C] -- A;
draw 1/2[C,A] -- B;
endfig;
beginfig(8)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle;
draw 1/2[A,B] -- C;
draw 1/2[B,C] -- A;
draw 1/2[C,A] -- B;
draw 1/3 A + 1/3 B + 1/3 C
withpen pencircle scaled 4bp;
endfig;
beginfig(9)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle;
draw A--B withpen pencircle scaled 2bp;

endfig;
beginfig(10)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle;
draw A--B withcolor (green + red);

endfig;
beginfig(11)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B;
draw B--C dashed evenly;
draw C--A dashed withdots;

endfig;
beginfig(12)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B withpen pencircle scaled 2bp withcolor .8white;
draw B--C withpen pencircle scaled 2bp withcolor .6white;
draw C--A withpen pencircle scaled 2bp withcolor .4white;

endfig;
beginfig(13)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle;
draw 1/2[A,B] -- C dashed evenly;
draw 1/2[B,C] -- A dashed evenly;
draw 1/2[C,A] -- B dashed evenly;
draw 1/3 A + 1/3 B + 1/3 C
withpen pencircle scaled 4bp
withcolor red;
endfig;
beginfig(14)
draw (0,0)--(3cm,0) dashed evenly scaled 2;
draw (0,-5mm)--(3cm,-5mm) dashed evenly;

endfig;
beginfig(15)
draw (0,0)--(3cm,0)
dashed dashpattern(on 2bp off 3bp);

endfig;
beginfig(16)
draw (0,0)--(3cm,0) dashed dashpattern(on 1bp off 2bp on 10bp off 2bp);
endfig;
beginfig(17)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
drawarrow C--B--A;
drawarrow A--C withpen pencircle scaled 2bp;

endfig;
beginfig(18)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw C--B--A--cycle;
drawdblarrow A--C withpen pencircle scaled 2bp;

endfig;
beginfig(19)
draw (-1.5cm,0)--(1.5cm,0);
draw (0,-1.5cm)--(0,1.5cm);
drawarrow (0,0)--(1cm,0)
withpen pencircle scaled 2bp;
drawarrow (0,0)--(0,1cm)
withpen pencircle scaled 2bp;
endfig;
beginfig(20)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
fill A--B--C--cycle withcolor .8 white;

endfig;
beginfig(21)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
fill A--B--C--cycle withcolor .8 white;
draw A--B--C--cycle;

endfig;
beginfig(22)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
fill A--B--C--cycle withcolor .8 white;
draw A--B--C--cycle withpen pencircle scaled 2bp;
endfig;
beginfig(23)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle withpen pencircle scaled 2bp;
fill A--B--C--cycle withcolor .8 white;
endfig;
beginfig(24)
pair A, B, C, D;
A:=(0,0); B:=(1cm,0);
C:=(1cm,1cm); D:=(0,1cm);
fill A--C--B--D--cycle withcolor .8white;
endfig;
beginfig(25)
pair A, B, C, D;
A:=(0,0); B:=(1cm,0);
C:=(1cm,1cm); D:=(0,1cm);
path p;
p := A--C--B--D--cycle;
fill p withcolor .8white;
draw p;
endfig;
beginfig(26)
pair A, B, C, D;
A:=(-1.5cm,-1.5cm); B:=(1.5cm,-1.5cm);
C:=(1.5cm,1.5cm); D:=(-1.5cm,1.5cm);
fill A--C--B--D--cycle withcolor .8white;
draw (-1.5cm,0)--(1.5cm,0);
draw (0,-1.5cm)--(0,1.5cm);
drawarrow (0,0)--(1cm,0)
withpen pencircle scaled 2bp;
drawarrow (0,0)--(0,1cm)
withpen pencircle scaled 2bp;
endfig;
beginfig(27)
pair A;
A := (0,0);
draw A withpen pencircle scaled 4bp;
label.top(btex Au dessus etex, A);
label.bot(btex En dessous etex, A);
label.rt (btex � droite etex, A);
label.lft(btex � gauche etex, A);

endfig;
beginfig(28)
pair A;
A := (0,0);
draw A withpen pencircle scaled 4bp;
label.ulft(btex En haut � gauche etex, A);
label.urt (btex En haut � droite etex, A);
label.llft(btex En bas � gauche etex, A);
label.lrt (btex En bas � droite etex, A);

endfig;
beginfig(29)
pair A;
A := (0,0);
dotlabel.urt(btex $A$ etex, A);

endfig;
beginfig(30)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle;
dotlabel.llft(btex $A$ etex, A);
dotlabel.lrt(btex $B$ etex, B);
dotlabel.top(btex $C$ etex, C);
endfig;
beginfig(31)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle;
label.bot(btex $1$ etex, 1/2[A,B]);
label.lft(btex $1$ etex, 1/2[A,C]);
label.urt(btex $\sqrt 2$ etex, 1/2[B,C]);
endfig;
beginfig(32)
u:=1cm;
pair A,B,C,D,E,F,G;
A := (-u,u);
B := (0,u);
C := (u,u);
D := (-u,0);
E := (0,0);
F := (u,0);
draw A--D; draw A--E; draw A--F;
draw B--D; draw B--E; draw B--F;
draw C--D; draw C--E; draw C--F;
dotlabel.top(btex $a$ etex, A);
dotlabel.top(btex $b$ etex, B);
dotlabel.top(btex $c$ etex, C);
dotlabel.bot(btex $a'$ etex, D);
dotlabel.bot(btex $b'$ etex, E);
dotlabel.bot(btex $c'$ etex, F);
endfig;
beginfig(33)
draw fullcircle;

endfig;
beginfig(34)
draw (0,0) withpen pencircle scaled 4bp;
draw fullcircle scaled 1cm;

endfig;
beginfig(35)
draw (0,0) withpen pencircle scaled 4bp;
draw fullcircle scaled 1cm shifted (1cm,1cm);

endfig;
beginfig(36)
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C--cycle;
fill fullcircle scaled 4bp shifted A withcolor white;
fill fullcircle scaled 4bp shifted B withcolor white;
fill fullcircle scaled 4bp shifted C withcolor white;
draw fullcircle scaled 4bp shifted A;
draw fullcircle scaled 4bp shifted B;
draw fullcircle scaled 4bp shifted C;
endfig;
beginfig(37)
draw (0,0) .. (0,1cm) .. (1cm,0) .. (1cm,1cm);
draw (0,0) withpen pencircle scaled 4bp;
draw (0,1cm) withpen pencircle scaled 4bp;
draw (1cm,0) withpen pencircle scaled 4bp;
draw (1cm,1cm) withpen pencircle scaled 4bp;

endfig;
beginfig(38)
draw (0,0) -- (0,1cm) .. (1cm,0) .. (1cm,1cm);

endfig;
beginfig(39)
draw (0,0) --- (0,1cm) .. (1cm,0) .. (1cm,1cm);

endfig;
beginfig(40)
draw (0,0) .. (0,1cm) .. (1cm,0) .. (1cm,1cm)
.. cycle;

endfig;
beginfig(41)
pair A, B, C, D;
A:=(0,0); B:=(1cm,0);
C:=(1cm,1cm); D:=(0,1cm);
draw A..B..C..D..cycle;
endfig;
beginfig(42)
draw (0,0) .. (1cm,1cm) .. cycle;
endfig;
beginfig(43)
draw (0,0){(0,1)} .. (2cm,0){(1,0)};

endfig;
beginfig(44)
draw (0,0){dir 90} .. (2cm,0){dir 0};

endfig;
beginfig(45)
draw (0,0){up} .. (2cm,0){right};

endfig;
beginfig(46)
draw (0,0){up} .. (2cm,0){up};
endfig;
beginfig(47)
draw (0,0){up} .. (2cm,0){up} .. cycle;
endfig;
beginfig(48)
alpha := 30;
draw (0,0) -- 2cm*dir 0;
draw (0,0) -- 2cm*dir alpha;
draw 1cm * dir 0 {dir 90} ..
1cm * dir alpha {dir(90+alpha)};
endfig;
beginfig(49)
alpha := 30;
draw (0,0) -- 2cm*dir 0;
draw (0,0) -- 2cm*dir alpha;
draw 1cm * dir 0 {dir 90} ..
1cm * dir alpha {dir(90+alpha)};
draw 1.1cm * dir 0 {dir 90} ..
1.1cm * dir alpha {dir(90+alpha)};
endfig;
beginfig(50)
def draw_angle(expr A, O, B, n) =
draw_angle_(A,O,B,5mm);
if n>1 : draw_angle_(A,O,B,4.5mm); fi;
if n>2 : draw_angle_(A,O,B,4mm); fi;
if n>3 : draw_angle_(A,O,B,5.5mm); fi;
enddef;
def draw_angle_(expr A,O,B,d) =
draw (O + d*unitvector(A-O))
{ d*unitvector(A-O) rotated 90 }
..
{ d*unitvector(B-O) rotated 90 }
(O + d*unitvector(B-O));
enddef;
pair A, B, C;
A := (0,0);
B := (3cm,0);
C := (1cm,2cm);
draw A--B--C--cycle;
draw_angle(B,A,C,1);
draw_angle(C,B,A,2);
draw_angle(A,C,B,3);
endfig;
beginfig(51)
u:=1cm;
path p;
p := (u,0){up}..(-u,0){down}--cycle;
fill p withcolor .8*white;
draw p withpen pencircle scaled 1bp;
endfig;
beginfig(52)
u:=1cm;
path p;
p := (u,0){up} ..
(-u,0){down} --
(-.2u,0){up} ..
(.2u,0){down} --
cycle;
fill p withcolor .8*white;
draw p withpen pencircle scaled 1bp;
endfig;
beginfig(53)
u:=1cm;
pair A,AA,B,BB,C,D;
A := ( .2u, .05u);
AA := ( .2u, -.05u);
B := ( u, .05u);
BB := ( u, -.05u);
C := (-.2u, 0);
D := ( -u, 0);
path p;
p:= B{up} .. D{down} .. BB{up} --
AA{down} .. C{up} .. A{down} -- cycle;
fill p withcolor .8*white;
draw p withpen pencircle scaled 1bp;
endfig;
beginfig(54)
u:=1cm;
pair A,B,C,D;
A:=(0,0);
B:=u*dir 60;
C:=u*dir -60;
D:=(2u,0);
draw A withpen pencircle scaled 4bp;
draw B withpen pencircle scaled 4bp;
draw C withpen pencircle scaled 4bp;
draw D withpen pencircle scaled 4bp;
draw A--D--B--D--C;
draw A{up}..B;
draw A{down}..C;
draw A{dir 30}..B;
draw A{dir -30}..C;
endfig;
beginfig(55)
draw (0,0) .. (1cm,1cm) .. (2cm,0);

endfig;
beginfig(56)
draw (0,0) .. tension 2 ..
(1cm,1cm) .. (2cm,0);

endfig;
beginfig(57)
draw (0,u) {right} ..
( u*dir -150 ){dir 120} ..
( u*dir -30 ){dir -120} ..
cycle;
endfig;
beginfig(58)
draw (0,u) {right} .. tension 2 ..
( u*dir -150 ){dir 120} .. tension 2 ..
( u*dir -30 ){dir -120} .. tension 2 ..
cycle;
endfig;
beginfig(59)
draw (0,u) {right} .. tension 4 ..
( u*dir -150 ){dir 120} .. tension 4 ..
( u*dir -30 ){dir -120} .. tension 4 ..
cycle;
endfig;
beginfig(60)
u:=.5cm;
pair A,B,C,D;
A:=(0,0); B:=(-u,2u);
C:=(4u,3u); D:=(3u,0);
draw A.. controls B and C .. D
withpen pencircle scaled 2pt;
draw B--C dashed evenly;
drawarrow A--B;
drawarrow D--C;

endfig;
beginfig(61)
pair A, B, C, D;
A = (0,0);
D = (2u,0);
B = (-u,2u);
C = (3u,3u);

draw A withpen pencircle scaled 4bp;
draw B withpen pencircle scaled 4bp;
draw C withpen pencircle scaled 4bp;
draw D withpen pencircle scaled 4bp;
draw A .. controls B and C .. D;

pair a[];
a[1] := A;
a[2] := B;
a[3] := C;
a[4] := D;

a[12] := 1/2 [ a[1], a[2] ];
a[23] := 1/2 [ a[2], a[3] ];
a[34] := 1/2 [ a[3], a[4] ];
a[123] := 1/2 [ a[12], a[23] ];
a[234] := 1/2 [ a[23], a[34] ];
a[1234] := 1/2 [ a[123], a[234] ];

draw a[1234] withpen pencircle scaled 4bp;
endfig;
beginfig(62)
vardef bezier(expr n,A,B,C,D) =
save a;
pair a[];
a[1] := A;
a[2] := B;
a[3] := C;
a[4] := D;

a[12] := 1/2 [ a[1], a[2] ];
a[23] := 1/2 [ a[2], a[3] ];
a[34] := 1/2 [ a[3], a[4] ];
a[123] := 1/2 [ a[12], a[23] ];
a[234] := 1/2 [ a[23], a[34] ];
a[1234] := 1/2 [ a[123], a[234] ];

if n>0:
bezier(n-1, a[1], a[12], a[123], a[1234]);
bezier(n-1, a[1234], a[234], a[34], a[4]);
else:
draw a[1234] withpen pencircle scaled 2bp;
fi;
enddef;

pair A, B, C, D;
A = (0,0);
D = (2u,0);
B = (-u,2u);
C = (3u,3u);

draw A withpen pencircle scaled 4bp;
draw B withpen pencircle scaled 4bp;
draw C withpen pencircle scaled 4bp;
draw D withpen pencircle scaled 4bp;

bezier(5,A,B,C,D);
endfig;
beginfig(63)
draw (0,0){up} .. (1cm, 1mm) .. (2cm,0){down};

endfig;
beginfig(64)
draw (0,0){up} ... (1cm, 1mm) ... (2cm,0){down};

endfig;
beginfig(65)
draw (0,0){curl 0} .. (0,1cm)..(1cm,0)..(1cm,1cm);

endfig;
beginfig(66)
draw (0,0){curl 1} .. (0,1cm)..(1cm,0)..(1cm,1cm);

endfig;
beginfig(67)
draw (0,0){curl 2} .. (0,1cm)..(1cm,0)..(1cm,1cm);

endfig;
beginfig(68)
pair A,B,C,D;
xpart A = ypart A = ypart B = xpart C = 0;
xpart B = ypart C = xpart D = ypart D = 2cm;
draw A--B--C--D--cycle withpen pencircle scaled 2bp;
endfig;
beginfig(69)
pair A,B,C,D,M;
numeric lambda, mu;
A=(0,0); B=(2cm,3cm);
C=(1cm,0); D=(-1cm,2cm);
M = lambda [A,B];
M = mu [C,D];
draw A--B;
draw C--D;
draw M withpen pencircle scaled 4bp;

endfig;
beginfig(70)
pair A,B,C,D,M;
A=(0,0); B=(2cm,3cm);
C=(1cm,0); D=(-1cm,2cm);
M = whatever [A,B];
M = whatever [C,D];
draw A--B;
draw C--D;
draw M withpen pencircle scaled 4bp;

endfig;
beginfig(71)
pair A,B,C,AA,BB,CC,G;
A=(0,0); B=(3cm,0); C=(1cm,2cm);
AA = 1/2 [B,C];
BB = 1/2 [C,A];
CC = 1/2 [A,B];
G = whatever [A,AA];
G = whatever [B,BB];
draw A--B--C--cycle;
draw A--AA dashed withdots;
draw B--BB dashed withdots;
draw C--CC dashed withdots;
draw G withpen pencircle scaled 4bp;
endfig;
beginfig(72)
path p;
p := fullcircle scaled 5mm;
draw p;
draw p shifted (1mm,2mm);
draw p shifted 2(1mm,2mm);
draw p shifted 3(1mm,2mm);
draw p shifted 4(1mm,2mm);
draw p shifted 5(1mm,2mm);

endfig;
beginfig(73)
path p;
p := (5mm,-5mm) {right} .. (2cm,0);
draw p;
draw p rotated 10;
draw p rotated 20;
draw p rotated 30;
draw p rotated 40;
draw p rotated 50;
draw p rotated 60;
draw p rotated 70;
draw p rotated 80;
draw p rotated 90;

endfig;
beginfig(74)
path p;
p := fullcircle scaled 5mm;
draw p;
draw p xscaled 2;
draw p xscaled 3;
draw p xscaled 4;

endfig;
beginfig(75)
pair A,B,C,D,E;
A := (1cm,0);
B := A rotated 72;
C := B rotated 72;
D := C rotated 72;
E := D rotated 72;
draw A--B--C--D--E--cycle;
endfig;
beginfig(76)
pair A,B,C,D,E;
A := (1cm,0);
B := A rotated 72;
C := B rotated 72;
D := C rotated 72;
E := D rotated 72;
draw A--C--E--B--D--cycle;
endfig;
beginfig(77)
pair A,B,C,D,E;
A := (1cm,0);
B := A rotated 72;
C := B rotated 72;
D := C rotated 72;
E := D rotated 72;
pair AA, BB, CC, DD, EE;
AA = whatever [A, C];
AA = whatever [B, D];
BB = whatever [B, D];
BB = whatever [C, E];
CC = whatever [C, E];
CC = whatever [D, A];
DD = whatever [D, A];
DD = whatever [E, B];
EE = whatever [E, B];
EE = whatever [A, C];
fill A--C--E--B--D--cycle withcolor .8white;
fill AA--BB--CC--DD--EE--cycle withcolor white;
draw A--C--E--B--D--cycle;
endfig;
beginfig(78)
path p;
p := (0,0) -- (1cm,0);
drawarrow p withpen pencircle scaled 2bp;
drawarrow p zscaled (1,2);

endfig;
beginfig(79)
u:=1cm;
path p; p := (0,0) -- (u,0);
pair A; A := (u,-u);
numeric a; a := 90;
drawarrow p withpen pencircle scaled 1bp;
drawarrow p rotatedaround( A, a );
drawarrow p shifted -A rotated a shifted A
withpen pencircle scaled 1bp dashed withdots;
endfig;
beginfig(80)
path p; p := (0,0) -- (u,0);
pair A; A := (u,-u);
numeric a; a := 90;
drawarrow p withpen pencircle scaled 1bp;
draw A withpen pencircle scaled 4bp;
label ulft ( btex $A$ etex, A );
draw (0,0) withpen pencircle scaled 4bp;
label bot ( btex $O$ etex, (0,0) );
for i=0 upto 10:
drawarrow p shifted -(i*A/10) withcolor red;
endfor;
for i=0 upto 10:
drawarrow p shifted -A rotated (i*a/10) withcolor green;
endfor;
for i=0 upto 10:
drawarrow p shifted -A rotated a shifted (i*A/10) withcolor blue;
endfor;
endfig;
beginfig(81)
pair A,B,C,AA,BB,CC,H;
A=(0,0); B=(3cm,0); C=(1cm,2cm);
AA - A = whatever * (B-C) rotated 90;
AA = whatever [B,C];
BB - B = whatever * (A-C) rotated 90;
BB = whatever [A,C];
CC - C = whatever * (A-B) rotated 90;
CC = whatever [A,B];
H = whatever [A,AA];
H = whatever [B,BB];
draw A--B--C--cycle;
draw A--AA;
draw B--BB;
draw C--CC;
draw H withpen pencircle scaled 4bp;
endfig;
beginfig(82)
pair A,B,C,H;
A=(0,0); B=(3cm,0); C=(1cm,2cm);
H - A = whatever * (B-C) rotated 90;
H - B = whatever * (A-C) rotated 90;
draw A--B--C--cycle;
draw H withpen pencircle scaled 4bp;
endfig;
beginfig(83)
pair A,B,C,O;
A=(0,0); B=(3cm,0); C=(1cm,2cm);
O - 1/2[B,C] = whatever * (B-C) rotated 90;
O - 1/2[A,B] = whatever * (A-B) rotated 90;
draw A--B--C--cycle;
draw O withpen pencircle scaled 4bp;
draw fullcircle scaled 2abs(O-A) shifted O;
endfig;
beginfig(84)
pair A,B,C,D;
u:=2cm;
A=(0,0); B=(u,0); C=(u,u); D=(0,u);

transform T;
A transformed T = 1/5[A,B];
B transformed T = 1/5[B,C];
C transformed T = 1/5[C,D];

path p;
p = A--B--C--D--cycle;
draw p;
draw p transformed T;

endfig;
beginfig(85)
pair A,B,C,D;
u:=2cm;
A=(0,0); B=(u,0); C=(u,u); D=(0,u);

transform T;
A transformed T = 1/5[A,B];
B transformed T = 1/5[B,C];
C transformed T = 1/5[C,D];

path p;
p = A--B--C--D--cycle;
for i=0 upto 100:
draw p;
p:= p transformed T;
endfor;

endfig;
beginfig(86)
u:=1cm;
pair A,B,C,D,E;
A := (0,u);
B := A rotated 72;
C := B rotated 72;
D := C rotated 72;
E := D rotated 72;
transform T;
A transformed T = 1/5[A,B];
B transformed T = 1/5[B,C];
C transformed T = 1/5[C,D];
path p;
p := A--B--C--D--E--cycle;
draw p;
p := p transformed T; draw p;
p := p transformed T; draw p;
p := p transformed T; draw p;
endfig;
beginfig(87)
u:=3mm;
fill fullcircle scaled 2u withcolor .8white;
fill fullcircle scaled u shifted (u*dir30)
withcolor .8white;
fill fullcircle scaled u shifted (u*dir150)
withcolor .8white;
endfig;
beginfig(88)
u:=3mm;
transform T;
(0,0) transformed T = (0,0);
(1,0) transformed T = (1,1);
(0,1) transformed T = (1,0);

fill fullcircle scaled 2u transformed T withcolor .8white;
fill fullcircle scaled u shifted (u*dir30) transformed T
withcolor .8white;
fill fullcircle scaled u shifted (u*dir150) transformed T
withcolor .8white;
endfig;
beginfig(89)
u:=3mm;
transform T;
xpart T = ypart T = 0;
xxpart T = 1;
yxpart T = 2;
xypart T = 3;
yypart T = 4;

fill fullcircle scaled 2u transformed T withcolor .8white;
fill fullcircle scaled u shifted (u*dir30) transformed T
withcolor .8white;
fill fullcircle scaled u shifted (u*dir150) transformed T
withcolor .8white;
endfig;
beginfig(90)
draw fullcircle scaled 1cm;
draw fullcircle scaled 5mm shifted (1cm*dir45);
draw fullcircle scaled 5mm shifted (1cm*dir135);
picture mypicture;
mypicture := currentpicture;
currentpicture := nullpicture;
draw mypicture;
draw mypicture shifted (1mm,1mm);
draw mypicture shifted (2mm,2mm);

endfig;
beginfig(91)
picture pic;
pic := nullpicture;
addto pic contour fullcircle scaled 1cm
withcolor .8white;
addto pic doublepath fullcircle scaled 1cm
withpen pencircle scaled .5bp;
addto pic also pic shifted (1mm,1mm);
draw pic;

endfig;
beginfig(92)
u:=3mm;
picture mickey;
mickey := nullpicture;
addto mickey contour fullcircle scaled 2u
withcolor .8white;
addto mickey contour fullcircle scaled u
shifted (u*dir30) withcolor .8white;
addto mickey contour fullcircle scaled u
shifted (u*dir150)
withcolor .8white;
draw mickey;
endfig;
beginfig(93)
u:=3mm;
picture mickey;
mickey := nullpicture;
addto mickey contour fullcircle scaled 2u
withcolor .8white;
addto mickey contour fullcircle scaled u
shifted (u*dir30) withcolor .8white;
addto mickey contour fullcircle scaled u
shifted (u*dir150) withcolor .8white;

transform T;
(0,0) transformed T = (0,0);
(1,0) transformed T = (1,1);
(0,1) transformed T = (1,0);

draw mickey transformed T;
endfig;
beginfig(94)
u:=3mm;
picture mickey;
fill fullcircle scaled 2u withcolor .8white;
fill fullcircle scaled u shifted (u*dir30)
withcolor .8white;
fill fullcircle scaled u shifted (u*dir150)
withcolor .8white;
mickey := currentpicture;
currentpicture := nullpicture;

transform T;
(0,0) transformed T = (0,0);
(1,0) transformed T = (1,1);
(0,1) transformed T = (1,0);

draw mickey transformed T;
endfig;
beginfig(95)
pair A,B;
path p;
A = (0,1cm);
B = A rotated 120;
p = A{dir 0} .. tension 2 .. B{dir 120};
draw p;
draw p rotated 120;
draw p rotated -120;
endfig;
beginfig(96)
pair A,B;
path p;
numeric n;
n:=5;
A = (0,1cm);
B = A rotated (2*360/n);
p = A{dir 180} .. tension 4 .. B{dir (180+2*360/n)};
draw p withcolor red;
draw p rotated (1*360/n);
draw p rotated (2*360/n);
draw p rotated (3*360/n);
draw p rotated (4*360/n);
endfig;
beginfig(97)
path c[], l[];
c[0] = fullcircle xscaled 1cm yscaled .5cm
shifted (0,1cm);
c[1] = c[0] rotated 120;
c[2] = c[1] rotated 120;
pair A;
A = (-.5cm,1cm);
l[0] = A{down} ..
(A xscaled -1 rotated 120){-down rotated 120};
l[1] = l[0] rotated 120;
l[2] = l[1] rotated 120;
draw c[0]; draw c[1]; draw c[2];
draw l[0]; draw l[1]; draw l[2];
endfig;
beginfig(98)
path c[], l[];
c[0] = fullcircle xscaled 1cm yscaled .5cm
shifted (0,1cm);
c[1] = c[0] rotated (360/4);
c[2] = c[1] rotated (360/4);
c[3] = c[2] rotated (360/4);
pair A;
A = (-.5cm,1cm);
l[0] = A{down} ..
(A xscaled -1 rotated (360/4))
{-down rotated (360/4)};
l[1] = l[0] rotated (360/4);
l[2] = l[1] rotated (360/4);
l[3] = l[2] rotated (360/4);
draw c[0]; draw c[1]; draw c[2]; draw c[3];
draw l[0]; draw l[1]; draw l[2]; draw l[3];
endfig;
beginfig(99)
pair A, B;
A := (0,0); B := (2cm,1cm);
draw A withpen pencircle scaled 4bp;
draw B withpen pencircle scaled 4bp;
draw fullcircle scaled abs(B-A) shifted 1/2[A,B];

endfig;
beginfig(100)
pair A;
A:=(2cm,2cm);
drawarrow origin--A;
drawarrow (origin--A) rotated -1/3 angle(A);
drawarrow (origin--A) rotated -2/3 angle(A);
drawarrow (origin--A) rotated -angle(A);

endfig;
beginfig(101)
pair A,B;
A:=(1cm,2cm); B:=(2cm,1cm);
numeric alpha;
alpha = angle(A) - angle(B);
drawarrow origin--A;
drawarrow origin--B;
drawarrow (origin--A) rotated -1/3 alpha;
drawarrow (origin--A) rotated -2/3 alpha;
drawarrow (origin--A) rotated -alpha;
endfig;
beginfig(102)
pair A,B,C;
A=(0,0); B=(3cm,0); C=(1cm,2cm);
draw A--B--C--cycle;
label.llft(TEX decimal(angle(C-A)-angle(B-A)), A);
label.lrt(TEX decimal(angle(A-B)-angle(C-B)), B);
label.urt(TEX decimal(angle(B-C)-angle(A-C)), C);
endfig;
beginfig(103)
pair A,AA,B,BB,C,CC,O,H;
A=(0,0); B=(3cm,0); C=(1cm,2cm);
AA = 1/2[B,C];
BB = 1/2[A,C];
CC = 1/2[A,B];
O - 1/2[BB,CC] = whatever * (BB-CC) rotated 90;
O - 1/2[AA,BB] = whatever * (AA-BB) rotated 90;
draw A--B--C--cycle;
draw AA withpen pencircle scaled 4bp;
draw BB withpen pencircle scaled 4bp;
draw CC withpen pencircle scaled 4bp;
draw fullcircle scaled 2abs(O-AA) shifted O;
% Il faut aussi tracer les hauteurs
pair AA,BB,CC;
AA - A = whatever * (B-C) rotated 90;
AA = whatever [B,C];
BB - B = whatever * (A-C) rotated 90;
BB = whatever [A,C];
CC - C = whatever * (A-B) rotated 90;
CC = whatever [A,B];
draw A--AA; draw B--BB; draw C--CC;
draw AA withpen pencircle scaled 4bp;
draw BB withpen pencircle scaled 4bp;
draw CC withpen pencircle scaled 4bp;
% Il passe aussi par le milieu de HA, HB, HC
H = whatever [A,AA];
H = whatever [B,BB];
draw 1/2 [A,H] withpen pencircle scaled 4bp;
draw 1/2 [B,H] withpen pencircle scaled 4bp;
draw 1/2 [C,H] withpen pencircle scaled 4bp;
endfig;
beginfig(104)
pair A,B,C,M,h;
u:=2cm;
A=(0,0); B=(2u,-.5u); C=(u,u);
draw A--B--C--cycle;
(M-A) = whatever * (
(A-C) rotated 1/2( angle(B-A) - angle(C-A)) );
(M-B) = whatever * (
(B-A) rotated 1/2( angle(C-B) - angle(A-B)) );
draw M--A; draw M--B; draw M--C;
M-h = whatever * (B-C) rotated 90;
h = whatever[B,C];
draw fullcircle scaled 2 abs(M-h) shifted M;
endfig;
beginfig(105)
path p;
p = (0,0){up} .. (2cm,0){down};
draw p;
draw point 0 of p withpen pencircle scaled 4bp;
draw point .5 of p withpen pencircle scaled 4bp;
draw point 1 of p withpen pencircle scaled 4bp;

endfig;
beginfig(106)
path p;
p = (0,0){up} .. (2cm,0){down};
draw p;
pair A;
A := point 0 of p;
B := A + 1cm*unitvector(direction 0 of p);
drawarrow A--B withpen pencircle scaled 1bp;
A := point .5 of p;
B := A + 1cm*unitvector(direction .5 of p);
drawarrow A--B withpen pencircle scaled 1bp;
A := point 1 of p;
B := A + 1cm*unitvector(direction 1 of p);
drawarrow A--B withpen pencircle scaled 1bp;

endfig;
beginfig(107)
u:=5mm;
path p;
p = (0,0) {curl 0} .. (u,2u) .. (2u,1.5u)
.. (3u,2u) .. {curl 0} (4u,0);
draw subpath(0,1) of p withcolor red;
draw subpath(1,2) of p withcolor green;
draw subpath(2,3) of p withcolor blue;
draw subpath(3,3.5) of p dashed evenly;
draw subpath(3.5,4) of p dashed withdots;

endfig;
beginfig(108)
u:=1cm;
path p,q;
p := (0,0){up} .. (u,2u){up};
q := (u,0){up} .. (0,2u){up};
draw p;
draw subpath(0,.4) of q withpen pencircle scaled 1bp;
draw subpath(.6,1) of q withpen pencircle scaled 1bp;
endfig;
beginfig(109)
u:=1cm;
path a,b,c,d;
a = (-u,-.2u){up} .. tension 1.2 .. (u,-.2u){down};
b = a rotated 90;
c = b rotated 90;
d = c rotated 90;
fill buildcycle(a,b,c,d) withcolor .8white;
draw a; draw b; draw c; draw d;

endfig;
beginfig(110)
u:=1cm;
path c[];
c[1] := fullcircle scaled u;
c[2] := c[1] shifted (0,.5u);
draw c[1] dashed evenly;
draw c[2] dashed evenly;
draw buildcycle(c[1],c[2]) withpen pencircle scaled 1bp;
endfig;
beginfig(111)
path a,b,c;
a = fullcircle scaled 2u shifted (.5u,0);
b = a rotated (360/3);
c = b rotated (360/3);
fill a withcolor red;
fill b withcolor green;
fill c withcolor blue;
fill buildcycle(a,b) withcolor red + green;
fill buildcycle(b,c) withcolor green + blue;
fill buildcycle(c,a) withcolor blue + red;
fill buildcycle(a,b,c) withcolor white;
draw a; draw b; draw c;
endfig;
beginfig(112)
def compute_curve(suffix f)(expr xmin, xmax, xinc) =
( (xmin,f(xmin))
for x=xmin+xinc step xinc until xmax:
.. (x,f(x))
endfor )
enddef;
vardef f(expr x) = x**2 + 1 enddef;
vardef g(expr x) = 2 - (x-1)**2 enddef;
path p, q;
p := compute_curve(f, -1, 1.5, .1) scaled 1cm;
q := compute_curve(g, -.5, 2, .1) scaled 1cm;
fill buildcycle(p,reverse q) withcolor red+green;
draw p withpen pencircle scaled 1bp;
draw q withpen pencircle scaled 1bp;
draw (-1cm,0) -- (2cm,0);
draw (0,g(-.5)*1cm) -- (0,f(1.5)*1cm);
endfig;
beginfig(113)
path p, q;
p = (0,0){up} .. (2cm,0){up};
q = (0,1cm){dir -60}..(1cm,-1cm)..{dir 60}(2cm,1cm);
draw p; draw q;
draw p intersectionpoint q withpen pencircle scaled 4bp;

endfig;
beginfig(114)
path p, q;
p = (0,0){up} .. (2cm,0){up};
q = (0,1cm){dir -60}..(1cm,-1cm)..{dir 60}(2cm,1cm);
draw p; draw q;
numeric a,b;
(a,whatever) = p intersectiontimes q;
draw point a of p withpen pencircle scaled 4bp;

endfig;
beginfig(115)
pair A,B;
path p;
A = (0,1cm);
B = A rotated 120;
p = A{dir 0} .. tension 2 .. B{dir 120};
numeric a;
(a,whatever) = p intersectiontimes (p rotated 120);
draw subpath(0,a-.02) of p;
draw subpath(a+.02,1) of p;
draw subpath(0,a-.02) of p rotated 120;
draw subpath(a+.02,1) of p rotated 120;
draw subpath(0,a-.02) of p rotated -120;
draw subpath(a+.02,1) of p rotated -120;
endfig;
beginfig(116)
u:=2cm;
pair A[], B[], C[], D[], E[];
path p[];

A[0] = u*up;
for i=1 upto 10:
A[i] := A[i-1] rotated 72;
endfor;
for i=0 upto 4:
p[i] := A[i]--A[i+1];
draw p[i];
draw (point 1 of p[i]) --
( (point 1 of p[i]) + 4mm*unitvector(direction 1 of p[i]));
draw (point 0 of p[i]) --
( (point 0 of p[i]) - 4mm*unitvector(direction 0 of p[i]));
endfor

for i=0 upto 9:
B[i] := 1/2[ A[i], A[i+1] ];
endfor;
B[5]:=B[0];

for i=0 upto 9:
C[i] := .8*B[i];
endfor;

for i=0 upto 4:
p[i] := B[i] --- C[i] .. C[i+2]{dir 72i};
draw p[i];
draw (point 2 of p[i]) --
( (point 2 of p[i]) + 4mm*unitvector(direction 2 of p[i]));
draw (point 0 of p[i]) --
( (point 0 of p[i]) - 4mm*unitvector(direction 0 of p[i]));
endfor;
for i=0 upto 4:
draw subpath(1,1.4) of p[i] withpen pencircle scaled 4bp withcolor white;
draw subpath(0,1.5) of p[i];
endfor;

for i=0 upto 4:
draw A[i] withpen pencircle scaled 4bp;
draw B[i] withpen pencircle scaled 4bp;
draw C[i] withpen pencircle scaled 4bp;
endfor;
endfig;
beginfig(117)
u:=2cm;
pair A, B, C, D, E;
path p, q, r;

A = u*up;
p := (-.2)[ A, A rotated 72 ] -- (1.2)[ A, A rotated 72 ];
for i=0 upto 5:
draw p rotated 72i;
endfor;
B := 1/2[ A, A rotated 72 ];
C := .8*B;

p := B --- C .. (C rotated (2*72)){right};
% On allonge le chemin p
p := ( (point 0 of p) - 4mm*unitvector(direction 0 of p))
--
(point 0 of p)
& p &
(point 2 of p)
--
( (point 2 of p) + 4mm*unitvector(direction 2 of p));

E = p intersectionpoint (p rotated 72);
q := p cutbefore fullcircle scaled -2mm shifted E;
r := p cutafter fullcircle scaled 2mm shifted E;

for i=0 upto 4:
draw q rotated 72i;
draw r rotated 72i;
draw A rotated 72i withpen pencircle scaled 4bp;
draw B rotated 72i withpen pencircle scaled 4bp;
draw C rotated 72i withpen pencircle scaled 4bp;
endfor;
endfig;
beginfig(118)
for i=0 step 1 until 3:
draw 1cm*right rotated (i*90)
withpen pencircle scaled 4bp;
endfor;

endfig;
beginfig(119)
draw for i=0 step 1 until 3:
1cm*right rotated (i*90) --
endfor cycle;

endfig;
beginfig(120)
n:=5;
draw for i=0 step 1 until n-1:
1cm*up rotated (i*360/n) --
endfor cycle;
endfig;
beginfig(121)
n:=7;
draw for i=0 step 1 until n-1:
1cm*up rotated (i*360/n) --
endfor cycle;
endfig;
beginfig(122)
path p;
p = (0,0) .. (-1cm,2cm) .. (2cm,1cm) .. (1cm,0);
draw p;
n:=10;
for i=0 step 1 until n:
draw point (i/n*length(p)) of p
withpen pencircle scaled 4bp;
endfor;
endfig;
beginfig(123)
path p;
p = (0,0) .. (-1cm,2cm) .. (2cm,1cm) .. (1cm,0);
draw p;
n:=10;
for i=0 step length(p)/n until length(p):
drawarrow (point i of p) --
1cm * unitvector(direction i of p)
shifted point i of p;
endfor;
endfig;
beginfig(124)
u:=1cm;
draw (-2u,0)--(2u,0);
draw (0,-2u)--(0,2u);
for i=-2u step u until 2u:
draw (i,u/20)--(i,-u/20);
draw (u/20,i)--(-u/20,i);
endfor;
endfig;
beginfig(125)
u:=1cm;
draw (-2u,0)--(2u,0);
draw (0,-2u)--(0,2u);
for i=-2u step u until 2u:
draw (i,u/10)--(i,-u/10);
draw (u/10,i)--(-u/10,i);
endfor;
for i=-2u step u/5 until 2u:
draw (i,u/20)--(i,-u/20);
draw (u/20,i)--(-u/20,i);
endfor;
endfig;
beginfig(126)
u:=1cm;
draw (-2u,0)--(2u,0);
draw (0,-2u)--(0,2u);
for i=-2u step u until 2u:
draw (i,2u)--(i,-2u);
draw (2u,i)--(-2u,i);
endfor;
endfig;
beginfig(127)
u:=1cm;
draw (-2u,0)--(2u,0);
draw (0,-2u)--(0,2u);
for i=-2u step u until 2u:
draw (i,2u)--(i,-2u);
draw (2u,i)--(-2u,i);
endfor;
for i=-2u step u/5 until 2u:
draw (i,2u)--(i,-2u) withpen pencircle scaled .2bp;
draw (2u,i)--(-2u,i) withpen pencircle scaled .2bp;
endfor;
endfig;
beginfig(128)
u := 5mm;
% vardef est n�cessaire pour pouvoir passer f en argument
vardef f(expr x) = x**2 -.1 enddef;
def axes(expr xmin,xmax,ymin,ymax) =
draw ( (xmin,0) -- (xmax,0) ) scaled u;
draw ( (0,ymin) -- (0,ymax) ) scaled u;
enddef;
def courbe(suffix f)(expr xmin, xmax, M) =
draw ( ( xmin, f(xmin) )
for i=1 upto M:
-- ( xmin + (i/M)*(xmax - xmin), f( xmin + (i/M)*(xmax - xmin) ))
endfor ) scaled u;
enddef;
vardef newton(suffix f)(expr y, h, M) =
save x,t;
numeric x,t; x:=y;
for i=1 upto M:
t := x - f(x)/( (f(x+h) - f(x))/h );
draw ( (x,f(x)) -- (t,0) -- (t,f(t)) ) scaled u;
x := t;
endfor;
enddef;
axes(-.5,2,-.5,4);
courbe(f,-.5,2, 100);
newton(f, 2, .01, 10);
endfig;
beginfig(129)
transform T;
u:=1cm;
z0=(0,0); z1=(2u,0); z3 = z1 rotated 90; z2 = z1+z3;
z0 transformed T = .1[z0,z1];
z1 transformed T = .1[z1,z2];
z2 transformed T = .1[z2,z3];
path p;
p = z0--z1--z2--z3--cycle;
fill p withcolor .8*white;
fill p transformed T withcolor white;
endfig;
beginfig(130)
transform T;
u:=1cm;
z0=(0,0); z1=(2u,0); z3 = z1 rotated 90; z2 = z1+z3;
z0 transformed T = .1[z0,z1];
z1 transformed T = .1[z1,z2];
z2 transformed T = .1[z2,z3];
path p;
p = z0--z1--z2--z3--cycle;
for i=0 upto 100:
fill p withcolor .8*white;
p := p transformed T;
fill p withcolor white;
p := p transformed T;
endfor;
endfig;
beginfig(131)
transform T;
u:=1cm;
z1=(0,2u);
n := 5;
for i=1 upto n-1:
z[i+1] = z1 rotated (360*i/n);
endfor;
z1 transformed T = .1[z1,z2];
z2 transformed T = .1[z2,z3];
z3 transformed T = .1[z3,z4];
path p;
p = for i=1 upto n: z[i] -- endfor cycle;
for i=0 upto 100:
fill p withcolor .8*white;
p := p transformed T;
fill p withcolor white;
p := p transformed T;
endfor;
endfig;
beginfig(132)
u:=1cm;
pair A[];
numeric n; n:=7;
A[0] = (u,0);
for i=1 upto n-1:
A[i] = A[0] rotated (360/n*i);
endfor;
for i=0 upto n-1:
draw A[i] withpen pencircle scaled 4bp;
for j=0 upto n-1:
if i<>j: draw A[i]--A[j] fi;
endfor;
endfor;
endfig;
beginfig(133)
u:=2cm;
numeric n,m; n:=4; m:=5;
pair A[], B[];
for i=1 upto n-1: A[i+1]-A[i] = (0,.2u); endfor;
for j=1 upto m-1: B[j+1]-B[j] = (0,.2u); endfor;
(0,0) for i=1 upto n: + A[i] endfor = (0,0);
(0,0) for j=1 upto m: + B[j] endfor = (4u,0);
for i=1 upto n:
draw A[i] withpen pencircle scaled 4bp;
endfor;
for j=1 upto m:
draw B[j] withpen pencircle scaled 4bp;
endfor;
for i=1 upto n:
for j=1 upto m:
draw A[i]--B[j];
endfor;
endfor;
endfig;
beginfig(134)
u:=1cm;
numeric n,m; n:=3; m:=3;
pair A[], B[];
for i=1 upto n-1: A[i+1]-A[i] = (.5u,0); endfor;
for j=1 upto m-1: B[j+1]-B[j] = (.5u,0); endfor;
(0,0) for i=1 upto n: + A[i] endfor = (0,0);
(0,0) for j=1 upto m: + B[j] endfor = (0,4u);
for i=1 upto n:
draw A[i] withpen pencircle scaled 4bp;
endfor;
for j=1 upto m:
draw B[j] withpen pencircle scaled 4bp;
endfor;
for i=1 upto n:
for j=1 upto m:
draw A[i]--B[j];
endfor;
endfor;
endfig;
beginfig(135)
pair A[], B[];
numeric n; n:=6;
for i=0 upto n-1:
A[i] = 1cm * right rotated (i*360/n);
B[i] = 2cm * right rotated (i*360/n);
endfor;
A[n] = A[0]; B[n] = B[0];
for i=0 upto n-1:
draw A[i] -- A[i+1] -- B[i+1] -- B[i];
draw A[i] withpen pencircle scaled 4bp;
draw B[i] withpen pencircle scaled 4bp;
endfor;
endfig;
beginfig(136)
numeric n; n:=5;
pair O,A,B,C,D;
O = (0,0);
A = 1cm*up;
B = 2cm*up rotatedabout(A,30);
C = 2cm*up;
D = 2cm*up rotatedabout(A,-30);
for i=0 upto n-1:
draw (O--A--C) rotated (i*360/n);
draw (B--A--D) rotated (i*360/n);
draw A rotated (i*360/n) withpen pencircle scaled 4bp;
draw B rotated (i*360/n) withpen pencircle scaled 4bp;
draw C rotated (i*360/n) withpen pencircle scaled 4bp;
draw D rotated (i*360/n) withpen pencircle scaled 4bp;
endfor;
draw O withpen pencircle scaled 4bp;
endfig;
beginfig(137)
path p; u:=1cm;
p = fullcircle xscaled -u yscaled 3u;
draw p;
for i=2 step .5 until 6:
draw (point 2 of p){down} .. (point i of p);
endfor;
endfig;
beginfig(138)
pair P[], Q[], R[], S[];
u:=.5cm;
for i=0 upto 4:
P[i] = u* down rotated (i*360/5);
endfor;
P[5] = P[0];
for i=0 upto 4:
Q[i] = 3*( 1/2[ P[i], P[i+1] ] );
endfor;
Q[5] = Q[0];
for i=0 upto 4:
R[i] = 1/3( Q[i] + Q[i+1] + P[i+1] );
endfor;
R[5] = R[0];
for i=0 upto 5:
S[i] = 1.5*Q[i];
endfor;
for i=0 upto 4:
draw P[i] -- P[i+1];
draw P[i+1] -- R[i];
draw Q[i] -- R[i];
draw R[i] -- Q[i+1];
draw Q[i] -- S[i];
draw S[i] -- S[i+1];
endfor;
endfig;
beginfig(139)
pair P[], Q[], R[], S[];
u:=.5cm;
for i=0 upto 4:
P[i] = u* down rotated (i*360/5);
endfor;
P[5] = P[0];
for i=0 upto 4:
Q[i] = 3*( 1/2[ P[i], P[i+1] ] );
endfor;
Q[5] = Q[0];
for i=0 upto 4:
R[i] = 1/3( Q[i] + Q[i+1] + P[i+1] );
endfor;
R[5] = R[0];
for i=0 upto 5:
S[i] = 1.5*Q[i];
endfor;
for i=0 upto 4:
draw P[i] -- P[i+1];
draw P[i+1] -- R[i];
draw Q[i] -- R[i];
draw R[i] -- Q[i+1];
draw Q[i] -- S[i];
draw S[i] -- S[i+1];
endfor;
draw P[2] -- P[3] -- P[4] -- P[0] -- P[1] --
R[0] -- Q[0] -- R[4] -- Q[4] -- R[3]
-- Q[3] -- R[2] -- Q[2] --
S[2] -- S[3] -- S[4] -- S[0] -- S[1] --
Q[1] -- R[1] -- cycle
withpen pencircle scaled 2bp;
endfig;
beginfig(140)
for i=1 step -.01 until 0:
fill fullcircle scaled (i*2cm) withcolor i*white;
endfor;
draw fullcircle scaled 2cm withpen pencircle scaled 2bp;
endfig;
beginfig(141)
u:=5mm;
path p;
p = (0,0) .. (-1,1) .. (2,0) .. (0,-3) .. cycle;
p := p shifted (-1,0);
for i=1 step -.01 until 0:
fill p scaled (i*u) withcolor i*white;
endfor;
draw p scaled u withpen pencircle scaled 2bp;
endfig;
beginfig(142)
z0 = (50,50);
z1 = z0 rotated 90;
z2 = z1 rotated 90;
z3 = z2 rotated 90;
path carre;
carre = z0--z1--z2--z3--cycle;
s := .01;
path rect;
z4 = s [z2,z3]; z5 = s [z1,z0];
rect = z1--z2--z4--z5--cycle;
for i=0 step s until 1:
fill rect shifted (i*(z0-z1)) withcolor i*white;
endfor;
draw carre withpen pencircle scaled 2bp;
endfig;
beginfig(143)
z0 = (50,50);
z1 = z0 rotated 90;
z2 = z1 rotated 90;
z3 = z2 rotated 90;
path carre;
carre = z0--z1--z2--z3--cycle;
s := .01;
for i=1 step -s until s:
fill carre scaled i withcolor i*white;
endfor;
endfig;
beginfig(144)
u:=1cm;
vardef degrade(expr p,q,M,N) =
save a,b;
numeric a,b;
a := length(p);
b := length(q);
for i=0 upto M:
draw (i/M) [ point 0 of p, point 0 of q ]
for j=1 upto N:
.. (i/M) [ point (j/N*a) of p, point (j/N*b) of q ]
endfor;
endfor;
enddef;
degrade(
(-.1u,-.1u) .. (.1u,.1u) .. cycle,
(-u,-u) -- (u,-u) -- (u,u) -- (-u,u) -- cycle,
10,
100);
endfig;
beginfig(145)
u:=1cm;
def couleur(expr c) = c*white enddef;
vardef degrade(expr p,q,M,N) =
save a,b;
numeric a,b;
a := length(p);
b := length(q);
for i=0 upto M:
draw (i/M) [ point 0 of p, point 0 of q ]
for j=1 upto N:
.. (i/M) [ point (j/N*a) of p, point (j/N*b) of q ]
endfor
withcolor couleur(i/M);
endfor;
enddef;
degrade(
(-.5u,-.5u) .. (.5u,.5u) .. cycle,
(-u,-u) -- (u,-u) -- (u,u) -- (-u,u) -- cycle,
255,
100);
endfig;
beginfig(146)
def degrade(expr p, q, N) =
begingroup
save n, m, M;
numeric n, m, M;
n := length(p);
m := length(q);
M := n*m; % Il faudrait prendre le ppcm
for i=0 upto N:
draw
(i/N)[ point 0 of p, point 0 of q ]
{ (i/N)[ direction 0 of p, direction 0 of q ] }
for j=1 upto M-1:
..
{ (i/N) [ direction 1 of subpath((j-1)*n/M,j*n/M) of p,
direction 1 of subpath((j-1)*m/M,j*m/M) of q ] }
(i/N)[ point (j*n/M) of p, point (j*m/M) of q ]
{ (i/N) [ direction 0 of subpath(j*n/M,(j+1)*n/M) of p,
direction 0 of subpath(j*m/M,(j+1)*m/M) of q ] }
endfor
..
{ (i/N)[ direction n of p, direction m of q ] }
(i/N)[ point n of p, point m of q ]
;
endfor;
endgroup;
enddef;
numeric u;
u := 2cm;
path p, q;
p := fullcircle scaled u;
q := (-u,-u)--(u,-u)--(u,u)--(-u,u)--cycle;
degrade(p,q,10);
endfig;
beginfig(147)
draw for i=0 step 10 until 360:
2cm* (sind(2*i), cosd(3*i)) ..
endfor cycle;
endfig;
beginfig(148)
for i=0 step .1 until 360:
col := i/360;
draw 2cm* (sind(2*i), cosd(3*i))
withpen pencircle scaled 2bp
withcolor
if col>.5: (2*(1-col)) [red, blue]
else: (1-2col) [blue, red]
fi;
endfor;
endfig;
beginfig(149)
def couleur(expr x) =
if x>.5: (2*(1-x)) [red, blue];
else: (1-2x) [blue, red]
fi
enddef;
for i=0 step .1 until 360:
draw 2cm* (sind(2*i), cosd(3*i))
withpen pencircle scaled 2bp
withcolor couleur(i/360);
endfor;
endfig;
beginfig(150)
for i=0 step 1 until 360:
pair P;
P = 2cm* (sind(2*i), cosd(3*i));
fill fullcircle scaled 4mm shifted P withcolor white;
draw fullcircle scaled 4mm shifted P;
endfor;
endfig;
beginfig(151)
for i=0 step 1 until 360:
pair P;
P = 2cm* (sind(2*i), cosd(3*i));
fill fullcircle scaled 4mm shifted P withcolor white;
draw fullcircle scaled 4mm shifted P;
endfor;
picture p;
p:=nullpicture;
for i=-180 step 1 until 180:
pair P;
P = 2cm* (sind(2*i), cosd(3*i));
addto p contour fullcircle scaled 4mm shifted P withcolor white;
addto p doublepath fullcircle scaled 4mm shifted P
withpen pencircle scaled .5bp;
endfor;
clip p to (.5cm,2.5cm) -- (.5cm,1.5cm)--
(-.5cm,1.5cm) -- (-.5cm,2.5cm)--cycle;
draw p;
endfig;
beginfig(152)
u:=5mm;
vardef project(expr x,y,z) =
x*(-1,-1) + y*(1,0) + z*(0,1)
enddef;
vardef f(expr x,y) = sind(x/u*180)*sind(y/u*180)*u enddef;
numeric m,M;
m:=-2u; M:=2u;
for i=m step .1u until M:
path p;
p =
for j=m step .1u until M:
project(i,j,f(i,j)) --
endfor
project(i,M,f(i,M));
fill (project(i,m,f(i,m)) - (0,3u)) -- p --
(project(i,M,f(i,M)) - (0,3u)) -- cycle
withcolor white;
draw (project(i,m,f(i,m)) - (0,3u)) -- p --
(project(i,M,f(i,M)) - (0,3u)) -- cycle;
draw p;
endfor;
endfig;
beginfig(153)
vardef project(expr x,y,z) =
x*(-1,-1) + y*(1,0) + z*(0,1)
enddef;
vardef f(expr x,y) = sind(x/u*180)*sind(y/u*180)*u enddef;
m:=-2u; M:=2u; inc:=.1u;
for i=m step inc until M:
for j=m step inc until M:
path p;
p = project(i,j,f(i,j)) --
project(i,j+inc,f(i,j+inc)) --
project(i+inc,j+inc,f(i+inc,j+inc)) --
project(i+inc,j,f(i+inc,j)) --
cycle;
fill p withcolor white;
draw p;
endfor
endfor;
endfig;
beginfig(154)
vardef project(expr x,y,z) =
x*(-1,-1) + y*(1,0) + z*(0,1)
enddef;
vardef f(expr x,y) = sind(x/u*180)*sind(y/u*180)*u enddef;
numeric m,M,inc,couleur;
m:=-2u; M:=2u; inc:=.1u;
for i=m step inc until M:
for j=m step inc until M:
path p;
p = project(i,j,f(i,j)) --
project(i,j+inc,f(i,j+inc)) --
project(i+inc,j+inc,f(i+inc,j+inc)) --
project(i+inc,j,f(i+inc,j)) --
cycle;
dfdx := (f(i,j) - f(i+inc,j))/inc;
dfdy := (f(i,j) - f(i,j+inc))/inc;
couleur := 1/sqrt( dfdx**2 + dfdy**2 + 1);
fill p withcolor couleur*(red+green);
endfor
endfor;
endfig;
beginfig(155)
vardef f(expr x,y) = sind(x/u*180)*sind(y/u*180)*u enddef;

boolean dessine_fil_de_fer; dessine_fil_de_fer := false;
color dessine_couleur; dessine_couleur := red+green;

vardef dessine(suffix f)(expr xmin, xmax, xinc, ymin, ymax, yinc) =
save i,j,p,dfdx,dfdy,project;
vardef project(expr x,y,z) =
x*(-1,-1) + y*(1,0) + z*(0,1)
enddef;
for i=m step inc until M:
for j=m step inc until M:
path p;
p = project(i,j,f(i,j)) --
project(i,j+inc,f(i,j+inc)) --
project(i+inc,j+inc,f(i+inc,j+inc)) --
project(i+inc,j,f(i+inc,j)) --
cycle;
dfdx := (f(i,j) - f(i+inc,j))/inc;
dfdy := (f(i,j) - f(i,j+inc))/inc;
couleur := 1/sqrt( dfdx**2 + dfdy**2 + 1);
fill p withcolor couleur*dessine_couleur;
if dessine_fil_de_fer: draw p fi;
endfor
endfor;
enddef;

% Il faudrait pouvoir choisir diff�rents
% types d'� �clairage �.
vardef f(expr x,y) = sind(x/u*180)*sind(y/u*180)*u enddef;
dessine(f,-2u,2u,.1u, -2u,2u,.1u);
endfig;
beginfig(156)
vardef random_path (expr n) =
save i, A ; numeric i; pair A[];
for i=0 upto n:
A[i] = (uniformdeviate(2u), uniformdeviate(2u));
endfor;
A[0]
for i=1 upto n:
.. A[i]
endfor
enddef;

vardef intersections(expr p,q) =
save a,b,N,i,j;
numeric N,i,j;
N:=10;
for i=0 step length(p)/N until length(p):
for j=0 step length(q)/N until length(p):
numeric a,b;
pair A;
(a,b) = (subpath(i,i+length(p)/N) of p)
intersectiontimes
(subpath(j,j+length(q)/N) of q);
if a <> -1:
A = point a of subpath(i,i+length(p)/N) of p;
show A;
draw A withpen pencircle scaled 4bp;
fi;
endfor;
endfor;
enddef;

path p,q;
p:=random_path(4);
q:=random_path(4);
draw p withcolor red;
draw q withcolor blue;
intersections(p,q);
endfig;
beginfig(157)
vardef auto_intersections(expr p) =
save a,b,N,i,j;
numeric N,i,j;
N:=100;
for i=0 step length(p)/N until length(p):
for j=i+2*length(p)/N
step length(p)/N
until length(p):
numeric a,b;
pair A;
(a,b) = (subpath(i,i+length(p)/N) of p)
intersectiontimes
(subpath(j,j+length(p)/N) of p);
if a <> -1:
A = point a of subpath(i,i+length(p)/N) of p;
show A;
draw A withpen pencircle scaled 4bp;
fi;
endfor;
endfor;
enddef;

u:=2cm;
path p,q;
p:=random_path(12);
draw p;
auto_intersections(p);
endfig;
beginfig(158)
path p;
p := (0,0){up} .. (1cm,1cm) .. (1cm,0);
draw p;
draw point 1/2length(p) of p
withpen pencircle scaled 4bp withcolor red;
draw point (arctime (1/2 arclength(p)) of p) of p
withpen pencircle scaled 4bp;

endfig;
beginfig(159)
vardef milieu(expr p) =
save l,i,tot,A,B;
numeric l,tot,i;
pair A,B;
tot := longueur(p);
l:=0;
B := point 0 of p;
for i:=0 step .01 until length(p):
A := B;
B := point i of p;
l := l+abs(B-A);
exitif l > 1/2 tot;
endfor;
1/2[A,B]
enddef;

path p;
p := (0,0){up} .. (1cm,1cm) .. (1cm,0);
draw p;
draw point 1/2length(p) of p withpen pencircle scaled 4bp withcolor red;
draw milieu(p) withpen pencircle scaled 4bp;
endfig;
beginfig(160)
vardef milieu_time(expr p) =
save l,i,tot,A,B,t;
numeric l,tot,i,t;
pair A,B;
tot := longueur(p);
l:=0;
B := point 0 of p;
for i:=0 step .01 until length(p):
t:=i;
A := B;
B := point i of p;
l := l+abs(B-A);
exitif l > 1/2 tot;
endfor;
t % Pas de point-virgule
enddef;

save arrowhead;
vardef arrowhead expr p =
save A,u; pair A,u;
A := milieu(p);
u := unitvector(direction milieu_time(p) of p);
A -- (A - ahlength*u rotated 15) --
(A - ahlength*u rotated -15) -- cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(161)
save arrowhead;
vardef arrowhead expr p =
save A,B,u; pair A,B,u;
A := milieu(p);
B := p intersectionpoint
(fullcircle scaled ahlength shifted A);
u := unitvector(direction milieu_time(p) of p);
A -- (A - ahlength*u rotated 30) -- B --
(A - ahlength*u rotated -30) -- cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(162)
save arrowhead;
vardef arrowhead expr p =
save A,u; pair A,u;
A := milieu(p);
u := unitvector(direction milieu_time(p) of p);
A -- (A - ahlength*u rotated 30) -- A --
(A - ahlength*u rotated -30) -- cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(163)
save arrowhead;
vardef arrowhead expr p =
save A,u,a,b; pair A,u; path a,b;
A := milieu(p);
u := unitvector(direction milieu_time(p) of p);
a := A{-u} .. (A - ahlength*u rotated 30);
b := A{-u} .. (A - ahlength*u rotated -30);
( a & reverse(a) & b & reverse(b) ) --cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(164)
pair A,B,C;
C = 3mm*up;
A = C rotated 120;
B = C rotated -120;
picture pic ;
pic:=nullpicture;
addto pic doublepath A--B--C--cycle withpen currentpen;
addto pic doublepath A withpen pencircle scaled 4bp;
addto pic doublepath B withpen pencircle scaled 4bp;
addto pic doublepath C withpen pencircle scaled 4bp;
for i=-3 upto 3:
for j=-3 upto 3:
draw pic shifted( i*(B-A) + j*(C-A) );
endfor;
endfor;
clip currentpicture to (-2cm,-2cm)--(2cm,-2cm)--(2cm,2cm)--(-2cm,2cm)--cycle;
endfig;
beginfig(165)
pair A,B,C;
C = 3mm*up;
A = C rotated 120;
B = C rotated -120;
picture pic ;
pic:=nullpicture;
path p;
p := A{(C-A) rotated 30} .. C{(C-A) rotated 30};
addto pic doublepath p withpen currentpen;
addto pic doublepath p rotated 120 withpen currentpen;
addto pic doublepath p rotated -120 withpen currentpen;
for i=-3 upto 3:
for j=-3 upto 3:
draw pic shifted( i*(B-A) + j*(C-A) );
endfor;
endfor;
clip currentpicture to (-2cm,-2cm)--(2cm,-2cm)--(2cm,2cm)--(-2cm,2cm)--cycle;
endfig;
beginfig(166)
ux:=2mm;
uy:=5mm;
numeric xmin, xmax, ymin, ymax, M;
xmin := -6.3; xmax := 12.6;
ymin := -2; ymax := 2;
M := 100;
draw (ux*xmin,0) -- (ux*xmax,0);
draw (0,uy*ymin) -- (0,uy*ymax);
pair a[];
for i=0 upto M:
a[i] := (
xmin + (i/M)*(xmax-xmin),
sind(180/3.14*( xmin + (i/M)*(xmax-xmin) ))
) xscaled ux yscaled uy;
endfor;
draw a[0] for i=1 upto M: --a[i] endfor;
endfig;
beginfig(167)
ux:=5mm;
uy:=2mm;
numeric xmin, xmax, ymin, ymax, M;
xmin := -2; xmax := 2;
ymin := -.1; ymax := 8;
M := 100;
draw (ux*xmin,0) -- (ux*xmax,0);
draw (0,uy*ymin) -- (0,uy*ymax);
pair a[];
for i=0 upto M:
a[i] := (
xmin + (i/M)*(xmax-xmin),
mexp(256*( xmin + (i/M)*(xmax-xmin) ))
) xscaled ux yscaled uy;
endfor;
draw a[0] for i=1 upto M: --a[i] endfor;
endfig;
beginfig(168)
ux:=5mm;
uy:=5mm;
numeric xmin, xmax, ymin, ymax, M;
xmin := .2; xmax := 3;
ymin := -1.6; ymax := 1.2;
M := 100;
draw (ux*-.1,0) -- (ux*xmax,0);
draw (0,uy*ymin) -- (0,uy*ymax);
pair a[];
for i=0 upto M:
a[i] := (
xmin + (i/M)*(xmax-xmin),
(1/256)*mlog(( xmin + (i/M)*(xmax-xmin) ))
) xscaled ux yscaled uy;
endfor;
draw a[0] for i=1 upto M: --a[i] endfor;
endfig;
beginfig(169)
path p;
p = fullcircle scaled 2cm;
z0 = (-1cm,0);
draw p;
draw z0 withpen pencircle scaled 2pt;

pair A[];
for i=0 step length(p)/100 until length(p):
pair M,N;
M = point i of p;
N-M = whatever * direction i of p;
N-z0 = whatever * direction i of p rotated 90;
A[i] := N;
endfor;
draw for i=0 step length(p)/100 until length(p):
A[i] ..
endfor cycle;
endfig;
beginfig(170)
vardef cardiodide(expr p, O) =
save i,M,N;
numeric i;
for i=0 step length(p)/100 until length(p):
hide(
pair M,N;
M = point i of p;
N-M = whatever * direction i of p;
N-O = whatever * direction i of p rotated 90;
)
N ..
endfor cycle
enddef;

path p;
p = fullcircle scaled 2cm;
z0 = (-1cm,0);
draw p;
draw z0 withpen pencircle scaled 2pt;
draw cardiodide(p,z0);
endfig;
beginfig(171)
vardef cardiodide(expr p, O) =
save i,M,N;
numeric i;
for i=0 step length(p)/100 until length(p):
hide(
pair M,N;
M = point i of p;
N-M = whatever * direction i of p;
N-O = whatever * direction i of p rotated 90;
)
N ..
endfor cycle
enddef;

path p;
p = fullcircle scaled 2cm;
z0 = (-1cm,0);
pickup pencircle scaled 1pt
draw p;
draw z0 withpen pencircle scaled 3pt;
draw cardiodide(p,z0);
pickup pencircle scaled .4pt
pair M,N;
i:=1.5;
M = point i of p;
N-M = whatever * direction i of p;
N-z0 = whatever * direction i of p rotated 90;
draw z0--N;
draw (-1/2)[N,M]--(3/2)[N,M];
draw N withpen pencircle scaled 3pt;
draw M withpen pencircle scaled 3pt;
endfig;
beginfig(172)
path p;
p := (-1cm,0) .. (1cm,-1cm) .. (8mm,0)
.. (1cm,1cm) .. (-1cm,1cm) .. cycle;
z0 = (-2cm,0);
draw p withpen pencircle scaled 1bp;
draw z0 withpen pencircle scaled 3pt;
draw cardiodide(p,z0);
endfig;
beginfig(173)
vardef inversion (expr O,k,M) =
if pair M:
(O + k*unitvector(M-O)/abs(M-O))
elseif path M:
for i=0 step length(M)/100 until length(M):
inversion(O,k,point i of M) ..
endfor
cycle
fi
enddef;

u:=4cm;
path p[],A,B;

z0 = (5u,0) rotated 10;

A = fullcircle scaled 2u;
B = A scaled 3;
draw inversion( z0, 2 (u**2), A )
withpen pencircle scaled 1pt;
draw inversion( z0, 2 (u**2), B )
withpen pencircle scaled 1pt;

p0 = fullcircle scaled 2u shifted (2u,0);
for i=0 upto 5:
if i<>0:
p[i] = p[i-1] rotated (360/6);
fi;
draw inversion( z0, 2 (u**2), p[i] );
endfor;
endfig;
beginfig(174)
def curve(expr p,i,q,j,t) =
point i of p {direction i of p} ..
tension t ..
point j of q {direction j of q}
enddef;

vardef sphere_with_holes (expr n) =
save i;
c[0] = fullcircle xscaled u yscaled 2u
shifted (4u,0) rotated (360/(2n)) ;
draw c[0];
for i=1 upto n-1:
c[i] = c[i-1] rotated (360/n);
draw c[i];
endfor;
l[0] = curve(c[0], 2, c[1], -2, 1);
draw l[0];
for i=1 upto n-1:
l[i] = l[i-1] rotated (360/n);
draw l[i];
endfor;
enddef;

u:=3mm;
path c[], l[];
sphere_with_holes(5);
endfig;
beginfig(175)
def curve(expr p,i,q,j,t) =
point i of p {direction i of p} ..
tension t ..
point j of q {direction j of q}
enddef;

vardef sphere_with_holes (expr n) =
save i;
c[0] = fullcircle xscaled u yscaled 2u
shifted (4u,0) rotated (360/(2n)) ;
for i=1 upto n-1:
c[i] = c[i-1] rotated (360/n);
endfor;
l[0] = curve(c[0], 2, c[1], -2, 1);
for i=1 upto n-1:
l[i] = l[i-1] rotated (360/n);
endfor;
fill for i=0 upto n-1:
( reverse subpath(2,6) of c[i] ) &
l[i] &
endfor
% To turn it into a cycle (ugly)
point length(l[n-1]) of l[n-1] -- cycle
withcolor .8white;
for i=0 upto n-1:
draw c[i]; draw l[i];
endfor;
enddef;

u:=3mm;
path c[], l[];
sphere_with_holes(5);
endfig;
beginfig(176)
path c[], l[];
sphere_with_holes(6);
def ellipse(expr a,b,c,d,e) =
draw curve(a,b,c,d,e) ;
draw curve(c,d,a,b,e) dashed evenly;
enddef;

ellipse (l[0], 2/3, l[2], 1/3, 4);
ellipse (l[1], 2/3, l[3], 1/3, 4);
ellipse (l[2], 2/3, l[4], 1/3, 4);
ellipse (l[3], 2/3, l[5], 1/3, 4);
ellipse (l[4], 2/3, l[0], 1/3, 4);
ellipse (l[5], 2/3, l[1], 1/3, 4);
endfig;
beginfig(177)
vardef bar(expr m,a,b,c) =
m = 1/3a + 1/3b + 1/3c
enddef;
vardef dbar(expr m,a,b,c) =
draw m--a; draw m--b; draw m--c;
draw m withpen pencircle scaled 4bp;
enddef;

pair P[], A,B,C;
for i=0 upto 4:
P[i] = 1cm * up rotated (i*360/5);
draw P[i] withpen pencircle scaled 4bp;
endfor;
bar(A, P[0], P[4], B);
bar(B, A, P[1], C);
bar(C, B, P[2], P[3]);
draw fullcircle scaled 2cm dashed evenly;
dbar(A, P[0], P[4], B);
dbar(B, A, P[1], C);
dbar(C, B, P[2], P[3]);
endfig;
beginfig(178)
% M est sur la bissectrice de l'angle A
vardef bissectrice(expr M,A,B,C) =
(M-A) = whatever * (
(A-C) rotated 1/2(angle(B-A) - angle(C-A)))
enddef;

% Le cercle inscrit
vardef cercle_inscrit(expr A,B,C) =
save M, h; pair M, h;
bissectrice(M,A,B,C);
bissectrice(M,B,C,A);
M-h = whatever * (B-C) rotated 90;
h = whatever[B,C];
fullcircle scaled 2 length(M-h) shifted M
enddef;

pair A,B,C,M;
u:=2cm;
A=(0,0); B=(2u,-.5u); C=(u,u);
draw A--B--C--cycle;
bissectrice(M, A,B,C);
bissectrice(M, B,C,A);
draw M--A; draw M--B; draw M--C;
draw cercle_inscrit(A,B,C);
endfig;
beginfig(179)
vardef premiere_trisectrice (expr M, A,B,C) =
(M-A) = whatever * ( (A-B) rotated 1/3 (angle(C-A) - angle(B-A)) )
enddef;

vardef deuxieme_trisectrice (expr M, A,B,C) =
(M-A) = whatever * ( (A-B) rotated 2/3 (angle(C-A) - angle(B-A)) )
enddef;

pair A,B,C,M[];
u:=2cm;
A=(0,0); B=(2u,-.5u); C=(u,u);
draw A--B--C--cycle;

premiere_trisectrice(M1,A,B,C);
deuxieme_trisectrice(M1,B,C,A);
premiere_trisectrice(M2,B,C,A);
deuxieme_trisectrice(M2,C,A,B);
premiere_trisectrice(M3,C,A,B);
deuxieme_trisectrice(M3,A,B,C);

draw M1--A; draw M1--B;
draw M2--B; draw M2--C;
draw M3--C; draw M3--A;

draw M1--M2--M3--cycle;
endfig;
beginfig(180)
save arrowhead;
vardef arrowhead expr p =
save A,u; pair A,u;
A := point length(p) of p;
u := unitvector(direction length(p) of p);
A -- (A - ahlength*u rotated 15) --
(A - ahlength*u rotated -15) -- cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(181)
save arrowhead;
vardef arrowhead expr p =
save A,B,u; pair A,B,u;
A := point length(p) of p;
B := p intersectionpoint
(fullcircle scaled ahlength shifted A);
u := unitvector(direction length(p) of p);
A -- (A - ahlength*u rotated 30) -- B --
(A - ahlength*u rotated -30) -- cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(182)
save arrowhead;
vardef arrowhead expr p =
save A,u; pair A,u;
A := point length(p) of p;
u := unitvector(direction length(p) of p);
A -- (A - ahlength*u rotated 30) -- A --
(A - ahlength*u rotated -30) -- cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(183)
save arrowhead;
vardef arrowhead expr p =
save A,u,a,b; pair A,u; path a,b;
A := point length(p) of p;
u := unitvector(direction length(p) of p);
a := A{-u} .. (A - ahlength*u rotated 30);
b := A{-u} .. (A - ahlength*u rotated -30);
( a & reverse(a) & b & reverse(b) ) --cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(184)
save arrowhead;
vardef arrowhead expr p =
save A,u; pair A,u;
A := point 1/2length(p) of p;
u := unitvector(direction 1/2length(p) of p);
A -- (A - ahlength*u rotated 15) --
(A - ahlength*u rotated -15) -- cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(185)
save arrowhead;
vardef arrowhead expr p =
save A,B,u; pair A,B,u;
A := point 1/2length(p) of p;
B := p intersectionpoint
(fullcircle scaled ahlength shifted A);
u := unitvector(direction 1/2length(p) of p);
A -- (A - ahlength*u rotated 30) -- B --
(A - ahlength*u rotated -30) -- cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(186)
save arrowhead;
vardef arrowhead expr p =
save A,u; pair A,u;
A := point 1/2length(p) of p;
u := unitvector(direction 1/2length(p) of p);
A -- (A - ahlength*u rotated 30) -- A --
(A - ahlength*u rotated -30) -- cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(187)
save arrowhead;
vardef arrowhead expr p =
save A,u,a,b; pair A,u; path a,b;
A := point 1/2length(p) of p;
u := unitvector(direction 1/2length(p) of p);
a := A{-u} .. (A - ahlength*u rotated 30);
b := A{-u} .. (A - ahlength*u rotated -30);
( a & reverse(a) & b & reverse(b) ) --cycle
enddef;

u:=1cm;
drawarrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(188)
def drawwhitearrow expr p = _apth:=p; _finwhitearr enddef;

def _finwhitearr text t =
draw _apth t;
fill arrowhead _apth t withcolor white;
draw arrowhead _apth t
enddef;

u:=1cm;
drawwhitearrow (0,0) .. (-u,u) .. (u,u);
endfig;
beginfig(189)
def draw_white_arrow expr p = _apth:=p; _fin_white_arr enddef;
def _fin_white_arr text t =
draw _apth t;
fill arrowhead _apth withcolor white;
draw arrowhead _apth t
enddef;

def draw_middle_arrow expr p = _apth:=p; _fin_middle_arr enddef;
def _fin_middle_arr text t =
draw _apth t;
filldraw arrowhead_middle _apth t
enddef;
vardef arrowhead_middle expr p =
save A,u; pair A,u;
A := point (arctime (.5arclength p) of p) of p;
u := unitvector(direction (arctime (.5arclength p) of p) of p);
A -- (A - ahlength*u rotated (.5ahangle) ) --
(A - ahlength*u rotated (-.5ahangle) ) -- cycle
enddef;

def draw_middle_white_arrow expr p = _apth:=p; _fin_middle_white_arr enddef;
let draw_white_middle_arrow = draw_middle_white_arrow;
def _fin_middle_white_arr text t =
draw _apth t;
fill arrowhead_middle _apth t withcolor white;
draw arrowhead_middle _apth t
enddef;

def draw_other_arrow expr p = _apth:=p; _fin_other_arr enddef;
def _fin_other_arr text t =
draw _apth t;
draw arrowhead_other _apth t
enddef;
vardef arrowhead_other expr p =
save A,u,a,b; pair A,u; path a,b;
A := point (length p) of p;
u := unitvector(direction (length p) of p);
a := A{-u} .. (A - ahlength*u rotated 30);
b := A{-u} .. (A - ahlength*u rotated -30);
( a & reverse(a) & b & reverse(b) ) --cycle
enddef;

def draw_other_middle_arrow expr p = _apth:=p; _fin_other_middle_arr enddef;
let draw_middle_other_arrow = draw_other_middle_arrow;
def _fin_other_middle_arr text t =
draw _apth t;
draw arrowhead_other_middle _apth t
enddef;
vardef arrowhead_other_middle expr p =
save A,u,a,b; pair A,u; path a,b;
A := point (arctime (.5arclength p) of p) of p;
u := unitvector(direction (arctime (.5arclength p) of p) of p);
a := A{-u} .. (A - ahlength*u rotated 30);
b := A{-u} .. (A - ahlength*u rotated -30);
( a & reverse(a) & b & reverse(b) ) --cycle
enddef;

path p;
p := halfcircle scaled 2cm;
p := (0,0) .. (3cm,1cm) .. (-1cm,3cm);
p := p scaled .3;
draw_middle_arrow p;
draw_white_arrow p scaled 1.3 withpen pencircle scaled 1bp;
draw_white_middle_arrow p scaled 1.6;
draw_other_middle_arrow p scaled 1.8 withpen pencircle scaled 1bp;
draw_other_arrow p scaled 2 withpen pencircle scaled 1bp;
endfig;
beginfig(190)
vardef mylabel(expr pic, p, t) =
save A; pair A;
A = point t of p +
8bp * unitvector(direction t of p) rotated 90;
label(pic, A);
enddef;
path p; u:=1cm;
p = (0,0)..(-u,u)..(u,u);
draw p;
for i=0 step .2 until length(p):
draw point i of p withpen pencircle scaled 4bp;
mylabel(btex $A$ etex,p,i);
endfor;
endfig;
beginfig(191)
vardef mylabel(expr pic, p, t) =
save A; pair A;
A = point t of p +
8bp * unitvector(direction t of p) rotated 90;
label(pic, A);
enddef;
path p; u:=1cm;
p = (0,0)..(-u,u)..(u,u);
draw p;
for i=0 step .2 until length(p):
draw point i of p withpen pencircle scaled 4bp;
mylabel(TEX decimal(i),p,i);
endfor;
endfig;
beginfig(192)
vardef mylabel(expr pic, p, t) =
save A,a; pair A; numeric a;
a := angle(direction t of p rotated 90);
show(a);
a := a + 45/2;
if a>180: a := a - 360 fi;
save ll, lr, ul, ur;
pair ul,ur,ll,lr;
ll := llcorner pic;
lr := lrcorner pic;
ul := ulcorner pic;
ur := urcorner pic;
A = point t of p +
8bp * unitvector(direction t of p) rotated 90;
label(pic shifted ll, A +
if (a >= 0) and (a <= 45): 1/2(ur-ul)
elseif (a >= 45) and (a <= 90): 1/2(ur-ul) + 1/2(ur-lr)
elseif (a >= 90) and (a <= 135): 1/2(ur-lr)
elseif (a >= 135) and (a <= 180): 1/2(ll-lr) + 1/2(ur-lr)
elseif (a >= -180) and (a <= -135): 1/2(ll-lr)
elseif (a >= -135) and (a <= -90): 1/2(ll-ul) + 1/2(ll-lr)
elseif (a >= -90) and (a <= -45): 1/2(ll-ul)
elseif (a >= -45) and (a <= 0): 1/2(ll-ul) - 1/2(ll-lr)
else: hide(show "BUG") (0,0)
fi);
draw A withpen pencircle scaled 2bp withcolor red;
enddef;
path p; u:=1cm;
p = (0,0)..(-u,u)..(u,u);
p := reverse fullcircle scaled 2u;
draw p;
for i=0 step length(p)/10 until length(p):
draw point i of p withpen pencircle scaled 4bp;
mylabel(TEX decimal(i),p,i);
endfor;
endfig;
beginfig(193)
n:=8;
u:=5mm;
for i=0 upto n-1:
for j=0 upto n-1:
if odd(i+j):
fill (0,0)--(u,0)--(u,u)--(0,u)--cycle
shifted (i*u,j*u) withcolor .8white;
fi;
endfor;
endfor;
for i=0 upto n:
draw (0,i*u)--(n*u,i*u);
draw (i*u,0)--(i*u,n*u);
endfor;
endfig;
beginfig(194)
n:=8;
u:=5mm;
for i=0 upto n-1:
for j=0 upto n-1:
if odd(i+j):
for k=0 step u/5 until u:
draw ( (k,0)--(u,u-k) )
shifted (i*u,j*u);
draw ( (0,k)--(u-k,u) )
shifted (i*u,j*u);
endfor;
fi;
endfor;
endfor;
for i=0 upto n:
draw (0,i*u)--(n*u,i*u);
draw (i*u,0)--(i*u,n*u);
endfor;
endfig;
beginfig(195)
n:=8;
u:=5mm;
for i=0 upto n-1:
for j=0 upto n-1:
if odd(i+j):
for k=0 step u/5 until 4/5 u:
if odd(k*5/u):
fill ( (k,0)--(u,u-k)--(u,u-k-u/5)--
(k+u/5,0)--cycle )
shifted (i*u,j*u) withcolor .8white;
else:
fill ( (0,k)--(u-k,u)--(u-k-u/5,u)--
(0,k+u/5)--cycle )
shifted (i*u,j*u) withcolor .8white;
fi;
endfor;
fi;
endfor;
endfor;
for i=0 upto n:
draw (0,i*u)--(n*u,i*u);
draw (i*u,0)--(i*u,n*u);
endfor;
endfig;
beginfig(196)
vardef trace (suffix f)(expr a,b,inc) =
save i; numeric i;
for i=a step inc until b:
(i*1cm, f(i)*1cm) ..
endfor (b*1cm, f(b)*1cm)
enddef;

vardef axes =
save p; picture p;
p:=nullpicture;
addto p doublepath (-infinity,0)--(infinity,0) withpen currentpen;
addto p doublepath (0,-infinity)--(0,infinity) withpen currentpen;
clip p to bbox currentpicture;
draw p;
enddef;

vardef trace_rectangles_left (suffix f)(expr a,b,inc) =
save i; numeric i;
for i=a step inc until b-inc:
path p;
p = (i,0)--(i+inc,0)--(i+inc,f(i))--(i,f(i))--cycle;
p := p scaled 1cm;
fill p withcolor .8*white;
draw p;
endfor;
enddef;

vardef f(expr x) = 2 ** x enddef;

trace_rectangles_left(f,-2,2,.5);
draw trace(f, -2,2,.1);
axes;
endfig;
beginfig(197)
vardef trace_trapezes (suffix f)(expr a,b,inc) =
save i; numeric i;
for i=a step inc until b-inc:
path p;
p = (i,0)--(i+inc,0)--(i+inc,f(i+inc))--(i,f(i))--cycle;
p := p scaled 1cm;
fill p withcolor .8*white;
draw p;
endfor;
enddef;

vardef f(expr x) = 4 - x**2 enddef;

trace_trapezes(f,-2,2,.5);
draw trace(f, -2,2,.1);
axes;
endfig;
beginfig(198)
vardef trace_rectangles_right (suffix f)(expr a,b,inc) =
save i; numeric i;
for i=a step inc until b-inc:
path p;
p = (i,0)--(i+inc,0)--(i+inc,f(i+inc))--(i,f(i+inc))--cycle;
p := p scaled 1cm;
fill p withcolor .8*white;
draw p;
endfor;
enddef;

trace_rectangles_right(f,-2,2,.5);
draw trace(f, -2,2,.1);
axes;
endfig;
beginfig(199)
vardef maxf(suffix f)(expr a,b) =
save m,i; numeric m,i;
m:=f(a);
for i=a step (b-a)/100 until b:
if m<f(i): m:=f(i); fi;
endfor;
m
enddef;

vardef trace_rectangles_max (suffix f)(expr a,b,inc) =
save i; numeric i;
for i=a step inc until b-inc:
path p; numeric m;
m:=maxf(f,i,i+inc);
p = (i,0)--(i+inc,0)--(i+inc,m)--(i,m)--cycle;
p := p scaled 1cm;
fill p withcolor .8*white;
draw p;
endfor;
enddef;

vardef f(expr x) = 4 - x**2 enddef;

trace_rectangles_max(f,-2,2,.5);
draw trace(f, -2,2,.1);
axes;
endfig;
beginfig(200)
vardef minf(suffix f)(expr a,b) =
save m,i; numeric m,i;
m:=f(a);
for i=a step (b-a)/100 until b:
if m>f(i): m:=f(i); fi;
endfor;
m
enddef;

vardef trace_rectangles_min (suffix f)(expr a,b,inc) =
save i; numeric i;
for i=a step inc until b-inc:
path p; numeric m;
m:=minf(f,i,i+inc);
p = (i,0)--(i+inc,0)--(i+inc,m)--(i,m)--cycle;
p := p scaled 1cm;
fill p withcolor .8*white;
draw p;
endfor;
enddef;

vardef f(expr x) = 4 - x**2 enddef;

trace_rectangles_min(f,-2,2,.5);
draw trace(f, -2,2,.1);
axes;
endfig;
beginfig(201)
u:=2cm;
vardef koch(expr A,B,n) =
save C; pair C;
C = A rotatedaround(1/3[A,B], 120);
if n>0:
koch( A, 1/3[A,B], n-1);
koch( 1/3[A,B], C, n-1);
koch( C, 2/3[A,B], n-1);
koch( 2/3[A,B], B, n-1);
else:
draw A--1/3[A,B]--C--2/3[A,B]--B;
fi;
enddef;
z0=(u,0);
z1=z0 rotated 120;
z2=z1 rotated 120;
koch( z0, z1, 4 );
koch( z1, z2, 4 );
koch( z2, z0, 4 );
endfig;
beginfig(202)
u:=2cm;
vardef koch(expr A,B,n) =
save C; pair C;
C = A rotatedaround(1/3[A,B], -120);
if n>0:
koch( A, 1/3[A,B], n-1);
koch( 1/3[A,B], C, n-1);
koch( C, 2/3[A,B], n-1);
koch( 2/3[A,B], B, n-1);
else:
draw A--1/3[A,B]--C--2/3[A,B]--B;
fi;
enddef;
z0=(u,0);
z1=z0 rotated 120;
z2=z1 rotated 120;
koch( z0, z1, 4 );
koch( z1, z2, 4 );
koch( z2, z0, 4 );
endfig;
beginfig(203)
pair A,B,C,D;
u := 3cm;
A := (0,0);
B := (u,0);
D := B rotated 72;
C := (u,0) + D;
draw A--B--C--D--cycle;
draw A--C;
draw btex $B'$ etex shifted 1/3 (A+B+C);
draw btex $B$ etex shifted 1/3 (A+D+C);

endfig;
beginfig(204)
pair A,B,C,D,E,F;
numeric d[];
u := 3cm;
A := (0,0);
B := (u,0);
D := B rotated 72;
C := (u,0) + D;
d[0] := 1;
d[1] := sqrt( 2*(1+cosd(72)) );
d[2] := sqrt( 2*(1-cosd(36)) );
A := A;
B := C;
C := D;
draw A--B--C--cycle;
E := (d1/(d0+d1)) [A,C];
F := (d0/(d0+d2)) [A,B];
draw E--C--F--cycle;
draw btex $A$ etex shifted 1/3(E+C+F);
draw B--C--F--cycle;
draw btex $B$ etex shifted 1/3(B+C+E);
draw E--F--A--cycle;
draw btex $B'$ etex shifted 1/3(E+F+A);
endfig;
beginfig(205)
pair A,B,C,D,E,F;
numeric d[];
u := 3cm;
A := (0,0);
B := (u,0);
D := B rotated 72;
C := (u,0) + D;
draw A--B--C--cycle;
d[0] := 1;
d[1] := sqrt( 2*(1+cosd(72)) );
d[2] := sqrt( 2*(1-cosd(36)) );
E := (d1/(d0+d1)) [A,C];
F := (d0/(d0+d2)) [A,B];
draw E--F--B--cycle;
draw btex $A'$ etex shifted 1/3(E+F+B);
draw E--A--F--cycle;
draw btex $B$ etex shifted 1/3(E+A+F);
draw C--E--B--cycle;
draw btex $B'$ etex shifted 1/3(C+E+B);
endfig;
beginfig(206)
pair A,B,C,D,E,F;
numeric d[];
u := 3cm;
A := (0,0);
B := (u,0);
D := B rotated 72;
C := (u,0) + D;
d[0] := 1;
d[1] := sqrt( 2*(1+cosd(72)) );
d[2] := sqrt( 2*(1-cosd(36)) );
A := A;
B := C;
C := D;
E := (d1/(d0+d1)) [A,C];
F := (d0/(d0+d2)) [A,B];
B := 3*(C-E);
C := 3*(F-E);

draw A--B--C--cycle;

D := (d0/(d0+d2)) [C,A];
draw B--C--D--cycle;
draw btex $A$ etex shifted 1/3(B+C+D);
draw B--D--A--cycle;
draw btex $B'$ etex shifted 1/3(B+D+A);
endfig;
beginfig(207)
pair A,B,C,D,E,F;
numeric d[];
u := 3cm;
A := (0,0);
B := (u,0);
D := B rotated 72;
C := (u,0) + D;
d[0] := 1;
d[1] := sqrt( 2*(1+cosd(72)) );
d[2] := sqrt( 2*(1-cosd(36)) );

% B'
E := (d1/(d0+d1)) [A,C];
F := (d0/(d0+d2)) [A,B];

% A'
A := 2*(E-E);
C := 2*(B-E);
B := 2*(F-E);

draw A--B--C--cycle;
D := (d0/(d0+d2)) [A,B];
draw C--D--B--cycle;
draw btex $A'$ etex shifted 1/3(C+D+B);
draw C--A--D--cycle;
draw btex $B$ etex shifted 1/3(C+A+D);
endfig;
beginfig(208)
vardef pave(expr t, A, B, C, n) =
save D, E, d;
pair D,E;
numeric d[];
d[0] := 1;
d[1] := sqrt( 2*(1+cosd(72)) );
d[2] := sqrt( 2*(1-cosd(36)) );
if n>0:
if t=1:
D := (d0/(d0+d2)) [A,C];
pave(1,B,C,D,n-1);
pave(4,B,D,A,n-1);
elseif t=2:
D := (d0/(d0+d2)) [A,B];
pave(2,C,D,B,n-1);
pave(3,C,A,D,n-1);
elseif t=3:
D := (d1/(d0+d1)) [A,B];
E := (d0/(d0+d2)) [A,C];
pave(1,D,C,E,n-1);
pave(3,B,C,D,n-1);
pave(4,D,E,A,n-1);
elseif t=4:
D := (d1/(d0+d1)) [A,C];
E := (d0/(d0+d2)) [A,B];
pave(2,D,E,B,n-1);
pave(3,D,A,E,n-1);
pave(4,C,D,B,n-1);
fi;
else:
draw A--B--C--cycle;
if t=1:
fill A--B--C--cycle withcolor green + blue;
draw A--C withpen pencircle scaled 1bp;
draw A--B withpen pencircle scaled 1bp;
elseif t=2:
fill A--B--C--cycle withcolor green + blue;
draw A--B withpen pencircle scaled 1bp;
draw A--B withpen pencircle scaled 1bp;
elseif t=3:
fill A--B--C--cycle withcolor green + red;
draw A--C withpen pencircle scaled 1bp;
draw C--B withpen pencircle scaled 1bp;
elseif t=4:
fill A--B--C--cycle withcolor green + red;
draw B--C withpen pencircle scaled 1bp;
draw A--B withpen pencircle scaled 1bp;
fi;
fi;
enddef;
numeric M;
M := 6;
pair A,B,C,D;
u := 3cm;
A := (0,0);
B := (u,0);
D := B rotated 72;
C := (u,0) + D;
pave(3,A,C,D,M);
pave(4,A,B,C,M);
endfig;
beginfig(209)
u:=1cm;

def milieu (expr s, ss, n) =
if n<>0:
for i="A","BA","BBA":
milieu(s&i, ss, n-1);
endfor;
else:
dessine(s&ss);
fi;
enddef;

def doit(expr N) =
for n=1 upto N:
for i="A","BA","BBA":
for j="","B","BB":
milieu(i,j,n-1);
endfor;
endfor;
endfor;
milieu("","",0);
enddef;

vardef A(expr a) =
save x,y,n;
numeric x,y,n;
x := xpart a;
y := ypart a;
n:=x*x+y*y;
(-x/n, y/n)
enddef;

vardef B(expr a) =
save x,y,n;
numeric x,y,n;
x := 1 + xpart a;
y := ypart a;
n := x*x+y*y;
(-x/n, y/n)
enddef;

def dessine(expr s) =
_dessine(s, dir(60), up, dir(120));
_dessine(s, dir(60), dir(31), dir(2));
_dessine(s, dir(120), dir(149), dir(178));
enddef;

def _dessine(expr s, a,b,c) =
pair p[];
p[0] := a;
p[1] := b;
p[2] := c;

for i=0 upto length(s)-1:
if (substring(i,i+1) of s) = "A":
for j=0 upto 2: p[j] := A( p[j] ); endfor;
elseif (substring(i,i+1) of s) = "B":
for j=0 upto 2: p[j] := B( p[j] ); endfor;
else: show("Ceci n'est pas un g�n�rateur : "&substring(i,i+1) of s)
fi;
endfor;
if (xpart p[0] < 2) and (xpart p[0] > -2) and
(xpart p[2] > -2) and (xpart p[2] < 2) and
(ypart p[0] < 2) and (ypart p[2] < 2):
draw ( p[0] .. p[1] .. p[2] ) scaled u;
fi;

enddef;

fill (dir(60) .. up .. dir(120) --
(dir120+up) -- (dir60+up) -- cycle) scaled u
withcolor red+green;
doit(7);
draw (u*dir(60)) withpen pencircle scaled 4bp;
draw (0,u) withpen pencircle scaled 4bp;
draw (u*dir(60) -- u*dir(60)+u*up) shifted (0u,0);
draw (u*dir(60) -- u*dir(60)+u*up) shifted (1u,0);
draw (u*dir(60) -- u*dir(60)+u*up) shifted (-u,0);
draw (u*dir(60) -- u*dir(60)+u*up) shifted (-2u,0);
endfig;
beginfig(210)
u:=5mm;
pickup pencircle scaled 1pt;
for i=0 upto 500:
draw (u*normaldeviate, u*normaldeviate);
endfor;
endfig;
beginfig(211)
u:=2cm;
pickup pencircle scaled 1pt;
for i=0 upto 500:
draw (u*uniformdeviate(1), u*uniformdeviate(1));
endfor;
endfig;
beginfig(212)
numeric n;
n:=10;
path p;
p := for i=0 upto n-1:
((1cm + 3mm*normaldeviate,0) rotated (i*360/n)) ..
endfor cycle;
fill p withcolor .8white;
draw p;
endfig;
beginfig(213)
m:=500;
u:=1cm;
pair A,B;
A:=(0,0);
for i=0 upto m:
B:=(i/m*3u, (ypart A)+normaldeviate/m*30u);
draw A--B;
A:=B;
endfor;
draw (0,0)--(3u,0);
endfig;
beginfig(214)
m:=50;
pair A[], B[];
A[0]=(0,0);
for i=0 upto m:
A[i+1]=(i/m*3u, (ypart A[i])+(uniformdeviate(2)-1)/m*30u);
endfor;
B[0]=A[0];
B[1]=A[1];
B[2]=A[2];
B[3]=A[3];
for i=4 upto m+1:
B[i] = ( A[i-4] + A[i-3] + A[i-2] + A[i-1] + A[i])/5;
endfor;
for i=0 upto m:
draw B[i]--B[i+1] withpen pencircle scaled 2pt
withcolor .5*white;
endfor;
for i=0 upto m:
draw A[i]--A[i+1];
endfor;
draw (0,0)--(3u,0);
endfig;
def rescale_currentpic :=
if xpart (lrcorner currentpicture - llcorner currentpicture) > 4cm:
currentpicture := currentpicture scaled ( 4cm /
xpart (lrcorner currentpicture - llcorner currentpicture) );
fi;
enddef;
beginfig(215)
vardef check_pascal =
save again;
boolean again;
again := false;
% Distance entre deux points sur le cercle : au moins 1mm
for i=0 upto 5:
for j=i+1 upto 5:
show( decimal(i) &" "& decimal(j) &" "& decimal(abs(A[i]-A[j])/2mm) );
if abs(A[i]-A[j]) < 2mm:
again := true;
fi;
endfor;
endfor;
% Distance entre deux des M[i] : au moins 2mm, au plus 10cm
for i=0 upto 2:
for j=i+1 upto 2:
if (abs(M[i]-M[j]) > 10cm) or (abs(M[i]-M[j]) < 2mm):
again := true;
fi;
endfor;
endfor;
% Distance entre un A[i] et un M[i] : au moins 2mm
for i=0 upto 5:
for j=0 upto 2:
if abs(A[i]-M[j]) < 2mm:
again := true;
fi;
endfor;
endfor;
% Distance entre le cercle et l'un des M[i] : au plus 10cm
if abs(M[0])>10cm:
again:=true;
fi;
show again;
not again
enddef;

forever:
path C;
C := fullcircle scaled 6cm;
pair A[], M[];
for i=0 upto 5:
A[i] := point uniformdeviate(length(C)) of C;
endfor;
M[0] = whatever[ A[0], A[1] ];
M[0] = whatever[ A[3], A[4] ];
M[1] = whatever[ A[1], A[2] ];
M[1] = whatever[ A[4], A[5] ];
M[2] = whatever[ A[2], A[3] ];
M[2] = whatever[ A[5], A[0] ];
exitif check_pascal;
endfor;

draw C;
draw A[0]--A[1] withcolor red;
draw A[3]--A[4] withcolor red;
draw A[0]--M[0] withcolor red dashed evenly;
draw A[3]--M[0] withcolor red dashed evenly;

draw A[1]--A[2] withcolor green;
draw A[4]--A[5] withcolor green;
draw A[1]--M[1] withcolor green dashed evenly;
draw A[4]--M[1] withcolor green dashed evenly;

draw A[2]--A[3] withcolor blue;
draw A[5]--A[0] withcolor blue;
draw A[2]--M[2] withcolor blue dashed evenly;
draw A[5]--M[2] withcolor blue dashed evenly;

draw M[0]--M[1]--M[2]--cycle withpen pencircle scaled 2bp;
for i=0 upto 2:
draw M[i] withpen pencircle scaled 6bp;
endfor;
for i=0 upto 5:
draw A[i] withpen pencircle scaled 6bp;
endfor;
rescale_currentpic;
endfig;
beginfig(216)
vardef pascal(expr C) =
forever:
pair A[], M[];
for i=0 upto 5:
A[i] := point uniformdeviate(length(C)) of C;
endfor;
M[0] = whatever[ A[0], A[1] ];
M[0] = whatever[ A[3], A[4] ];
M[1] = whatever[ A[1], A[2] ];
M[1] = whatever[ A[4], A[5] ];
M[2] = whatever[ A[2], A[3] ];
M[2] = whatever[ A[5], A[0] ];
exitif check_pascal;
endfor;

draw C;
draw A[0]--A[1] withcolor red;
draw A[3]--A[4] withcolor red;
draw A[0]--M[0] withcolor red dashed evenly;
draw A[3]--M[0] withcolor red dashed evenly;

draw A[1]--A[2] withcolor green;
draw A[4]--A[5] withcolor green;
draw A[1]--M[1] withcolor green dashed evenly;
draw A[4]--M[1] withcolor green dashed evenly;

draw A[2]--A[3] withcolor blue;
draw A[5]--A[0] withcolor blue;
draw A[2]--M[2] withcolor blue dashed evenly;
draw A[5]--M[2] withcolor blue dashed evenly;

draw M[0]--M[1]--M[2]--cycle withpen pencircle scaled 2bp;
for i=0 upto 2:
draw M[i] withpen pencircle scaled 6bp;
endfor;
for i=0 upto 5:
draw A[i] withpen pencircle scaled 6bp;
endfor;
enddef;

pascal(fullcircle xscaled 6cm yscaled 3cm);
rescale_currentpic;
endfig;
beginfig(217)
pascal((for i=-2cm step .1cm until 2cm:
(i, (i/1cm)**2 *1cm) ..
endfor (2.1cm,4.41cm)) rotated 30);
rescale_currentpic;
endfig;
beginfig(218)
vardef pascal(expr C) =
forever:
pair A[], M[];

numeric t[];
for i=0 upto 5:
t[i] = uniformdeviate(length(C));
endfor;
for i=0 upto 5:
for j=0 upto 4:
if t[j]>t[j+1]:
tt:=t[j]; t[j]:=t[j+1]; t[j+1]:=tt;
fi;
endfor;
endfor;
for i=0 upto 5:
A[i] = point t[i] of C;
endfor;

M[0] = whatever[ A[0], A[1] ];
M[0] = whatever[ A[3], A[4] ];
M[1] = whatever[ A[1], A[2] ];
M[1] = whatever[ A[4], A[5] ];
M[2] = whatever[ A[2], A[3] ];
M[2] = whatever[ A[5], A[0] ];
exitif check_pascal;
endfor;

draw C;
draw A[0]--A[1] withcolor red;
draw A[3]--A[4] withcolor red;
draw A[0]--M[0] withcolor red dashed evenly;
draw A[3]--M[0] withcolor red dashed evenly;

draw A[1]--A[2] withcolor green;
draw A[4]--A[5] withcolor green;
draw A[1]--M[1] withcolor green dashed evenly;
draw A[4]--M[1] withcolor green dashed evenly;

draw A[2]--A[3] withcolor blue;
draw A[5]--A[0] withcolor blue;
draw A[2]--M[2] withcolor blue dashed evenly;
draw A[5]--M[2] withcolor blue dashed evenly;

draw M[0]--M[1]--M[2]--cycle withpen pencircle scaled 2bp;
for i=0 upto 2:
draw M[i] withpen pencircle scaled 6bp;
endfor;
for i=0 upto 5:
draw A[i] withpen pencircle scaled 6bp;
endfor;
enddef;

pascal(fullcircle scaled 6cm);
rescale_currentpic;
endfig;
beginfig(219)
pascal(fullcircle xscaled 6cm yscaled 3cm);
rescale_currentpic;
endfig;
beginfig(220)
pascal(fullcircle xscaled 6cm yscaled 3cm);
rescale_currentpic;
endfig;
beginfig(221)
vardef barycentre(text t) =
save n, G;
pair G; numeric n;
G := origin; n:=0;
for a=t:
G:=G+a;
n:=n+1;
endfor;
G/n
enddef;

pair A[];
n:=10;
for i=0 upto n:
A[i] = 1cm*(normaldeviate, normaldeviate);
draw A[i] withpen pencircle scaled 4bp;
endfor;
draw barycentre(A[0] for i=1 upto 10: ,A[i] endfor)
withpen pencircle scaled 4bp withcolor red;
endfig;
beginfig(222)
vardef barycentre(text t) =
save a, i, n, G, X;
pair G,X; numeric n,i;
G := origin; n:=0; i:=0;
for a=t:
show("i = "& decimal(i));
show a;
if odd(i):
show("odd");
n:=n+a;
G:= G + a*X;
else:
show("even");
X:=a;
fi;
i:=i+1;
endfor;
G/n
enddef;

pair A[];
n:=10;
for i=0 upto n:
A[i] = 1cm*(normaldeviate, normaldeviate);
draw A[i] withpen pencircle scaled 4bp;
endfor;
draw barycentre(A[0],0 for i=1 upto 10: ,A[i],i endfor)
withpen pencircle scaled 4bp withcolor red;
endfig;
beginfig(223)
numeric n;
n:=10;
path p;
p := for i=0 upto n-1:
((1cm + 3mm*normaldeviate,0) rotated (i*360/n)) ..
endfor cycle;
for i=0 step 2mm until 3cm:
draw fullcircle scaled i;
endfor;
clip currentpicture to p;
draw p;

endfig;
beginfig(224)
u := 5mm;
draw (-2u,0) -- (2u,0);
draw (0,-u) -- (0,4u);
draw (-2u,4u) for i=-1.9 step .1 until 2.01: .. (i*u, i*i*u) endfor
withpen pencircle scaled 1bp;
draw bbox currentpicture withpen pensquare scaled 2bp withcolor .8white;
draw bbox currentpicture withpen pensquare scaled 2bp withcolor .8white;
endfig;
beginfig(225)
path p;
p := (0,0) -- (2cm,0);
def doit (suffix p)(expr t) =
begingroup
interim linecap := t;
draw p withpen pencircle scaled 5mm withcolor .8white;
endgroup;
draw point 0 of p withpen pencircle scaled 4bp;
draw point 1 of p withpen pencircle scaled 4bp;
p := p shifted (0,-7mm)
enddef;
doit(p,rounded);
doit(p,butt);
doit(p,squared);

endfig;
beginfig(226)
path p;
p := (0,0) -- (1cm,5mm) -- (2cm,0);
def doit (suffix p)(expr t) =
begingroup
interim linejoin := t;
draw p withpen pencircle scaled 5mm withcolor .8white;
endgroup;
draw point 0 of p withpen pencircle scaled 4bp;
draw point 1 of p withpen pencircle scaled 4bp;
draw point 2 of p withpen pencircle scaled 4bp;
p := p shifted (0,-7mm)
enddef;
doit(p,rounded);
doit(p,mitered);
doit(p,beveled);

endfig;
beginfig(227)
path p;
p := (0,0) -- (2cm,0);
vardef doit (suffix p)(expr t) =
interim linecap := t;
draw p withpen pencircle scaled 5mm withcolor .8white;
draw point 0 of p withpen pencircle scaled 4bp;
draw point 1 of p withpen pencircle scaled 4bp;
draw point 2 of p withpen pencircle scaled 4bp;
p := p shifted (0,-7mm)
enddef;
doit(p,rounded);
doit(p,butt);
doit(p,squared);

endfig;
beginfig(228)
draw fullcircle scaled 2cm;
special("0 0 moveto 10 10 rlineto -10 10 rlineto stroke");

endfig;
beginfig(229)
draw fullcircle shifted (.5,.5) xscaled 18.2cm yscaled 4cm;
special(
"/Times-Roman findfont 150 scalefont setfont " &
"0 0 moveto (ABCabc) false charpath clip stroke " &
"gsave 300 0 translate " &
" 2 4 600 {dup 0 moveto 0 exch 0 exch 0 360 arc stroke} for " &
"grestore "
);

endfig;
beginfig(230)
draw fullcircle shifted (.5,.5) xscaled 18.2cm yscaled 4cm;
special(
"gsave " &
"/Times-Roman findfont 150 scalefont setfont " &
"0 0 moveto (ABCabc) false charpath clip stroke " &
"gsave 300 0 translate " &
" 2 4 600 {dup 0 moveto 0 exch 0 exch 0 360 arc stroke} for " &
"grestore " &
"grestore "
);

endfig;
beginfig(231)
path p;
p =
(0,u)
for i=.1 step .1 until 10:
hide( pair A; A = (i*u, (sind (i*180/3.14))/i *u);
draw A withpen pencircle scaled 2pt )
.. A
endfor;
draw p;
endfig;
beginfig(232)
vardef inversion (expr O,k,M) =
if pair M:
(O + k*unitvector(M-O)/abs(M-O))
elseif path M:
for i=0 step length(M)/10 until length(M):
hide(
draw O--inversion(O,k,point i of M)--(point i of M);
draw inversion(O,k,point i of M) withpen pencircle scaled 2pt;
draw point i of M withpen pencircle scaled 2pt withcolor red;
draw O withpen pencircle scaled 2pt;
)
inversion(O,k,point i of M) ..
endfor
cycle
fi
enddef;

path p[];
p1=fullcircle scaled 2u shifted (u,0);
p2=fullcircle scaled 2u shifted (-u,0);
draw p1 dashed withdots scaled .25;
draw p2 dashed withdots scaled .25;
z0 = (.5u,2u);
draw inversion( z0, 2 (u**2), p1 );
draw inversion( z0, 2 (u**2), p2 );
endfig;
beginfig(233)
path p;
p := (0,0) -- (1cm,0);
show ahangle;
begingroup
interim ahangle := 30;
interim linejoin := mitered;
interim linecap := butt;
drawarrow p withpen pencircle scaled 2bp;
endgroup;
begingroup
interim ahangle := 60;
drawarrow p shifted (0,-5mm) withpen pencircle scaled 2bp;
endgroup;

endfig;
beginfig(234)
numeric x;
x = sind(60);
draw TEX("$\sin 60 = " & decimal(x) & "$");

endfig;
beginfig(235)
picture _TEX_pic;

def largeur(expr p) =
if picture p:
xpart( lrcorner(p) - llcorner(p) )
elseif string p:
hide(_TEX_pic := TEX(p);)
xpart( lrcorner(_TEX_pic) - llcorner(_TEX_pic) )
else:
hide( errmessage("largeur: wrong type"); 0)
fi
enddef;

def hauteur(expr p) =
if picture p:
ypart(ulcorner(p))
elseif string p:
hide(_TEX_pic := TEX(p);)
ypart(ulcorner(_TEX_pic))
else:
hide( errmessage("hauteur: wrong type"); 0)
fi
enddef;

def profondeur (expr p) =
if picture p:
-ypart(llcorner(p))
elseif string p:
hide(_TEX_pic := TEX(p);)
-ypart(llcorner(_TEX_pic))
else:
hide( errmessage("profondeur: wrong type"); 0)
fi
enddef;

picture p;
string s;
s := "\huge\LaTeX";
p := TEX(s);
drawarrow (0,0) -- (largeur(s),0) withcolor red;
drawarrow (0,0) -- (0,hauteur(s)) withcolor green;
drawarrow (0,0) -- (0,-profondeur(s)) withcolor blue;
draw p;
draw bbox p;
endfig;
beginfig(236)
def reddraw text t = draw t withcolor red enddef;
draw (0,0) -- (2cm,0);
reddraw (0,0) -- (2cm,5mm) withpen pencircle scaled 2bp;

endfig;
beginfig(237)
path _myfill_p;

def myfill expr p =
_myfill_p := p;
_myfill
enddef;

def _myfill text t =
fill _myfill_p t;
draw _myfill_p t withcolor red;
enddef;

myfill fullcircle scaled 1cm withcolor .8white withpen pencircle scaled 2bp;
endfig;
beginfig(238)
boxit.a(btex Essai etex);
a.c = (0,0);
drawboxed(a);

endfig;
beginfig(239)
circleit.a(btex Essai etex);
a.c = (0,0);
drawboxed(a);

endfig;
beginfig(240)
rboxit.a(btex Essai etex);
a.c = (0,0);
drawboxed(a);

endfig;
beginfig(241)
boxit.a(btex Essai etex);
a.c = (0,0);
drawunboxed(a);

endfig;
beginfig(242)
circleit.a(btex Essai etex);
a.c = (0,0);
a.dx = a.dy;
drawboxed(a);
endfig;
beginfig(243)
circleit.a(btex Essai etex);
a.c = (0,0);
a.dx = a.dy;
drawunboxed(a);
for i=0 step 10 until 360:
draw (0,0) -- 1cm*right rotated i cutbefore bpath.a;
endfor;
endfig;
beginfig(244)
circleit.a(btex D�but etex);
a.c = (0,0);
a.dx = a.dy;
circleit.b(btex Fin etex);
b.c = (2cm,0);
b.dx = b.dy;
drawboxed(a,b);
drawarrow a.c {dir 45} .. b.c {dir -45}
cutbefore bpath.a cutafter bpath.b;
drawarrow b.c {dir -135} .. a.c {dir 135}
cutbefore bpath.b cutafter bpath.a;
endfig;
beginfig(245)
circleit.a(btex D�but etex);
a.c = (0,0);
a.dx = a.dy;
circleit.b(btex Fin etex);
b.c = (2cm,0);
b.dx = b.dy;
drawunboxed(a,b);
drawarrow a.c {dir 45} .. b.c {dir -45}
cutbefore bpath.a cutafter bpath.b;
drawarrow b.c {dir -135} .. a.c {dir 135}
cutbefore bpath.b cutafter bpath.a;
endfig;
beginfig(246)
boxjoin(
a.dx = a.dy;
b.dx = b.dy;
a.e + (5mm,0) = b.w;
);
circleit.a(btex D�but etex);
a.c = (0,0);
circleit.b(btex Fin etex);
drawboxed(a,b);
drawarrow a.c {dir 45} .. b.c {dir -45}
cutbefore bpath.a cutafter bpath.b;
drawarrow b.c {dir -135} .. a.c {dir 135}
cutbefore bpath.b cutafter bpath.a;
endfig;
beginfig(247)
% Toujours mettre la commande boxjoin au d�but.
boxjoin(a.e = b.w);
boxit.a(btex A etex);
boxit.b(btex B etex);
boxit.c(btex C etex);
boxit.d(btex D etex);
drawboxed(a,b,c,d);
endfig;
beginfig(248)
boxjoin(a.e = b.w);
boxit.a(btex a etex);
boxit.b(btex b etex);
boxit.c(btex c etex);
boxit.d(btex d etex);
drawboxed(a,b,c,d);
endfig;
beginfig(249)
boxjoin(a.se = b.sw; a.ne = b.nw);
boxit.a(btex a etex);
boxit.b(btex b etex);
boxit.c(btex c etex);
boxit.d(btex d etex);
drawboxed(a,b,c,d);
endfig;
beginfig(250)
boxjoin(a.se = b.sw; a.ne = b.nw);
boxit.a1(btex a etex);
boxit.a2(btex b etex);
boxit.a3(btex c etex);
boxit.a4(btex d etex);
drawboxed(a1,a2,a3,a4);
endfig;
beginfig(251)
draw (0,0) -- (5cm,0) withcolor red;
draw btex a etex ;
draw btex b etex shifted (1cm,0);
draw btex c etex shifted (2cm,0);
draw btex d etex shifted (3cm,0);
draw btex e etex shifted (4cm,0);
endfig;
beginfig(252)
draw (0,0) -- (5cm,0) withcolor red;
boxjoin(b.c - a.c = (1cm,0));
boxit a (btex a etex);
boxit b (btex b etex);
boxit c (btex c etex);
boxit d (btex d etex);
boxit e (btex e etex);
drawunboxed(a,b,c,d,e);
endfig;
beginfig(253)
vardef boxTEX expr s =
save p,h,l;
picture p;
numeric h,l;
p := TEX(s);
h := max(ypart ulcorner(p), abs(ypart llcorner(p)));
l := xpart lrcorner(p);
setbounds p to (0,-h)--(l,-h)--(l,h)--(0,h)--cycle;
p
enddef;

draw (0,0) -- (5cm,0) withcolor red;
boxjoin(b.c - a.c = (1cm,0));
boxit a (boxTEX "a");
boxit b (boxTEX "b");
boxit c (boxTEX "c");
boxit d (boxTEX "d");
boxit e (boxTEX "e");
drawunboxed(a,b,c,d,e);
endfig;
beginfig(254)
draw (0,0) -- (5cm,0) withcolor red;
boxjoin(b.c - a.c = (1cm,0));
boxit a (boxTEX "a");
boxit b (boxTEX "b");
boxit c (boxTEX "c");
boxit d (boxTEX "d");
boxit e (boxTEX "e");
drawboxed(a,b,c,d,e);
endfig;
beginfig(255)
let OLD_beginbox_ = beginbox_;
def beginbox_(expr pp,sp)(suffix $)(text t) =
_n_ := str $;
generic_declare(pair) _n.off, _n.c;
generic_declare(string) pproc_._n, sproc_._n;
generic_declare(picture) pic_._n;
pproc_$:=pp; sproc_$:=sp;
pic_$ = nullpicture;
for _p_=t:
pic_$:=
if picture _p_: _p_
else: _p_ infont defaultfont scaled defaultscale
fi;
endfor
$c = $off + (.5[xpart llcorner pic_$, xpart urcorner pic_$], 0)
enddef;

draw (0,0) -- (5cm,0) withcolor red;
boxjoin(b.c - a.c = (1cm,0));
boxit a (btex a etex);
boxit b (btex b etex);
boxit c (btex c etex);
boxit d (btex d etex);
boxit e (btex e etex);
drawunboxed(a,b,c,d,e);
endfig;
beginfig(256)
draw (0,0) -- (5cm,0) withcolor red;
boxjoin(b.c - a.c = (1cm,0));
boxit a (btex a etex);
boxit b (btex b etex);
boxit c (btex c etex);
boxit d (btex d etex);
boxit e (btex e etex);
drawboxed(a,b,c,d,e);
endfig;
beginfig(257)
let OLD_boxit = boxit;
let OLD_sizebox_ = sizebox_;
let OLD_clearb_ = clearb_;

vardef boxit@#(text tt) =
beginbox_("boxpath_","sizebox_",@#,tt);
generic_declare(pair) _n.sw, _n.s, _n.se, _n.e, _n.ne, _n.n, _n.nw, _n.w;
0 = xpart (@#nw-@#sw) = ypart(@#se-@#sw);
0 = xpart(@#ne-@#se) = ypart(@#ne-@#nw);
@#s = .5[@#sw,@#se];
@#n = .5[@#ne,@#nw];
xpart @#w = xpart @#nw;
xpart @#e = xpart @#ne;
ypart @#w = ypart @#c = ypart @#e;
@#ne-@#c = (@#dx,@#dy) +
(xpart(.5*(urcorner pic_@# - llcorner pic_@#)), ypart urcorner pic_@#);
@#c-@#sw = (@#dx,@#dy) +
(xpart(.5*(urcorner pic_@# - llcorner pic_@#)), -ypart lrcorner pic_@#);
endbox_(clearb_,@#);
enddef;

draw (0,0) -- (5cm,0) withcolor red;
boxjoin(b.c - a.c = (1cm,0));
boxit a (btex a etex);
boxit b (btex b etex);
boxit c (btex c etex);
boxit d (btex d etex);
boxit e (btex e etex);
drawboxed(a,b,c,d,e);
endfig;
beginfig(258)
draw (0,0) -- (5cm,0) withcolor red;
boxjoin(b.c - a.c = (1cm,0); b.ne - b.se = a.nw - a.sw);
boxit a (btex a etex);
boxit b (btex b etex);
boxit c (btex c etex);
boxit d (btex d etex);
boxit e (btex e etex);
drawboxed(a,b,c,d,e);
endfig;
beginfig(259)
vardef boxit@#(text tt) =
beginbox_("boxpath_","sizebox_",@#,tt);
generic_declare(pair) _n.sw, _n.s, _n.se, _n.e, _n.ne, _n.n, _n.nw, _n.w;
0 = xpart (@#nw-@#sw) = ypart(@#se-@#sw);
0 = xpart(@#ne-@#se) = ypart(@#ne-@#nw);
@#s = .5[@#sw,@#se];
@#n = .5[@#ne,@#nw];
xpart @#w = xpart @#nw;
xpart @#e = xpart @#ne;
ypart @#w = ypart @#c = ypart @#e;
@#ne-@#c = (@#dx,@#dyup) +
(xpart(.5*(urcorner pic_@# - llcorner pic_@#)), ypart urcorner pic_@#);
@#c-@#sw = (@#dx,@#dydown) +
(xpart(.5*(urcorner pic_@# - llcorner pic_@#)), -ypart lrcorner pic_@#);
endbox_(clearb_,@#);
enddef;

def sizebox_(suffix $) =
if unknown $.dx: $.dx=defaultdx; fi
if unknown $.dyup:
if unknown $.dy:
$.dyup=defaultdy
else:
$.dyup=$.dy
fi;
fi;
if unknown $.dydown:
if unknown $.dy:
$.dydown=defaultdy
else:
$.dydown=$.dy
fi;
fi;
enddef;

vardef clearb_(suffix $) =
_n_ := str $;
generic_redeclare(numeric) _n.sw, _n.s, _n.se, _n.e, _n.ne, _n.n, _n.nw, _n.w,
_n.c, _n.off, _n.dx, _n.dy, _n.dyup, _n.dy_down;
enddef;

draw (0,0) -- (5cm,0) withcolor red;
boxjoin(b.c - a.c = (1cm,0); ypart( b.ne - a.ne ) = 0; ypart( b.se - a.se ) = 0;);
boxit a (btex a etex);
boxit b (btex b etex);
boxit c (btex c etex);
boxit d (btex d etex);
boxit e (btex e etex);
drawboxed(a,b,c,d,e);
endfig;
beginfig(260)
draw (0,0) -- (5cm,0) withcolor red;
picture p;
numeric h;
p := btex b etex;
h = ypart ( ulcorner p - llcorner p );
boxjoin(
b.c - a.c = (1cm,0);
ypart( b.ne - a.ne ) = 0;
ypart( a.ne - a.se ) = h+2defaultdy;
);
boxit a (btex a etex);
boxit b (btex b etex);
boxit c (btex c etex);
boxit d (btex d etex);
boxit e (btex e etex);
drawboxed(a,b,c,d,e);
endfig;
beginfig(261)
% Les lignes suivantes n'ont pas l'effet escompt�...
let beginbox_ = OLD_beginbox_;
let boxit = OLD_boxit;
let sizebox_ = OLD_sizebox_;
let clearb_ = OLD_clearb_;

% On recopie donc les d�finitions initiales des macros que l'on a modifi�es...
extra_beginfig := "";
extra_endfig := "";
input boxes;

% Et on regarde sur un exemple si �a marche...
draw (0,0) -- (5cm,0) withcolor red;
boxjoin(b.c - a.c = (1cm,0));
boxit a (btex a etex);
boxit b (btex b etex);
boxit c (btex c etex);
boxit d (btex d etex);
boxit e (btex e etex);
drawboxed(a,b,c,d,e);
endfig;
beginfig(262)
boxit.a1(btex $a$ etex);
boxit.b1(btex etex);
boxit.a2(btex $b$ etex);
boxit.b2(btex etex);
boxit.a3(btex $c$ etex);
boxit.b3(btex etex);
boxit.a4(btex $d$ etex);
boxit.b4(btex etex);
for i=1 upto 4:
% Les boites a[i] et b[i] sont coll�es
a[i].e = b[i].w;
% Il y a un peu d'espace entre b[i] et a[i+1]
b[i].e + (5mm,0) = a[i+1].w;
% La hauteur des boites est la m�me
a[i].n - a[i].s = a[i+1].n - a[i+1].s = b[i].n - b[i].s ;
% Les b[i] ne sont pas tr�s larges
b[i].e - b[i].w = (2mm,0);
endfor;
drawboxed(a1,b1,a2,b2,a3,b3,a4,b4);
for i=1 upto 3:
drawarrow b[i].c {up} .. a[i+1].c {down}
cutafter bpath.a[i+1];
endfor;
endfig;
beginfig(263)
boxit.a(btex A etex);
boxit.b(btex B etex);
boxit.c(btex C etex);
boxit.d(btex D etex);
boxit.e(btex E etex);

b.c-a.c = (1cm,0);
c.c-b.c = (b.c-a.c) rotated 72;
d.c-c.c = (c.c-b.c) rotated 72;
e.c-d.c = (d.c-c.c) rotated 72;
a.c-e.c = (e.c-d.c) rotated 72;
b.c-a.c = (a.c-e.c) rotated 72;

drawboxed(a,b,c,d,e);

drawarrow a.c -- b.c cutbefore bpath.a cutafter bpath.b;
drawarrow b.c -- c.c cutbefore bpath.b cutafter bpath.c;
drawarrow c.c -- d.c cutbefore bpath.c cutafter bpath.d;
drawarrow d.c -- e.c cutbefore bpath.d cutafter bpath.e;
drawarrow e.c -- a.c cutbefore bpath.e cutafter bpath.a;
endfig;
beginfig(264)
boxit.a(btex A etex);
boxit.b(btex B etex);
boxit.c(btex C etex);
boxit.d(btex D etex);
boxit.e(btex E etex);

d.c = 1cm*up;
e.c = 1cm*up rotated (1*72);
a.c = 1cm*up rotated (2*72);
b.c = 1cm*up rotated (3*72);
c.c = 1cm*up rotated (4*72);

drawunboxed(a,b,c,d,e);

drawarrow a.c -- b.c cutbefore bpath.a cutafter bpath.b;
drawarrow b.c -- c.c cutbefore bpath.b cutafter bpath.c;
drawarrow c.c -- d.c cutbefore bpath.c cutafter bpath.d;
drawarrow d.c -- e.c cutbefore bpath.d cutafter bpath.e;
drawarrow e.c -- a.c cutbefore bpath.e cutafter bpath.a;
endfig;
beginfig(265)
def linkboxes(suffix a,b) =
drawarrow a.c -- b.c cutbefore bpath.a cutafter bpath.b;
enddef;

boxit.a(btex A etex);
boxit.b(btex B etex);
boxit.c(btex C etex);
boxit.d(btex D etex);
boxit.e(btex E etex);

d.c = 1cm*up;
e.c = 1cm*up rotated (1*72);
a.c = 1cm*up rotated (2*72);
b.c = 1cm*up rotated (3*72);
c.c = 1cm*up rotated (4*72);

drawunboxed(a,b,c,d,e);

linkboxes(a,b);
linkboxes(b,c);
linkboxes(c,d);
linkboxes(d,e);
linkboxes(e,a);
endfig;
beginfig(266)
boxit a(btex Essai etex);
fill bpath a withcolor .5[red,white];
drawboxed(a);

endfig;
beginfig(267)
def drawredboxed(text t) =
forsuffixes a=t:
fill bpath a withcolor .5[red,white];
endfor;
drawboxed(t);
enddef;

circleit.a(btex D�but etex);
a.c = (0,0);
a.dx = a.dy;
circleit.b(btex Fin etex);
b.c = (2cm,0);
b.dx = b.dy;
drawredboxed(a,b);
drawarrow a.c {dir 45} .. b.c {dir -45}
cutbefore bpath.a cutafter bpath.b;
drawarrow b.c {dir -135} .. a.c {dir 135}
cutbefore bpath.b cutafter bpath.a;

endfig;
beginfig(268)
def drawcoloredboxed(expr c)(text t) =
forsuffixes a=t:
fill bpath a withcolor c;
endfor;
drawboxed(t);
enddef;

circleit.a(btex D�but etex);
a.c = (0,0);
a.dx = a.dy;
circleit.b(btex Fin etex);
b.c = (2cm,0);
b.dx = b.dy;
drawcoloredboxed(.5[red,white], a);
drawcoloredboxed(.5[blue,white], b);
drawarrow a.c {dir 45} .. b.c {dir -45}
cutbefore bpath.a cutafter bpath.b;
drawarrow b.c {dir -135} .. a.c {dir 135}
cutbefore bpath.b cutafter bpath.a;

endfig;
beginfig(269)
def begindiag =
begingroup;
save _diag_x, _diag_x_max, _diag_y, _diag_y_max, _diag;
numeric _diag_x, _diag_x_max, _diag_y, _diag_y_max;
string _diag[][];
% Num�ro de ligne et de colonne courrants
_diag_x = -1; _diag_y = 0;
% Num�ro de ligne et de colonne maximaux
_diag_x_max = _diag_y_max = 0;
save _diag_ar_n, _diag_ar_source, _diag_ar_but, _diag_ar_up, _diag_ar_down;
% Nombre de fl�ches
numeric _diag_ar_n; _diag_ar_n=-1;
% Source et but de la fl�che
pair _diag_ar_source[], _diag_ar_but[];
% Ce qu'il faut �crire au dessus ou au dessous
string _diag_ar_up[], _diag_ar_down[];
save _diag_ar_curved, _diag_ar_shape, _diag_ar_color, _diag_ar_width;
% � courbure � (c'est une distance)
numeric _diag_ar_curved[];
% Forme de la fl�che
string _diag_ar_shape[];
% Couleur, �paisseur, pointill�s
color _diag_ar_color[];
numeric _diag_ar_width[];
picture _diag_ar_dashed[];
enddef;

def node expr A =
_diag_x := _diag_x + 1;
_diag_x_max := max(_diag_x,_diag_x_max);
_diag[_diag_x][_diag_y] := A;
enddef;

def nextline =
_diag_x := -1;
_diag_y := _diag_y + 1;
_diag_y_max := max(_diag_y, _diag_y_max);
enddef;

tertiarydef a => b = a, b enddef;
def even (expr a) = not odd(a) enddef;

vardef rarrowto(expr a,b)(text t) =
save i,p;
_diag_ar_n := _diag_ar_n + 1;
_diag_ar_source[_diag_ar_n] = (_diag_x, _diag_y);
_diag_ar_but[_diag_ar_n] = (_diag_x + a, _diag_y + b);

numeric i; i:=0;
string current;
for p=t:
if even(i):
current := p;
else:
if current = "above":
_diag_ar_up[_diag_ar_n] = p;
elseif current = "below":
_diag_ar_down[_diag_ar_n] = p;
elseif current = "shape":
_diag_ar_shape[_diag_ar_n] = p;
elseif current = "curved":
_diag_ar_curved[_diag_ar_n] = p;
elseif current = "color":
_diag_ar_color[_diag_ar_n] = p;
elseif current = "width":
_diag_ar_width[_diag_ar_n] = p;
elseif current = "dashed":
_diag_ar_dashed[_diag_ar_n] = p;
else:
errmessage("rarrowto: Wrong argument "&ditto&current&ditto);
fi;
fi;
i := i + 1;
endfor;
if odd i:
errmessage("rarrowto: Odd number of arguments "&decimal(i));
fi;
enddef;

%% Les t�tes de fl�ches

picture withsmalldots, notdashed;
withsmalldots := withdots scaled .3;
notdashed := dashpattern(on 50cm);

vardef diag_arrow_head (expr p, t) =
save A,B,C,u; pair A,B,C,u;
B := point t of p;
u := -unitvector(direction t of p);
A := B + ahlength*u rotated(-ahangle);
C := B + ahlength*u rotated(+ahangle);
A .. {-u} B {u} .. C
enddef;

vardef diag_arrow_bar (expr p, t) =
save A,B,C,u; pair A,B,C,u;
B := point t of p;
u := unitvector(direction t of p);
A := B + ahlength*sind(ahangle)*u rotated(90);
C := B + ahlength*sind(ahangle)*u rotated(-90);
A .. B .. C
enddef;

%% Les fl�ches

def diag_draw_arrow_default(suffix a,b)(expr curved, w, col, dash) =
p = a.c ..
(1/2 [a.c,b.c] + curved*unitvector(b.c-a.c) rotated 90)
.. b.c;
pp := p cutbefore bpath.a cutafter bpath.b;
draw pp
withcolor col withpen pencircle scaled w dashed dash;
draw diag_arrow_head (pp, length(pp))
withcolor col withpen pencircle scaled w;
enddef;

def diag_draw_arrow_middle(suffix a,b)(expr curved, w, col, dash) =
p = a.c ..
(1/2 [a.c,b.c] + curved*unitvector(b.c-a.c) rotated 90)
.. b.c;
pp := p cutbefore bpath.a cutafter bpath.b;
draw pp
withcolor col withpen pencircle scaled w dashed dash;
draw diag_arrow_head(p,1)
withcolor col withpen pencircle scaled w;
enddef;

def diag_draw_arrow_epi(suffix a,b)(expr curved, w, col, dash) =
p = a.c ..
(1/2 [a.c,b.c] + curved*unitvector(b.c-a.c) rotated 90)
.. b.c;
pp := p cutbefore bpath.a cutafter bpath.b;
draw pp
withcolor col withpen pencircle scaled w dashed dash;
draw diag_arrow_head (pp, length(pp))
withcolor col withpen pencircle scaled w;
path ppp;
ppp := pp cutafter (fullcircle scaled 1mm shifted point length(pp) of pp);
draw diag_arrow_head(ppp, length(ppp))
withcolor col withpen pencircle scaled w;
enddef;

def diag_draw_arrow_mono(suffix a,b)(expr curved, w, col, dash) =
p = a.c ..
(1/2 [a.c,b.c] + curved*unitvector(b.c-a.c) rotated 90)
.. b.c;
pp := p cutbefore bpath.a cutafter bpath.b;
path ppp;
ppp := pp cutbefore (fullcircle scaled 1mm shifted point 0 of pp);
draw ppp
withcolor col withpen pencircle scaled w dashed dash;
draw diag_arrow_head (pp, length(pp))
withcolor col withpen pencircle scaled w;
draw diag_arrow_head(ppp, 0)
withcolor col withpen pencircle scaled w;
enddef;

vardef diag_draw_arrow_inj(suffix a,b)(expr curved, w, col, dash) =
p = a.c ..
(1/2 [a.c,b.c] + curved*unitvector(b.c-a.c) rotated 90)
.. b.c;
pp := p cutbefore bpath.a cutafter bpath.b;
path ppp;
ppp := pp cutbefore (fullcircle scaled 1mm shifted point 0 of pp);
draw ppp
withcolor col withpen pencircle scaled w dashed dash;
draw diag_arrow_head (pp, length(pp))
withcolor col withpen pencircle scaled w;
save u,A,B,C;
pair u,A,B,C;
A := point 0 of ppp;
u := unitvector(direction 0 of ppp);
B := A + ahlength*(-u) rotated (-ahangle);
C := A + 2 ahlength*sind(ahangle)*u rotated 90;
draw C {-u} .. B .. A {u}
withcolor col withpen pencircle scaled w dashed dash;
enddef;

def diag_draw_arrow_mapsto(suffix a,b)(expr curved, w, col, dash) =
p = a.c ..
(1/2 [a.c,b.c] + curved*unitvector(b.c-a.c) rotated 90)
.. b.c;
pp := p cutbefore bpath.a cutafter bpath.b;
draw pp
withcolor col withpen pencircle scaled w dashed dash;
draw diag_arrow_head (pp, length(pp))
withcolor col withpen pencircle scaled w;
draw diag_arrow_bar (pp, 0)
withcolor col withpen pencircle scaled w;
enddef;

def diag_draw_arrow_half_dotted(suffix a,b)(expr curved, w, col, dash) =
p = a.c ..
(1/2 [a.c,b.c] + curved*unitvector(b.c-a.c) rotated 90)
.. b.c;
pp := p cutbefore bpath.a cutafter bpath.b;
draw subpath(0,1) of pp
withcolor col withpen pencircle scaled w dashed withsmalldots;
draw subpath(1,2) of pp
withcolor col withpen pencircle scaled w;
draw diag_arrow_head (pp, length(pp))
withcolor col withpen pencircle scaled w;
enddef;

%% Fin des fl�ches

def color_to_string (expr a) =
"("&
decimal(redpart a)
&","&
decimal(greenpart a)
&","&
decimal(bluepart a)
&")"
enddef;

def enddiag =
save i,j,k,l,mm,a,A,p,b;
for i=0 upto _diag_x_max:
for j=0 upto _diag_y_max:
if known _diag[i][j]:
circleit.a[i][j]( _diag[i][j] );
a[i][j].dx = a[i][j].dy;
a[i][j].c = 1cm * (i,-j);
drawunboxed( a[i][j] );
fi;
endfor;
endfor;
for m=0 upto _diag_ar_n:
% V�rifier que le but existe
i := xpart _diag_ar_source[m];
j := ypart _diag_ar_source[m];
k := xpart _diag_ar_but[m];
l := ypart _diag_ar_but[m];

% On trace la fl�che. Le chemin est mis dans la variable p.
path p,pp;
if unknown _diag_ar_shape[m]: _diag_ar_shape[m] := "default" fi;
if unknown _diag_ar_color[m]: _diag_ar_color[m] := black fi;
if unknown _diag_ar_width[m]: _diag_ar_width[m] := .5bp fi;
if unknown _diag_ar_curved[m]: _diag_ar_curved[m] := 0 fi;
if unknown _diag_ar_dashed[m]: _diag_ar_dashed[m] := notdashed fi;
% On ne peut PAS utiliser m dans une cha�ne ce caract�res que l'on donne
% � scantokens, car m est une variable de boucle. C'est vraiment sp�cial,
% une variable de boucle.
mm := m;
scantokens(
"diag_draw_arrow_"& _diag_ar_shape[m]
&"("
&"a[i][j], a[k][l],_diag_ar_curved[mm],_diag_ar_width[mm],"
&"_diag_ar_color[mm],_diag_ar_dashed[mm]"
&");"
);

% On �crit des choses au dessus ou au dessous des fl�ches
pair A;
A = point 1/2 length(p) of p;
if known _diag_ar_up[m]:
boxit.b[m](_diag_ar_up[m]);
b[m].c = A + 4bp*unitvector(direction 1/2 length(p) of p rotated 90);
drawunboxed(b[m]);
fi;
if known _diag_ar_down[m]:
boxit.c[m](_diag_ar_down[m]);
c[m].c = A + 4bp*unitvector(direction 1/2 length(p) of p rotated -90);
drawunboxed(c[m]);
fi;
endfor;
endgroup;
enddef;

begindiag;
node "A";
rarrowto(1,0, "above" => "a",
"shape" => "middle",
"curved" => 3mm,
"dashed" => withsmalldots);
rarrowto(0,1, "below" => "b",
"color" => blue,
"shape" => "mapsto",
"dashed" => evenly);
node "A";
rarrowto(1,0, "above" => "c", "width" => 1bp, "shape" => "inj");
rarrowto(0,1, "below" => "d", "shape" => "mono");
node "A";
nextline;
node "A";
rarrowto(1,0, "below" => "e", "shape" => "epi");
node "A";
rarrowto(1,-1, "below" => "f", "curved" => -3mm, "shape" => "half_dotted");
enddiag;
endfig;
beginfig(270)
draw begingraph(3cm,2cm)
gdraw "data1";
endgraph;

endfig;
beginfig(271)
draw begingraph(3cm,2cm)
gdraw "data1" withpen pencircle scaled 2bp;
endgraph;
endfig;
beginfig(272)
draw begingraph(3cm,2cm)
gdraw "data1" dashed evenly;
endgraph;
endfig;
beginfig(273)
draw begingraph(3cm,2cm)
gdraw "data1" withcolor red;
endgraph;
endfig;
beginfig(274)
draw begingraph(3cm,2cm)
gdraw "data1" withpen pencircle scaled 2bp;
gdraw "data2" ;
endgraph;
endfig;
beginfig(275)
draw begingraph(3cm,2cm)
gdraw "data1" ;
gdraw "data2" dashed evenly;
gdraw "data3" dashed withdots;
endgraph;
endfig;
beginfig(276)
draw begingraph(3cm,2cm)
gdraw "data1" withcolor red;
gdraw "data2" withcolor blue;
endgraph;
endfig;
beginfig(277)
draw begingraph(3cm,2cm)
gdraw "data1" plot btex $\bullet$ etex;
endgraph;

endfig;
beginfig(278)
picture gros_point;
draw (0,0) withpen pencircle scaled 4bp;
gros_point := currentpicture;
currentpicture := nullpicture;
draw begingraph(3cm,2cm)
gdraw "data1" plot gros_point;
endgraph;
endfig;
beginfig(279)
picture gros_point;
gros_point := nullpicture;
addto gros_point doublepath (0,0)
withpen pencircle scaled 4bp;
draw begingraph(3cm,2cm)
gdraw "data1" plot gros_point;
endgraph;
endfig;
beginfig(280)
picture croix;
croix := nullpicture;
addto croix doublepath (-2bp,2bp)--(2bp,-2bp)
withpen pencircle scaled 1bp;
addto croix doublepath (-2bp,-2bp)--(2bp,2bp)
withpen pencircle scaled 1bp;
picture gros_carre;
gros_carre := nullpicture;
addto gros_carre contour unitsquare shifted (-.5,-.5) scaled 2bp;

draw begingraph(3cm,2cm)
gdraw "data1";
gdraw "data1" plot croix;
gdraw "data2";
gdraw "data2" plot gros_carre;
endgraph;
endfig;
beginfig(281)
draw begingraph(3cm,2cm)
gdata("data1",
v,
glabel(gros_point, v1, v2);
);
endgraph;

endfig;
beginfig(282)
draw begingraph(3cm,2cm)
path p;
gdata("data1",
v,
augment.p(v1,v2);
);
gdraw p;
endgraph;

endfig;
beginfig(283)
interim linecap := squared;
interim linejoin := mitered;
draw begingraph(3cm,2cm)
path p;
gdata("data1",
v,
augment.p(v1,v2);
);
gdraw p withpen pencircle scaled 2bp;
gdraw p withpen pencircle scaled 1bp withcolor .8white;
endgraph;
endfig;
beginfig(284)
draw begingraph(3cm,2cm)
gdata("data1",
v,
path p;
augment p (v1,0);
augment p (v1,v2);
gdraw p;
);
endgraph;
endfig;
beginfig(285)
draw begingraph(3cm,2cm)
gdata("data1",
v,
path p;
augment p (v1,0);
augment p (v1,v2);
gdraw p withpen pencircle scaled 4bp;
);
endgraph;
endfig;
beginfig(286)
interim linecap:=2;
draw begingraph(3cm,2cm)
gdata("data1",
v,
path p;
augment p (v1,0);
augment p (v1,v2);
gdraw p withpen pencircle scaled 4bp;
);
endgraph;
endfig;
beginfig(287)
draw begingraph(3cm,2cm)
gdata("data1", v,
path p;
augment p (v1,0);
augment p (v1,v2);
augment p (v1 Sadd "1",v2);
augment p (v1 Sadd "1",0);
gdraw p--cycle;
);
endgraph;
endfig;
beginfig(288)
draw begingraph(3cm,2cm)
gdata("data1", v,
path p;
augment p (v1,0);
augment p (v1,v2);
augment p (v1 Sadd "1",v2);
augment p (v1 Sadd "1",0);
gfill p--cycle withcolor .8white;
gdraw p--cycle;
);
endgraph;
endfig;
beginfig(289)
draw begingraph(3cm,2cm)
gdata("data1", v,

% Le dessus
path p;
augment p (v1,v2);
augment p (v1 Sadd "1",v2);
augment p (v1 Sadd "1.5", v2 Sadd "10");
augment p (v1 Sadd ".5", v2 Sadd "10");
gfill p--cycle withcolor white;
gdraw p--cycle;

% Le c�t�
path p;
augment p (v1 Sadd "1",0);
augment p (v1 Sadd "1",v2);
augment p (v1 Sadd "1.5", v2 Sadd "10");
augment p (v1 Sadd "1.5", "10");
gfill p--cycle withcolor .5white;
gdraw p--cycle;

% Le devant
path p;
augment p (v1,0);
augment p (v1,v2);
augment p (v1 Sadd "1",v2);
augment p (v1 Sadd "1",0);
gfill p--cycle withcolor .8white;
gdraw p--cycle;

);
endgraph;
endfig;
beginfig(290)
draw begingraph(3cm,2cm)
path p,q;
gdata("data1", v,
augment.p(v1,v2);
);
q:= (xpart point 0 of p, 0) -- p --
(xpart point length(p) of p, 0) -- cycle;
gfill q withcolor .8white;
gdraw p withpen pencircle scaled 2bp;
endgraph;
endfig;
beginfig(291)
draw begingraph(3cm,2cm)
gdata("data1",
v,
path p;
augment p ("0", i);
augment p (v2, i);
augment p (v2, i Sadd ".5");
augment p (0, i Sadd ".5");
gfill p--cycle withcolor .8white;
gdraw p--cycle;
);
autogrid(otick.bot,);
endgraph;
endfig;
beginfig(292)
draw begingraph(3cm,2cm)
gdraw "data1";
glabel.bot(btex Abscisse etex, OUT);
glabel.lft(btex Ordonn�e etex, OUT);
endgraph;

endfig;
beginfig(293)
draw begingraph(3cm,2cm)
gdraw "data1" withcolor red;
glabel.lft(btex 1 etex, 8);
gdraw "data2" withcolor blue;
glabel.bot(btex 2 etex, 9);
endgraph;

endfig;
beginfig(294)
draw begingraph(3cm,2cm)
gdraw "data1";
glabel.bot(btex Abscisse etex, OUT);
glabel.lft(btex Ordonn�e etex rotated 90, OUT);
endgraph;
endfig;
beginfig(295)
% La l�gende
color couleur[];
couleur[0] := red;
couleur[1] := green;
couleur[2] := blue;
picture p[], legende;
legende := nullpicture;
for i=0 upto 2:
p[i] := nullpicture;
addto p[i] also TEX("Courbe " & decimal(i+1))
withcolor couleur[i];
addto legende doublepath ( (0,0)--(5mm,0) )
shifted (0, -5mm*i)
withpen currentpen withcolor couleur[i];
addto legende also p[i]
shifted 1/2(lrcorner p[i] - ulcorner p[i])
shifted (0, -5mm*i);
endfor;
% Les courbes
draw begingraph(3cm,2cm)
for i=1 upto 3:
gdraw "data" & decimal(i) withcolor couleur[i-1];
endfor;
glabel.top(legende,OUT);
endgraph;
endfig;
beginfig(296)
draw begingraph(3cm,2cm)
setcoords(-linear,log);
gdraw "data1";
endgraph;

endfig;
beginfig(297)
draw begingraph(3cm,2cm)
gdraw "data1";
endgraph;

endfig;
beginfig(298)
draw begingraph(3cm,2cm)
setrange( (whatever,0), (whatever,whatever) );
gdraw "data1";
endgraph;

endfig;
beginfig(299)
draw begingraph(3cm,2cm)
setrange(whatever, 0, whatever, whatever);
gdraw "data1";
endgraph;

endfig;
beginfig(300)
vardef TEX primary s =
write "verbatimtex" to "mptextmp.mp";
write "\documentclass[12pt]{article}" to "mptextmp.mp";
write "\usepackage[T1]{fontenc}" to "mptextmp.mp";
write "\usepackage{amsmath,amssymb}" to "mptextmp.mp";
write "\begin{document}" to "mptextmp.mp";
write "etex" to "mptextmp.mp";
write "btex "&s&" etex" to "mptextmp.mp";
write EOF to "mptextmp.mp";
scantokens "input mptextmp"
enddef;
vardef mylabel(expr pic, p, t) =
save A; pair A;
A = point t of p +
8bp * unitvector(direction t of p) rotated 90;
label(pic, A);
enddef;
path p; u:=1cm;
p = (0,0)..(-u,u)..(u,u);
draw p;
for i=0 step .2 until length(p):
draw point i of p withpen pencircle scaled 4bp;
mylabel(TEX("$"&decimal(round(5*i))&"$"),p,i);
endfor;

endfig;
beginfig(301)
path p;
p := subpath(1,3) of fullcircle scaled 2cm;
interim linejoin := mitered;
interim linecap := butt;

interim ahangle := 30;
drawarrow p withpen pencircle scaled 2bp;

interim ahangle := 45;
drawarrow p shifted (0,-5mm) withpen pencircle scaled 2bp;

interim ahangle := 60;
drawarrow p shifted (0,-10mm) withpen pencircle scaled 2bp;

endfig;
beginfig(302)
path p;
p := subpath(1,3) of fullcircle scaled 2cm;
interim linejoin := mitered;
interim linecap := butt;
interim ahangle := 30;

interim ahlength := 2bp;
drawarrow p withpen pencircle scaled 2bp;

interim ahlength := 4bp;
drawarrow p shifted (0,-5mm) withpen pencircle scaled 2bp;

interim ahlength := 6bp;
drawarrow p shifted (0,-10mm) withpen pencircle scaled 2bp;

endfig;
beginfig(303)
draw TEX( "Nous sommes le "&
decimal(day) &"/"&
decimal(month) &"/"&
decimal(year) &"." );

endfig;
beginfig(304)
path p;
p := (0,0) -- (2cm,0);
def doit (suffix p)(expr t) =
begingroup
interim linecap := t;
draw p withpen pencircle scaled 5mm withcolor .8white;
endgroup;
draw point 0 of p withpen pencircle scaled 4bp;
draw point 1 of p withpen pencircle scaled 4bp;
p := p shifted (0,-7mm)
enddef;
doit(p,rounded);
doit(p,butt);
doit(p,squared);

endfig;
beginfig(305)
path p;
p := (0,0) -- (1cm,5mm) -- (2cm,0);
def doit (suffix p)(expr t) =
begingroup
interim linejoin := t;
draw p withpen pencircle scaled 5mm withcolor .8white;
endgroup;
draw point 0 of p withpen pencircle scaled 4bp;
draw point 1 of p withpen pencircle scaled 4bp;
draw point 2 of p withpen pencircle scaled 4bp;
p := p shifted (0,-7mm)
enddef;
doit(p,rounded);
doit(p,mitered);
doit(p,beveled);

endfig;
bye;