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Figure 0001: fig0100.asy (Compiled with Asymptote version 1.87svn-r4652) |
size(10cm);
path g=box((-1,-1),(1,1));
pen [] col= new pen[]{gray,yellow};
real k=sqrt(10)/4;
transform T=scale(k)*rotate(degrees(acos(17/(16*k*sqrt(2)))));
int nb=10;
for (int i=0; i<nb; ++i) filldraw(T^i*g,col[i%2]);
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Figure 0002: fig0200.asy (Compiled with Asymptote version 1.87svn-r4652) |
size(10cm);
path g=box((-1,-1),(1,1));
pen [] col= new pen[]{gray,yellow};
path pairToSquare(pair pt){ return pt -- I*pt -- -pt -- -I*pt --cycle; }
int nb=10;
for (int i=0; i<nb; ++i)
{
filldraw(g,col[i%2]);
g=pairToSquare(relpoint(g,1/16));
}
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Figure 0003: fig0300.asy (Compiled with Asymptote version 1.87svn-r4652) |
// On définit ce qu'est l'objet 'rectangle'
// On peut comparer ça à la définition d'une voiture:
// elle a des propriètés: la couleur, le nombre de portes...
// elle a aussi des actions (ou méthodes en info): ouvrir la porte, tourner le volant, avancer...
struct rectangle
{
pair A,B,C,D; // Ce sont des propriétés (au sens informatique): ses sommets.
path path(){return A--B--C--D--cycle;} // Ceci est une action du rectangle (renvoyer le chemin du rectangle)
};
// Le constructeur de l'objet (une action qui renvoie l'objet).
// Chaque fois que l'on va définir une variable 'X' de type 'rectangle'
// c'est le retour de l'action rectangle.init qui est affecté à X.
rectangle operator init() {return new rectangle;}
// La fonction rectangle qui prend en argument le coin inférieur gauche
// et le coin supérieur droit retourne un rectangle.
// On notera comment l'on récupére une propriété ou une action d'un
// objet grâce au '.' en écrivant objet.propriété ou
// objet.action(les_paramètres).
rectangle rectangle(pair gb, pair dh)
{
rectangle retour;
retour.A=(dh.x,gb.y);
retour.B=dh;
retour.C=(gb.x,dh.y);
retour.D=gb;
return retour;
}
// On peut alors définir tous les opérateurs que l'on veut sur les
// rectangles.
// par exemple la multiplication d'un réal par un rectangle (x*rectangle):
rectangle operator *(real x, rectangle rectangle)
{
rectangle retour;
retour.A=rectangle.A+x*(rectangle.B-rectangle.A);
retour.B=rectangle.B+x*(rectangle.C-rectangle.B);
retour.C=rectangle.C+x*(rectangle.D-rectangle.C);
retour.D=rectangle.D+x*(rectangle.A-rectangle.D);
return retour;
}
// Ici, cette opération est commutative (rectangle*x=x*rectangle):
rectangle operator *(rectangle rectangle,real x){return x*rectangle;}
// On dit ici comment "Asymptote" doit convertir, si besoin est, un type 'rectangle'
// en 'path' puis en 'path[]' (tableau de 'path').
path operator cast(rectangle rectangle){return rectangle.path();}
path[] operator cast(rectangle rectangle){return rectangle.path();}
//Par exemple, dans le code:
/*
rectangle SQ=rectangle((0,0), (1,1));
draw(SQ);
*/
// 'draw' attend un type 'path' donc 'SQ' sera automatiquement converti.
// Maintenant on peut travailler avec cette structure
size(10cm);
rectangle SQ=rectangle((0,0), (1,1));
pen [] col= new pen[]{gray,yellow};
int nb=10;
for (int i=0; i<nb; ++i) {
filldraw(SQ,col[i%2]);
SQ=.25*SQ;
}
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Figure 0004: fig0350.asy (Compiled with Asymptote version 1.87svn-r4652) |
/* Copié depuis La police Pictchou */
// Il faut copiler ce document pour obtenir les fichiers main1.eps, main2.eps,..., main5.eps
eval(quote{
size(1cm);
defaultfilename='main1';
currentpen += 0.5bp;
currentpen += squarecap;
currentpen += miterjoin;
currentpen += linetype(" ",false);
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..controls (157,369.664) and (123,456.332)..(123,587)
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..controls (1090.33,802.664) and (1177,894)..(1177,962)
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..controls (737.664,861) and (757,832)..(773,832)
--(802,832)--(802,905)--(758,948)
--cycle^^(1162,847)..controls (1162,813.664) and (1080.33,746.332)..(917,645)
--(932,544)--(932,515)--(946,515)
..controls (1090,593) and (1176.67,674.664)..(1206,760)
--(1206,775)..controls (1199.33,823) and (1184.67,847)..(1162,847)
--cycle^^(773,789)..controls (773,715) and (792,671.664)..(830,659)
--(860,659)--(874,746)--(860,789)
--cycle^^(802,616)..controls (818,530) and (837.332,487)..(860,487)
--(888,515)--(888,602)--(874,616)
--(874,630)--cycle^^(960,457)--(975,357)
--(1192,530)--(1192,630)--cycle^^(845,443)
--(845,414)..controls (851,356) and (865.332,327)..(888,327)
--(903,327)..controls (925,327) and (939.332,351.332)..(946,400)
..controls (936.664,438) and (917.332,457)..(888,457)
--cycle);
});
eval(quote{
size(1cm);
defaultfilename='main2';
currentpen += 0.5bp;
currentpen += squarecap;
currentpen += miterjoin;
currentpen += linetype(" ",false);
fill((768,1854)..controls (819.332,1854) and (850.664,1804.67)..(862,1706)
..controls (846.664,1473.33) and (833.332,1357)..(822,1357)
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--(822,1061)..controls (877.332,1183) and (917.664,1245.67)..(943,1249)
..controls (1057,1249) and (1164.67,1190.67)..(1266,1074)
..controls (1304.67,1052) and (1354,980.332)..(1414,859)
..controls (1458.67,836.332) and (1481,800.332)..(1481,751)
..controls (1481,641) and (1387,448.332)..(1199,173)
..controls (1139,173) and (1103,119.332)..(1091,12)
--(1078,12)..controls (1078,92.6641) and (1055.33,133)..(1010,133)
..controls (974.664,133) and (957,146.332)..(957,173)
--(970,187)--(1051,160)..controls (1151.67,160) and (1227.67,240.664)..(1279,402)
--(1279,415)..controls (1249.67,415) and (1214,455.332)..(1172,536)
..controls (1134,536) and (1093.67,563)..(1051,617)
..controls (961,631) and (916,662.332)..(916,711)
..controls (954.664,935) and (990.664,1047)..(1024,1047)
--(1037,1047)--(970,778)..controls (1028.67,778) and (1073.67,764.664)..(1105,738)
--(1118,738)..controls (1172,908) and (1199,1024.67)..(1199,1088)
..controls (1173,1139.33) and (1096.67,1179.67)..(970,1209)
..controls (940.664,1197) and (887,1116.33)..(809,967)
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..controls (822,1787) and (804,1818.33)..(768,1827)
..controls (693.332,1827) and (612.664,1486.33)..(526,805)
--(607,751)--(607,725)--(594,725)
..controls (502,743) and (421.332,796.664)..(352,886)
..controls (297.332,948.664) and (234.332,980)..(163,980)
--(123,980)--(83,940)--(83,926)
..controls (132.332,926) and (177,894.664)..(217,832)
--(190,792)..controls (235.332,745.332) and (320.664,606.332)..(446,375)
--(634,241)--(620,227)--(607,227)
--(594,241)--(580,241)..controls (553.332,106.332) and (531,39)..(513,39)
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..controls (298.664,605.664) and (182,762.664)..(2,886)
..controls (40.6641,975.332) and (90,1020)..(150,1020)
--(163,1020)..controls (248.332,1020) and (351.664,957.332)..(473,832)
--(486,832)..controls (574.664,1513.33) and (655.332,1854)..(728,1854)
--cycle^^(1252,1047)--(1145,698)--(1252,630)
..controls (1273.33,630) and (1305,715.332)..(1347,886)
..controls (1317.67,982) and (1286,1035.67)..(1252,1047)
--cycle^^(56,899)--(163,819)--(163,832)
..controls (140.332,876.664) and (104.664,899)..(56,899)
--cycle^^(1373,832)..controls (1373,789.332) and (1346.33,708.664)..(1293,590)
--(1373,536)--(1387,536)--(1454,738)
..controls (1436,794) and (1413.67,825.332)..(1387,832)
--cycle^^(970,751)--(957,738)..controls (975,684) and (992.664,657)..(1010,657)
--(1064,657)--(1105,698)--cycle^^(1131,671)
--(1105,630)..controls (1121.67,585.332) and (1157.33,563)..(1212,563)
--(1226,563)--(1226,577)..controls (1226,605.664) and (1194.33,637)..(1131,671)
--cycle^^(1266,563)--(1239,509)..controls (1253.67,464.332) and (1280.67,442)..(1320,442)
--(1347,483)--(1347,496)..controls (1332.33,532) and (1305.33,554.332)..(1266,563)
--cycle);
});
eval(quote{
size(1cm);
defaultfilename='main3';
currentpen += 0.5bp;
currentpen += squarecap;
currentpen += miterjoin;
currentpen += linetype(" ",false);
fill((1012,1850)..controls (1079.33,1850) and (1127.33,1811.33)..(1156,1734)
--(1041,1171)--(1055,1171)--(1098,1200)
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..controls (1407,1041) and (1440.67,992.664)..(1460,896)
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--(1113,159)--(1127,14)--(1113,0)
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--(968,159)--(954,173)--(954,188)
..controls (954.664,201.332) and (1012.33,230.332)..(1127,275)
..controls (1177.67,330.332) and (1226,426.664)..(1272,564)
..controls (1202,564) and (1149,592.664)..(1113,650)
..controls (1076.33,650) and (1018.33,679)..(939,737)
..controls (939,811.664) and (987.332,917.664)..(1084,1055)
--(1113,1026)--(1041,867)--(1055,867)
--(1156,809)--(1171,809)..controls (1228.33,913) and (1257,990.332)..(1257,1041)
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..controls (975.332,1807) and (903,1546.67)..(809,1026)
--(752,997)..controls (693.332,997) and (649.664,1161)..(621,1489)
..controls (583,1631) and (549.332,1708)..(520,1720)
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});
eval(quote{
size(1cm);
defaultfilename='main4';
currentpen += 0.5bp;
currentpen += squarecap;
currentpen += miterjoin;
currentpen += linetype(" ",false);
fill((522,1850)--(552,1850)..controls (624.664,1850) and (664.332,1700.67)..(671,1402)
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});
eval(quote{
size(1cm);
defaultfilename='main5';
currentpen += 0.5bp;
currentpen += squarecap;
currentpen += miterjoin;
currentpen += linetype(" ",false);
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--(1043,932)--(1015,932)--(974,974)
--(974,1002)--(1057,1767)--(1043,1808)
--(1015,1808)..controls (945,1808) and (880.332,1543.67)..(821,1015)
--(779,988)--(751,988)..controls (718.332,988) and (690.664,1219.67)..(668,1683)
..controls (649.332,1683) and (640,1697)..(640,1725)
--(626,1739)--(584,1739)..controls (547.332,1719.67) and (529,1696.33)..(529,1669)
--(542,1349)--(529,1335)--(529,1321)
--(542,1266)--(542,1238)--(529,1238)
--(542,1168)--(542,960)--(556,821)
--(542,821)--(556,807)--(556,695)
..controls (593.332,695) and (621.332,676.664)..(640,640)
--(612,612)..controls (606,640) and (569,654)..(501,654)
..controls (361.664,811.332) and (245.664,890)..(153,890)
--(83,862)--(83,835)..controls (146.332,835) and (193,797.664)..(223,723)
--(209,682)..controls (255.664,632.664) and (339,493.332)..(459,264)
..controls (521,199.332) and (586,167)..(654,167)
--(695,181)--(709,167)--(709,153)
--(682,125)--(598,125)--(584,28)
--(556,28)--(529,56)--(529,97)
--(542,111)--(403,264)..controls (261,541.332) and (154.332,694.332)..(83,723)
..controls (45,735.664) and (17.332,759)..(0,793)
..controls (32,885.664) and (97,932)..(195,932)
..controls (281,918.664) and (383,849)..(501,723)
--(501,1029)--(487,1099)--(501,1099)
--(487,1113)--(487,1224)--(501,1238)
--(487,1252)--(501,1391)--(487,1461)
--(501,1461)--(487,1474)--(487,1711)
..controls (510.332,1757) and (547.332,1780)..(598,1780)
..controls (690.664,1780) and (737,1622.67)..(737,1308)
--(751,1224)--(737,1210)--(737,1196)
--(765,1043)..controls (787.664,1043) and (824.664,1261)..(876,1697)
..controls (911.332,1799) and (962.332,1850)..(1029,1850)
--cycle^^(70,807)--(70,793)--(167,723)
--(167,737)..controls (161.664,759) and (129.332,782.332)..(70,807)
--cycle);
});
for (int n=1; n < 11; ++n) {
picture pic;
label(pic,graphic("main"+(string)(n < 6 ? n : 5)+".eps"),(n < 6 ? -3.5cm : 0,0));
if(n > 5)
label(pic, reflect(N,S)*graphic("main"+(string)(n-5)+".eps"), (1cm,0));
add(pic, (4*(n%6),-2*floor(n/6))*1cm);
}
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Figure 0005: fig0360.asy (Compiled with Asymptote version 1.87svn-r4652) |
// Carte à points 1.
import carteApoints;
settings.outformat="pdf";
add(scale(0.5)*carteApoints(1).fit()); //fig0360.pdf
shipout(bbox(2mm));
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Figure 0006: fig0370.asy (Compiled with Asymptote version 1.87svn-r4652) |
// Carte à points 2.
import carteApoints;
settings.outformat="pdf";
add(scale(0.5)*carteApoints(8).fit()); //fig0370.pdf
shipout(bbox(2mm));
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Figure 0007: fig0400.asy (Compiled with Asymptote version 1.87svn-r4652) |
// Toutes les cartes à points dans un seul pdf: fig0400.pdf
import carteApoints;
import animation;
settings.outformat="pdf";
animation A;
real sc=1/3;
for (int i=1; i < 10; i += 2) {
picture pic;
add(pic,scale(sc)*bbox(carteApoints(i),3mm));
add(pic,shift((0,2.8*min(pic).y))*scale(sc)*bbox(carteApoints(i+1),3mm));
A.add(pic);
}
A.movie();
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Figure 0008: fig0405.asy (Compiled with Asymptote version 1.87svn-r4652) |
// PDF version of this picture: fig0405.pdf
import labelpath;
size(17cm,0);
usepackage("mathrsfs, amsfonts,amsmath,amssymb");
picture pic, pic1, pic2, pic3;
real u=1, Y=pi+0.2;
path cle=scale(u)*unitcircle;
path arcg=arc((0,0),1.5*u,115,155);
void addtick(picture pic=currentpicture, Label L, pair z, pair dir=E, pen p=currentpen)
{
transform R=rotate(degrees(dir));
real width=1.5mm;
Label L=L.copy();
L.position(z);
L.align(NoAlign,E);
L.align.dir=R*L.align.dir*1.3*width/mm;
L.p(p);
pic.add(new void(frame f, transform t) {
path g=(-width,0)--(width,0);
picture opic;
draw(opic,shift(t*z)*R*g,p);
add(f,opic.fit());
});
add(pic,L);
}
path roll(picture pic=currentpicture, real x, int nb=50)
{
real stp=x/(nb-1);
return operator --(...
sequence(new guide(int t){
real tt=t*stp;
return shift(expi(tt))*((x-tt)*(-sin(tt),cos(tt)));
},nb));
}
labelpath("\tiny Sens direct",reverse(arcg));
draw(arcg, Arrow());
draw(Label("$\mathscr{C}$",Relative(0.625)), cle,bp+grey);
dot("$O$", (0,0), S);
dot("$0$", point(cle,0));
dot("$I$", point(cle,0), 2*W);
dot("$J$", point(cle,1), 2*S);
dot("$K$", point(cle,2), 2*W);
dot("$L$", point(cle,3), 2*N);
draw("$1$",(0,0)--point(cle,2),Arrows);
pic.add(currentpicture);// Save the common picture.
// Starting picture 1
pair yM=(u,Y*u), ym=(u,-Y*u);
draw(ym--yM, linewidth(bp), Arrow(TeXHead));
arrow("\underline{Axe des réels}",(u,-0.75*Y*u),W,1cm);
real x=2.2, y=-1.25;
addtick(Label("$1$", align=E),(u,1));
addtick(Label("$2$", align=E),(u,2));
addtick(Label("$-1$", align=E),(u,-1));
addtick(Label("$x$", align=E),(u,x));
addtick(Label("$y$", align=E),(u,y));
pic1.add(currentpicture);
erase();
// Starting picture 2
add(pic);
real t=x+0.1;
draw((u,0)--yM, bp+grey, Arrow(TeXHead));
path tg=arc((0,0),u,0,degrees(t));
draw(tg,linewidth(bp));
addtick(Label("$1$", align=E),u*(cos(1),sin(1)),dir(degrees(1.0)));
addtick(Label("$1$", align=E),(u,1), grey);
addtick(Label("$2$", align=E),(u,2),grey);
addtick(Label("$\frac{\pi}{2}$", align=E),(u,pi/2),grey);
addtick(Label("$\pi$", align=E),(u,pi),grey);
addtick(Label("$-1$", align=E),(u,-1));
addtick(Label("$x$", align=E),(u,x), grey);
addtick(Label("$x$", align=E),u*(cos(x),sin(x)),dir(degrees(x)));
addtick(Label("$y$", align=E),(u,-x));
dot("$M$", u*expi(x), -2*u*expi(x));
draw(Label("+",Relative(0.5)), roll(x), dotted, Arrow(Relative(0.5)));
draw(roll(1), dotted);
draw(Label("+",Relative(0.5)), roll(pi/2), dotted, Arrow(Relative(0.5)));
draw(Label("+",Relative(0.5)), roll(pi,100), dotted, Arrow(Relative(0.5)));
path g=u*expi(t)--shift(u*expi(t))*((Y-t)*u*expi(pi/2+t));
draw(g,linewidth(bp), Arrow(TeXHead));
addtick(Label("$\pi$", align=E),arcpoint(g,(pi-t)*u),expi(t));
pic3.add(currentpicture);
draw(ym--(u,0), linewidth(bp));
pic2.add(currentpicture);
erase();
// Starting picture 3
draw(ym--(u,0), linewidth(bp)+grey);
path tg=arc((0,0),u,0,degrees(-t));
draw(tg,linewidth(bp));
addtick(Label("$-1$", align=E),u*(cos(-1),sin(-1)),dir(degrees(-1.0)));
addtick(Label("$-1$", align=E),(u,-1), grey);
addtick(Label("$-2$", align=E),(u,-2),grey);
addtick(Label("$-\frac{\pi}{2}$", align=E),(u,-pi/2),grey);
addtick(Label("$-\pi$", align=E),(u,-pi),grey);
dot("$N$", u*expi(-x), -2*u*expi(-x));
g=roll(-x);
draw(Label("$-$",align=2*I*dir(g,0.5),Relative(0.5)), g, dotted, Arrow(NoFill,Relative(0.5)));
g=roll(-1);
draw(g, dotted);
g=roll(-pi/2);
draw(Label("$-$",align=2*I*dir(g,0.5),Relative(0.5)), g, dotted, Arrow(NoFill,Relative(0.5)));
g=roll(-pi,100);
draw(Label("$-$",align=2*I*dir(g,0.5),Relative(0.5)), g, dotted, Arrow(NoFill,Relative(0.5)));
g=u*expi(-t)--shift(u*expi(-t))*((Y-t)*u*expi(-pi/2-t));
draw(g, linewidth(bp), Arrow(TeXHead));
addtick(Label("$-\pi$", align=E),arcpoint(g,(pi-t)*u),expi(-t));
////////////////////////////////////////////////////////////
pic3.add(currentpicture);
erase();
add(pic1);
add(shift(4*u,0)*pic2);
add(shift(8*u,0)*pic3);
shipout(format="pdf");
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Figure 0009: fig0410.asy (Compiled with Asymptote version 1.87svn-r4652) |
size(10cm);
path cle=unitcircle;
path roll(picture pic=currentpicture, real x, int nb=50)
{
real stp=x/(nb-1);
return operator --(...
sequence(new guide(int t){
real tt=t*stp;
return shift(expi(tt))*((x-tt)*(-sin(tt),cos(tt)));
},nb));
}
real y=4*pi;
pair yM=(1,y), ym=(1,-y);
int nb=100;
real stp=2*y/nb;
path[] g;
for (int i=1; i <= nb; ++i) {
real t=-y+i*stp;
g.push(roll(-y+i*stp/2,50+round(20*i*stp))--reverse(roll(y-i*stp/2,50+round(20*i*stp)))--cycle);
}
pen p1=blue, p2=0.9*red;
fill(g,p1);
fill(g,fillrule(1)+p2);
unfill(cle);
draw(cle,white);
shipout(rotate(-90)*bbox(Fill(lightyellow)));
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Figure 0010: fig0420.asy (Compiled with Asymptote version 1.87svn-r4652) |
import stats;
path ell(pair O, real a, real b, int t=1)
{
path g=ellipse(O,a,b);
return subpath(g, t > 0 ? -1 : 1, t > 0 ? 1 : 3);
}
size(10cm,0);
real a=1, b=1.75, d=0.1, dl=1.5;
pen p1=1.5bp+white, p2=1.5bp+black;
pen fp=grey;
int n=8, nm=floor(n/2);
real step=1/n;
for (int line=0; line < 7; ++line) {
pair p=(0,0);
picture pic;
transform Sh=shift(line*(0,-2.5*b));
for (int i=0; i <= nm; ++i) {
real t=cos(i*step);
real t=0.75-i*step;
real na=a*(0.25+0.75*t);
path g1=ell(p,na,b,1);
path g2=ell(p,na,b,-1);
fill(pic, g1--g2--cycle, fp);
label(pic,(string)round(unitrand()),p,white);
draw(pic, g1, p1);
draw(pic, g2, p2);
if(i != 0) {
transform T=shift(-2p);
label(pic,(string)round(unitrand()),T*p,white);
fill(pic, T*(g1--g2--cycle), fp);
draw(pic, T*g1, p1);
draw(pic, T*g2, p2);
}
if(i != nm) p += na+d+dl*t;
}
add(Sh*pic);
pair M=(p.x,0);
picture pic2=reflect(M,M+N)*pic;
add(Sh*pic2);
add(Sh*reflect(3*M,3*M+N)*pic2);
}
shipout(bbox(1mm,Fill(lightgrey)));
Dernière modification/Last modified: Sun Sep 20 18:47:39 CEST 2009
Philippe Ivaldi