Asymptote using three.asy – fig0010

Category: Asymptote,Examples 3D,three.asyPh. Ivaldi @ 14 h 50 min

 (Compiled with Asymptote version 2.14svn-r5318)
```
/* One may view this animated example */
import three;

size(12cm);
currentprojection=orthographic(1,1,1.5);
currentlight=(1,0,1);

triple P00=-X-Y+0.5*Z, P03=-X+Y, P33=X+Y, P30=X-Y;

triple[][] P={
{P00,P00+(-0.5,0.5,-1),P03+(0,-0.5,1),P03},
{P00+(0.5,-0.5,-1),(-0.5,-0.5,0.5),(-0.5,0.5,-1.5),P03+(0.5,0,1)},
{P30+(-0.5,0,1),(0.5,-0.5,-1.5),(0.5,0.5,1),P33+(-0.5,0,1)},
{P30,P30+(0,0.5,1),P33+(0,-0.5,1),P33}
};

surface s=surface(patch(P));
draw(s,15,15,yellow,meshpen=grey);
draw(sequence(new path3(int i){
return s.s[i].external();},s.s.length), bp+red);

dot("P[0][0]",P[0][0], align=N, black);
dot("P[0][3]",P[0][3], black);
dot("P[3][3]",P[3][3], align=S, black);
dot("P[3][0]",P[3][0], align=W, black);

draw(Label("P[0][1]",align=SW,EndPoint),P[0][0]--P[0][1], Arrow3);
draw(Label("P[1][0]",align=SE,EndPoint),P[0][0]--P[1][0], Arrow3);

draw(Label("P[0][2]",align=E,EndPoint),P[0][3]--P[0][2], Arrow3);
draw(Label("P[1][3]",EndPoint),P[0][3]--P[1][3], Arrow3);

draw(Label("P[2][3]",EndPoint),P[3][3]--P[2][3], Arrow3);
draw(Label("P[3][2]",EndPoint),P[3][3]--P[3][2], Arrow3);

draw(Label("P[3][1]",EndPoint),P[3][0]--P[3][1], Arrow3);
draw(Label("P[2][0]", align=W,EndPoint),P[3][0]--P[2][0], Arrow3);

dot("P[1][1]",P[1][1], align=S);
dot("P[1][2]",P[1][2], align=E);
dot("P[2][2]",P[2][2], align=N);
dot("P[2][1]",P[2][1], align=W);

for (int i=0; i < s.s.length; ++i)
dot(s.s[i].internal(), bp+red);

if(!is3D())
shipout(bbox(Fill(lightgrey)));

```

Étiquettes : , , , ,

Asymptote using three.asy – fig0020

Category: Asymptote,Examples 3D,three.asyPh. Ivaldi @ 15 h 50 min

 (Compiled with Asymptote version 2.14svn-r5318)
```
import three;
import palette;

size(12cm);
currentprojection=orthographic(1,1,1.5);
currentlight=(1,0,1);

triple P00=-X-Y+0.5*Z, P03=-X+Y, P33=X+Y, P30=X-Y;

triple[][] P={
{P00,P00+(-0.5,0.5,-1),P03+(0,-0.5,1),P03},
{P00+(0.5,-0.5,-1),(-0.5,-0.5,0.5),(-0.5,0.5,-1.5),P03+(0.5,0,1)},
{P30+(-0.5,0,1),(0.5,-0.5,-1.5),(0.5,0.5,1),P33+(-0.5,0,1)},
{P30,P30+(0,0.5,1),P33+(0,-0.5,1),P33}
};

surface s=surface(patch(P));
// s.colors(palette(s.map(zpart),Rainbow()));

draw(s);
draw(sequence(new path3(int i){
return s.s[i].external();},s.s.length), bp+orange);

if(!is3D())
shipout(bbox(Fill(lightgrey)));

```

Étiquettes : , , , , ,

Asymptote using three.asy – fig0030

Category: Asymptote,Examples 3D,three.asyPh. Ivaldi @ 16 h 50 min

 (Compiled with Asymptote version 2.14svn-r5318)
```
import three;

size(10cm);
currentlight=(0,0,1);

surface sf=surface(patch(P=new triple[][] {
{(0,0,0),(1,0,0),(1,0,0),(2,0,0)},
{(0,1,0),(1,0,1),(1,0,1),(2,1,0)},
{(0,1,0),(1,0,-1),(1,0,-1),(2,1,0)},
{(0,2,0),(1,2,0),(1,2,0),(2,2,0)}
}));

draw(sf,surfacepen=yellow);
draw(sf.s[0].vequals(0.5),squarecap+2bp+blue,currentlight);
draw(sf.s[0].uequals(0.5),squarecap+2bp+red,currentlight);

```

Étiquettes : , , , , ,

Official Asymptote example – BezierPatch

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 7 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
```/* This code comes from The Official Asymptote Gallery */

import three;

size(10cm);
currentlight=Viewport;

surface s=surface(patch(new triple[][] {
{(0,0,0),(1,0,0),(1,0,0),(2,0,0)},
{(0,1,0),(1,0,1),(1,0,1),(2,1,0)},
{(0,1,0),(1,0,-1),(1,0,-1),(2,1,0)},
{(0,2,0),(1,2,0),(1,2,0),(2,2,0)}}));

draw(s,yellow);
draw(s.s[0].vequals(0.5),squarecap+2bp+blue,currentlight);
draw(s.s[0].uequals(0.5),squarecap+2bp+red,currentlight);

```

Étiquettes : , , ,

Official Asymptote example – BezierSurface

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 8 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
```/* This code comes from The Official Asymptote Gallery */

import three;

string viewpoint="
COO=-684.0787963867188 206.90650939941406 218.13809204101562
C2C=0.8244762420654297 -0.563306450843811 0.0540805421769619
ROO=1009.7407942621448
ROLL=17.39344555165265
";

// viewpoint=getstring("viewpoint",viewpoint);
currentprojection=perspective(viewpoint);

triple[][][] P={
{
{(-1.6,0,1.875),(-2.3,0,1.875),(-2.7,0,1.875),(-2.7,0,1.65),},
{(-1.6,-0.3,1.875),(-2.3,-0.3,1.875),(-2.7,-0.3,1.875),(-2.7,-0.3,1.65),},
{(-1.5,-0.3,2.1),(-2.5,-0.3,2.1),(-3,-0.3,2.1),(-3,-0.3,1.65),},
{(-1.5,0,2.1),(-2.5,0,2.1),(-3,0,2.1),(-3,0,1.65),}
},{
{(-2.7,0,1.65),(-2.7,0,1.425),(-2.5,0,0.975),(-2,0,0.75),},
{(-2.7,-0.3,1.65),(-2.7,-0.3,1.425),(-2.5,-0.3,0.975),(-2,-0.3,0.75),},
{(-3,-0.3,1.65),(-3,-0.3,1.2),(-2.65,-0.3,0.7275),(-1.9,-0.3,0.45),},
{(-3,0,1.65),(-3,0,1.2),(-2.65,0,0.7275),(-1.9,0,0.45),}
},{
{(-2.7,0,1.65),(-2.7,0,1.875),(-2.3,0,1.875),(-1.6,0,1.875),},
{(-2.7,0.3,1.65),(-2.7,0.3,1.875),(-2.3,0.3,1.875),(-1.6,0.3,1.875),},
{(-3,0.3,1.65),(-3,0.3,2.1),(-2.5,0.3,2.1),(-1.5,0.3,2.1),},
{(-3,0,1.65),(-3,0,2.1),(-2.5,0,2.1),(-1.5,0,2.1),}
},{
{(-2,0,0.75),(-2.5,0,0.975),(-2.7,0,1.425),(-2.7,0,1.65),},
{(-2,0.3,0.75),(-2.5,0.3,0.975),(-2.7,0.3,1.425),(-2.7,0.3,1.65),},
{(-1.9,0.3,0.45),(-2.65,0.3,0.7275),(-3,0.3,1.2),(-3,0.3,1.65),},
{(-1.9,0,0.45),(-2.65,0,0.7275),(-3,0,1.2),(-3,0,1.65),}
}
};

picture pic;
size(pic,15cm);
size3(pic,10cm);
draw(pic,surface(P),blue);

```

Étiquettes : , , ,

Official Asymptote example – NURBSsurface

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 20 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
```/* This code comes from The Official Asymptote Gallery */

import three;

size(10cm);

currentprojection=perspective(50,80,50);

// Nonrational surface:
// udegree=3, vdegree=3, nu=5, nv=6;
real[] uknot={0,0,0,0,0.5,1,1,1,1};
real[] vknot={0,0,0,0,0.4,0.6,1,1,1,1};

triple[][] P={{
(-31.2061,12.001,6.45082),
(-31.3952,14.7353,6.53707),
(-31.5909,21.277,6.70051),
(-31.4284,25.4933,6.76745),
(-31.5413,30.3485,6.68777),
(-31.4896,32.2839,6.58385)
},{
(-28.279,12.001,7.89625),
(-28.4187,14.7353,8.00954),
(-28.5633,21.277,8.22422),
(-28.4433,25.4933,8.31214),
(-28.5266,30.3485,8.20749),
(-28.4885,32.2839,8.07099)
},{
(-20,12.001,10.0379),
(-20,14.7353,10.2001),
(-20,21.277,10.5076),
(-20,25.4933,10.6335),
(-20,30.3485,10.4836),
(-20,32.2839,10.2881)
},{
(-11.721,12.001,7.84024),
(-11.5813,14.7353,7.95269),
(-11.4367,21.277,8.16575),
(-11.5567,25.4933,8.25302),
(-11.4734,30.3485,8.14915),
(-11.5115,32.2839,8.01367)
},{
(-8.79391,12.001,6.39481),
(-8.60483,14.7353,6.48022),
(-8.40905,21.277,6.64204),
(-8.57158,25.4933,6.70832),
(-8.45874,30.3485,6.62943),
(-8.51041,32.2839,6.52653)
}
};

draw(P,uknot,vknot,new pen[] {red,green,blue,magenta});

// Rational Bezier patch:
// udegree=3, vdegree=3, nu=4, nv=4;
real[] uknot={0,0,0,0,1,1,1,1};
real[] vknot={0,0,0,0,1,1,1,1};
triple[][] P=scale3(20)*octant1.P;

// Optional weights:
real[][] weights=array(P.length,array(P[0].length,1.0));
weights[0][2]=5.0;

draw(P,uknot,vknot,weights,blue);

```

Étiquettes : , , ,

Official Asymptote example – soccerball

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 0 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
```/* This code comes from The Official Asymptote Gallery */

import graph3;
size(400);
currentlight.background=palegreen;

defaultrender=render(compression=Zero,merge=true);

real c=(1+sqrt(5))/2;

triple[] z={(c,1,0),(-c,1,0),(-c,-1,0),(c,-1,0)};
triple[] x={(0,c,1),(0,-c,1),(0,-c,-1),(0,c,-1)};
triple[] y={(1,0,c),(1,0,-c),(-1,0,-c),(-1,0,c)};

triple[][] Q={
{z[0],y[1],x[3],x[0],y[0],z[3]},
{z[1],x[0],x[3],y[2],z[2],y[3]},
{z[2],z[1],y[2],x[2],x[1],y[3]},
{z[3],z[0],y[0],x[1],x[2],y[1]},
{x[0],x[3],z[1],y[3],y[0],z[0]},
{x[1],x[2],z[2],y[3],y[0],z[3]},
{x[2],x[1],z[3],y[1],y[2],z[2]},
{x[3],x[0],z[0],y[1],y[2],z[1]},
{y[0],y[3],x[1],z[3],z[0],x[0]},
{y[1],y[2],x[2],z[3],z[0],x[3]},
{y[2],y[1],x[3],z[1],z[2],x[2]},
{y[3],y[0],x[0],z[1],z[2],x[1]}
};

path3 p=arc(O,Q[0][0],Q[0][1]);
real R=abs(point(p,reltime(p,1/3)));

triple[][] P;
for(int i=0; i < Q.length; ++i){
P[i]=new triple[] ;
for(int j=0; j < Q[i].length; ++j){
P[i][j]=Q[i][j]/R;
}
}

surface sphericaltriangle(triple center, triple A, triple B, triple C,
int nu=3, int nv=nu) {
path3 tri1=arc(center,A,B);
path3 tri2=arc(center,A,C);
path3 tri3=arc(center,B,C);
triple tri(pair p) {
path3 cr=arc(O,relpoint(tri2,p.x),relpoint(tri3,p.x));
return relpoint(cr,p.y);
};

return surface(tri,(0,0),(1-sqrtEpsilon,1),nu,nv,Spline);
}

for(int i=0; i < P.length; ++i){
triple[] pentagon=sequence(new triple(int k) {
path3 p=arc(O,P[i][0],P[i][k+1]);
return point(p,reltime(p,1/3));
},5);
pentagon.cyclic=true;
draw(sequence(new path3(int k) {
return arc(O,pentagon[k],pentagon[k+1]);},5),linewidth(2pt));
triple M=unit(sum(pentagon)/5);
for(int i=0; i < 5; ++i){
surface sf=sphericaltriangle(O,pentagon[i],M,pentagon[i+1]);
draw(sf,black);
}
}

for(int i=0; i < P.length; ++i){
for(int j=1; j <= 5; ++j){
triple K=P[i][0];
triple A=P[i][j];
triple B=P[i][(j % 5)+1];
path3[] p={arc(O,K,A),arc(O,A,B),arc(O,B,K)};
draw(subpath(p[0],reltime(p[0],1/3),reltime(p[0],2/3)),linewidth(4pt));
triple[] hexagon={point(p[0],reltime(p[0],1/3)),
point(p[0],reltime(p[0],2/3)),
point(p[1],reltime(p[1],1/3)),
point(p[1],reltime(p[1],2/3)),
point(p[2],reltime(p[2],1/3)),
point(p[2],reltime(p[2],2/3))};
hexagon.cyclic=true;
triple M=unit(sum(hexagon)/6);
for(int i=0; i < 6; ++i){
surface sf=sphericaltriangle(O,hexagon[i],M,hexagon[i+1]);
draw(sf,white);
}
}
}

```

Étiquettes : , , , , , ,

Official Asymptote example – splitpatch

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 9 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
```/* This code comes from The Official Asymptote Gallery */

import three;

size(300);

currentprojection=orthographic(0,0,1);

triple[][] A={
{(0,0,0),(1,0,0),(1,0,0),(2,0,0)},
{(0,4/3,0),(2/3,4/3,2),(4/3,4/3,2),(2,4/3,0)},
{(0,2/3,0),(2/3,2/3,0),(4/3,2/3,0),(2,2/3,0)},
{(0,2,0),(2/3,2,0),(4/3,2,0),(2,2,0)}
};

triple[][] B={
{(0.5,0,-1),(0.5,1,-1),(0.5,2,-1),(0.5,3,-1)},
{(0.5,0,0),(0.5,1,0),(0.5,2,0),(0.5,3,0)},
{(0.5,0,1),(0.5,1,1),(0.5,2,1),(0.5,3,1)},
{(0.5,0,2),(0.5,1,2),(0.5,2,2),(0.5,3,2)}
};

split S=split(A,B,10);
//write(S.T.length);

defaultrender.merge=true;

for(int i=0; i < S.T.length; ++i)
draw(surface(patch(S.T[i])),Pen(i));
draw(surface(patch(B)),blue);

```

Étiquettes : , ,

Official Asymptote example – teapot

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 21 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
```/* This code comes from The Official Asymptote Gallery */

import three;

size(20cm);

currentprojection=perspective(250,-250,250);
currentlight=Viewport;

triple[][][] Q={
{
{(39.68504,0,68.0315),(37.91339,0,71.75197),(40.74803,0,71.75197),(42.51969,0,68.0315)},
{(39.68504,-22.22362,68.0315),(37.91339,-21.2315,71.75197),(40.74803,-22.8189,71.75197),(42.51969,-23.81102,68.0315)},
{(22.22362,-39.68504,68.0315),(21.2315,-37.91339,71.75197),(22.8189,-40.74803,71.75197),(23.81102,-42.51969,68.0315)},
{(0,-39.68504,68.0315),(0,-37.91339,71.75197),(0,-40.74803,71.75197),(0,-42.51969,68.0315)}
},{
{(0,-39.68504,68.0315),(0,-37.91339,71.75197),(0,-40.74803,71.75197),(0,-42.51969,68.0315)},
{(-22.22362,-39.68504,68.0315),(-21.2315,-37.91339,71.75197),(-22.8189,-40.74803,71.75197),(-23.81102,-42.51969,68.0315)},
{(-39.68504,-22.22362,68.0315),(-37.91339,-21.2315,71.75197),(-40.74803,-22.8189,71.75197),(-42.51969,-23.81102,68.0315)},
{(-39.68504,0,68.0315),(-37.91339,0,71.75197),(-40.74803,0,71.75197),(-42.51969,0,68.0315)}
},{
{(-39.68504,0,68.0315),(-37.91339,0,71.75197),(-40.74803,0,71.75197),(-42.51969,0,68.0315)},
{(-39.68504,22.22362,68.0315),(-37.91339,21.2315,71.75197),(-40.74803,22.8189,71.75197),(-42.51969,23.81102,68.0315)},
{(-22.22362,39.68504,68.0315),(-21.2315,37.91339,71.75197),(-22.8189,40.74803,71.75197),(-23.81102,42.51969,68.0315)},
{(0,39.68504,68.0315),(0,37.91339,71.75197),(0,40.74803,71.75197),(0,42.51969,68.0315)}
},{
{(0,39.68504,68.0315),(0,37.91339,71.75197),(0,40.74803,71.75197),(0,42.51969,68.0315)},
{(22.22362,39.68504,68.0315),(21.2315,37.91339,71.75197),(22.8189,40.74803,71.75197),(23.81102,42.51969,68.0315)},
{(39.68504,22.22362,68.0315),(37.91339,21.2315,71.75197),(40.74803,22.8189,71.75197),(42.51969,23.81102,68.0315)},
{(39.68504,0,68.0315),(37.91339,0,71.75197),(40.74803,0,71.75197),(42.51969,0,68.0315)}
},{
{(42.51969,0,68.0315),(49.60629,0,53.1496),(56.69291,0,38.26771),(56.69291,0,25.51181)},
{(42.51969,-23.81102,68.0315),(49.60629,-27.77952,53.1496),(56.69291,-31.74803,38.26771),(56.69291,-31.74803,25.51181)},
{(23.81102,-42.51969,68.0315),(27.77952,-49.60629,53.1496),(31.74803,-56.69291,38.26771),(31.74803,-56.69291,25.51181)},
{(0,-42.51969,68.0315),(0,-49.60629,53.1496),(0,-56.69291,38.26771),(0,-56.69291,25.51181)}
},{
{(0,-42.51969,68.0315),(0,-49.60629,53.1496),(0,-56.69291,38.26771),(0,-56.69291,25.51181)},
{(-23.81102,-42.51969,68.0315),(-27.77952,-49.60629,53.1496),(-31.74803,-56.69291,38.26771),(-31.74803,-56.69291,25.51181)},
{(-42.51969,-23.81102,68.0315),(-49.60629,-27.77952,53.1496),(-56.69291,-31.74803,38.26771),(-56.69291,-31.74803,25.51181)},
{(-42.51969,0,68.0315),(-49.60629,0,53.1496),(-56.69291,0,38.26771),(-56.69291,0,25.51181)}
},{
{(-42.51969,0,68.0315),(-49.60629,0,53.1496),(-56.69291,0,38.26771),(-56.69291,0,25.51181)},
{(-42.51969,23.81102,68.0315),(-49.60629,27.77952,53.1496),(-56.69291,31.74803,38.26771),(-56.69291,31.74803,25.51181)},
{(-23.81102,42.51969,68.0315),(-27.77952,49.60629,53.1496),(-31.74803,56.69291,38.26771),(-31.74803,56.69291,25.51181)},
{(0,42.51969,68.0315),(0,49.60629,53.1496),(0,56.69291,38.26771),(0,56.69291,25.51181)}
},{
{(0,42.51969,68.0315),(0,49.60629,53.1496),(0,56.69291,38.26771),(0,56.69291,25.51181)},
{(23.81102,42.51969,68.0315),(27.77952,49.60629,53.1496),(31.74803,56.69291,38.26771),(31.74803,56.69291,25.51181)},
{(42.51969,23.81102,68.0315),(49.60629,27.77952,53.1496),(56.69291,31.74803,38.26771),(56.69291,31.74803,25.51181)},
{(42.51969,0,68.0315),(49.60629,0,53.1496),(56.69291,0,38.26771),(56.69291,0,25.51181)}
},{
{(56.69291,0,25.51181),(56.69291,0,12.7559),(42.51969,0,6.377957),(42.51969,0,4.251961)},
{(56.69291,-31.74803,25.51181),(56.69291,-31.74803,12.7559),(42.51969,-23.81102,6.377957),(42.51969,-23.81102,4.251961)},
{(31.74803,-56.69291,25.51181),(31.74803,-56.69291,12.7559),(23.81102,-42.51969,6.377957),(23.81102,-42.51969,4.251961)},
{(0,-56.69291,25.51181),(0,-56.69291,12.7559),(0,-42.51969,6.377957),(0,-42.51969,4.251961)}
},{
{(0,-56.69291,25.51181),(0,-56.69291,12.7559),(0,-42.51969,6.377957),(0,-42.51969,4.251961)},
{(-31.74803,-56.69291,25.51181),(-31.74803,-56.69291,12.7559),(-23.81102,-42.51969,6.377957),(-23.81102,-42.51969,4.251961)},
{(-56.69291,-31.74803,25.51181),(-56.69291,-31.74803,12.7559),(-42.51969,-23.81102,6.377957),(-42.51969,-23.81102,4.251961)},
{(-56.69291,0,25.51181),(-56.69291,0,12.7559),(-42.51969,0,6.377957),(-42.51969,0,4.251961)}
},{
{(-56.69291,0,25.51181),(-56.69291,0,12.7559),(-42.51969,0,6.377957),(-42.51969,0,4.251961)},
{(-56.69291,31.74803,25.51181),(-56.69291,31.74803,12.7559),(-42.51969,23.81102,6.377957),(-42.51969,23.81102,4.251961)},
{(-31.74803,56.69291,25.51181),(-31.74803,56.69291,12.7559),(-23.81102,42.51969,6.377957),(-23.81102,42.51969,4.251961)},
{(0,56.69291,25.51181),(0,56.69291,12.7559),(0,42.51969,6.377957),(0,42.51969,4.251961)}
},{
{(0,56.69291,25.51181),(0,56.69291,12.7559),(0,42.51969,6.377957),(0,42.51969,4.251961)},
{(31.74803,56.69291,25.51181),(31.74803,56.69291,12.7559),(23.81102,42.51969,6.377957),(23.81102,42.51969,4.251961)},
{(56.69291,31.74803,25.51181),(56.69291,31.74803,12.7559),(42.51969,23.81102,6.377957),(42.51969,23.81102,4.251961)},
{(56.69291,0,25.51181),(56.69291,0,12.7559),(42.51969,0,6.377957),(42.51969,0,4.251961)}
},{
{(-45.35433,0,57.40157),(-65.19685,0,57.40157),(-76.53543,0,57.40157),(-76.53543,0,51.02362)},
{(-45.35433,-8.503932,57.40157),(-65.19685,-8.503932,57.40157),(-76.53543,-8.503932,57.40157),(-76.53543,-8.503932,51.02362)},
{(-42.51969,-8.503932,63.77952),(-70.86614,-8.503932,63.77952),(-85.03937,-8.503932,63.77952),(-85.03937,-8.503932,51.02362)},
{(-42.51969,0,63.77952),(-70.86614,0,63.77952),(-85.03937,0,63.77952),(-85.03937,0,51.02362)}
},{
{(-42.51969,0,63.77952),(-70.86614,0,63.77952),(-85.03937,0,63.77952),(-85.03937,0,51.02362)},
{(-42.51969,8.503932,63.77952),(-70.86614,8.503932,63.77952),(-85.03937,8.503932,63.77952),(-85.03937,8.503932,51.02362)},
{(-45.35433,8.503932,57.40157),(-65.19685,8.503932,57.40157),(-76.53543,8.503932,57.40157),(-76.53543,8.503932,51.02362)},
{(-45.35433,0,57.40157),(-65.19685,0,57.40157),(-76.53543,0,57.40157),(-76.53543,0,51.02362)}
},{
{(-76.53543,0,51.02362),(-76.53543,0,44.64566),(-70.86614,0,31.88976),(-56.69291,0,25.51181)},
{(-76.53543,-8.503932,51.02362),(-76.53543,-8.503932,44.64566),(-70.86614,-8.503932,31.88976),(-56.69291,-8.503932,25.51181)},
{(-85.03937,-8.503932,51.02362),(-85.03937,-8.503932,38.26771),(-75.11811,-8.503932,26.5748),(-53.85826,-8.503932,17.00787)},
{(-85.03937,0,51.02362),(-85.03937,0,38.26771),(-75.11811,0,26.5748),(-53.85826,0,17.00787)}
},{
{(-85.03937,0,51.02362),(-85.03937,0,38.26771),(-75.11811,0,26.5748),(-53.85826,0,17.00787)},
{(-85.03937,8.503932,51.02362),(-85.03937,8.503932,38.26771),(-75.11811,8.503932,26.5748),(-53.85826,8.503932,17.00787)},
{(-76.53543,8.503932,51.02362),(-76.53543,8.503932,44.64566),(-70.86614,8.503932,31.88976),(-56.69291,8.503932,25.51181)},
{(-76.53543,0,51.02362),(-76.53543,0,44.64566),(-70.86614,0,31.88976),(-56.69291,0,25.51181)}
},{
{(48.18897,0,40.3937),(73.70078,0,40.3937),(65.19685,0,59.52755),(76.53543,0,68.0315)},
{(48.18897,-18.70866,40.3937),(73.70078,-18.70866,40.3937),(65.19685,-7.086619,59.52755),(76.53543,-7.086619,68.0315)},
{(48.18897,-18.70866,17.00787),(87.87401,-18.70866,23.38582),(68.0315,-7.086619,57.40157),(93.5433,-7.086619,68.0315)},
{(48.18897,0,17.00787),(87.87401,0,23.38582),(68.0315,0,57.40157),(93.5433,0,68.0315)}
},{
{(48.18897,0,17.00787),(87.87401,0,23.38582),(68.0315,0,57.40157),(93.5433,0,68.0315)},
{(48.18897,18.70866,17.00787),(87.87401,18.70866,23.38582),(68.0315,7.086619,57.40157),(93.5433,7.086619,68.0315)},
{(48.18897,18.70866,40.3937),(73.70078,18.70866,40.3937),(65.19685,7.086619,59.52755),(76.53543,7.086619,68.0315)},
{(48.18897,0,40.3937),(73.70078,0,40.3937),(65.19685,0,59.52755),(76.53543,0,68.0315)}
},{
{(76.53543,0,68.0315),(79.37007,0,70.15748),(82.20472,0,70.15748),(79.37007,0,68.0315)},
{(76.53543,-7.086619,68.0315),(79.37007,-7.086619,70.15748),(82.20472,-4.251961,70.15748),(79.37007,-4.251961,68.0315)},
{(93.5433,-7.086619,68.0315),(99.92125,-7.086619,70.68897),(97.79527,-4.251961,71.22047),(90.70866,-4.251961,68.0315)},
{(93.5433,0,68.0315),(99.92125,0,70.68897),(97.79527,0,71.22047),(90.70866,0,68.0315)}
},{
{(93.5433,0,68.0315),(99.92125,0,70.68897),(97.79527,0,71.22047),(90.70866,0,68.0315)},
{(93.5433,7.086619,68.0315),(99.92125,7.086619,70.68897),(97.79527,4.251961,71.22047),(90.70866,4.251961,68.0315)},
{(76.53543,7.086619,68.0315),(79.37007,7.086619,70.15748),(82.20472,4.251961,70.15748),(79.37007,4.251961,68.0315)},
{(76.53543,0,68.0315),(79.37007,0,70.15748),(82.20472,0,70.15748),(79.37007,0,68.0315)}
},{
{(0,0,89.29133),(22.67716,0,89.29133),(0,0,80.7874),(5.669294,0,76.53543)},
{(0,0,89.29133),(22.67716,-12.7559,89.29133),(0,0,80.7874),(5.669294,-3.174809,76.53543)},
{(0,0,89.29133),(12.7559,-22.67716,89.29133),(0,0,80.7874),(3.174809,-5.669294,76.53543)},
{(0,0,89.29133),(0,-22.67716,89.29133),(0,0,80.7874),(0,-5.669294,76.53543)}
},{
{(0,0,89.29133),(0,-22.67716,89.29133),(0,0,80.7874),(0,-5.669294,76.53543)},
{(0,0,89.29133),(-12.7559,-22.67716,89.29133),(0,0,80.7874),(-3.174809,-5.669294,76.53543)},
{(0,0,89.29133),(-22.67716,-12.7559,89.29133),(0,0,80.7874),(-5.669294,-3.174809,76.53543)},
{(0,0,89.29133),(-22.67716,0,89.29133),(0,0,80.7874),(-5.669294,0,76.53543)}
},{
{(0,0,89.29133),(-22.67716,0,89.29133),(0,0,80.7874),(-5.669294,0,76.53543)},
{(0,0,89.29133),(-22.67716,12.7559,89.29133),(0,0,80.7874),(-5.669294,3.174809,76.53543)},
{(0,0,89.29133),(-12.7559,22.67716,89.29133),(0,0,80.7874),(-3.174809,5.669294,76.53543)},
{(0,0,89.29133),(0,22.67716,89.29133),(0,0,80.7874),(0,5.669294,76.53543)}
},{
{(0,0,89.29133),(0,22.67716,89.29133),(0,0,80.7874),(0,5.669294,76.53543)},
{(0,0,89.29133),(12.7559,22.67716,89.29133),(0,0,80.7874),(3.174809,5.669294,76.53543)},
{(0,0,89.29133),(22.67716,12.7559,89.29133),(0,0,80.7874),(5.669294,3.174809,76.53543)},
{(0,0,89.29133),(22.67716,0,89.29133),(0,0,80.7874),(5.669294,0,76.53543)}
},{
{(5.669294,0,76.53543),(11.33858,0,72.28346),(36.85039,0,72.28346),(36.85039,0,68.0315)},
{(5.669294,-3.174809,76.53543),(11.33858,-6.349609,72.28346),(36.85039,-20.63622,72.28346),(36.85039,-20.63622,68.0315)},
{(3.174809,-5.669294,76.53543),(6.349609,-11.33858,72.28346),(20.63622,-36.85039,72.28346),(20.63622,-36.85039,68.0315)},
{(0,-5.669294,76.53543),(0,-11.33858,72.28346),(0,-36.85039,72.28346),(0,-36.85039,68.0315)}
},{
{(0,-5.669294,76.53543),(0,-11.33858,72.28346),(0,-36.85039,72.28346),(0,-36.85039,68.0315)},
{(-3.174809,-5.669294,76.53543),(-6.349609,-11.33858,72.28346),(-20.63622,-36.85039,72.28346),(-20.63622,-36.85039,68.0315)},
{(-5.669294,-3.174809,76.53543),(-11.33858,-6.349609,72.28346),(-36.85039,-20.63622,72.28346),(-36.85039,-20.63622,68.0315)},
{(-5.669294,0,76.53543),(-11.33858,0,72.28346),(-36.85039,0,72.28346),(-36.85039,0,68.0315)},
},{
{(-5.669294,0,76.53543),(-11.33858,0,72.28346),(-36.85039,0,72.28346),(-36.85039,0,68.0315)},
{(-5.669294,3.174809,76.53543),(-11.33858,6.349609,72.28346),(-36.85039,20.63622,72.28346),(-36.85039,20.63622,68.0315)},
{(-3.174809,5.669294,76.53543),(-6.349609,11.33858,72.28346),(-20.63622,36.85039,72.28346),(-20.63622,36.85039,68.0315)},
{(0,5.669294,76.53543),(0,11.33858,72.28346),(0,36.85039,72.28346),(0,36.85039,68.0315)}
},{
{(0,5.669294,76.53543),(0,11.33858,72.28346),(0,36.85039,72.28346),(0,36.85039,68.0315)},
{(3.174809,5.669294,76.53543),(6.349609,11.33858,72.28346),(20.63622,36.85039,72.28346),(20.63622,36.85039,68.0315)},
{(5.669294,3.174809,76.53543),(11.33858,6.349609,72.28346),(36.85039,20.63622,72.28346),(36.85039,20.63622,68.0315)},
{(5.669294,0,76.53543),(11.33858,0,72.28346),(36.85039,0,72.28346),(36.85039,0,68.0315)},
},{
{(0,0,0),(40.3937,0,0),(42.51969,0,2.12598),(42.51969,0,4.251961)},
{(0,0,0),(40.3937,22.62047,0),(42.51969,23.81102,2.12598),(42.51969,23.81102,4.251961)},
{(0,0,0),(22.62047,40.3937,0),(23.81102,42.51969,2.12598),(23.81102,42.51969,4.251961)},
{(0,0,0),(0,40.3937,0),(0,42.51969,2.12598),(0,42.51969,4.251961)}
},{
{(0,0,0),(0,40.3937,0),(0,42.51969,2.12598),(0,42.51969,4.251961)},
{(0,0,0),(-22.62047,40.3937,0),(-23.81102,42.51969,2.12598),(-23.81102,42.51969,4.251961)},
{(0,0,0),(-40.3937,22.62047,0),(-42.51969,23.81102,2.12598),(-42.51969,23.81102,4.251961)},
{(0,0,0),(-40.3937,0,0),(-42.51969,0,2.12598),(-42.51969,0,4.251961)}
},{
{(0,0,0),(-40.3937,0,0),(-42.51969,0,2.12598),(-42.51969,0,4.251961)},
{(0,0,0),(-40.3937,-22.62047,0),(-42.51969,-23.81102,2.12598),(-42.51969,-23.81102,4.251961)},
{(0,0,0),(-22.62047,-40.3937,0),(-23.81102,-42.51969,2.12598),(-23.81102,-42.51969,4.251961)},
{(0,0,0),(0,-40.3937,0),(0,-42.51969,2.12598),(0,-42.51969,4.251961)}
},{
{(0,0,0),(0,-40.3937,0),(0,-42.51969,2.12598),(0,-42.51969,4.251961)},
{(0,0,0),(22.62047,-40.3937,0),(23.81102,-42.51969,2.12598),(23.81102,-42.51969,4.251961)},
{(0,0,0),(40.3937,-22.62047,0),(42.51969,-23.81102,2.12598),(42.51969,-23.81102,4.251961)},
{(0,0,0),(40.3937,0,0),(42.51969,0,2.12598),(42.51969,0,4.251961)}
}
};

draw(surface(Q),blue,render(compression=Low));

```

Étiquettes : , , ,

Official Asymptote example – unitoctant

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 15 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
```/* This code comes from The Official Asymptote Gallery */

import graph3;

currentprojection=orthographic(5,4,2);

size(0,150);
patch s=octant1;
draw(surface(s),green+opacity(0.5));
draw(s.external(),blue);

triple[][] P=s.P;

for(int i=0; i < 4; ++i)
dot(P[i],red);

axes3("\$x\$","\$y\$",Label("\$z\$",align=Z));
triple P00=P[0][0];
triple P10=P[1][0];
triple P01=P[0][1];
triple P02=P[0][2];
triple P11=P[1][1];
triple P12=P[1][2];
triple Q11=XYplane(xypart(P11));
triple Q12=XYplane(xypart(P12));

draw(P11--Q11,dashed);
draw(P12--Q12,dashed);
draw(O--Q12--Q11--(Q11.x,0,0));
draw(Q12--(Q12.x,0,0));

label("\$(1,0,0)\$",P00,-2Y);
label("\$(1,a,0)\$",P10,-Z);
label("\$(1,0,a)\$",P01,-2Y);
label("\$(a,0,1)\$",P02,Z+X-Y);
label("\$(1,a,a)\$",P11,3X);
label("\$(a,a^2,1)\$",P12,7X+Y);

```

Étiquettes : ,

Animation with Asymptote – fig0200

Category: Animation,AsymptotePh. Ivaldi @ 3 h 20 min

 (Compiled with Asymptote version 1.86svn-r4626)
This animation is available in the Syracuse web site.
```
/* One may want to play with an interactive Java applet */
settings.render=0;
import three;
import animation;
animation A;

size(15cm);
currentprojection=orthographic(1,1,1.5);
currentlight=(1,0,1);

triple PXY=-X-Y;
triple P00=PXY+0.5*Z, P03=-X+Y, P33=X+Y, P30=X-Y;

triple[][] P0={
{PXY,PXY+(0,0.5,0),P03+(0,-0.5,0),P03},
{PXY+(0.5,0,0),(-0.5,-0.5,0),(-0.5,0.5,0),P03+(0.5,0,0)},
{P30+(-0.5,0,0),(0.5,-0.5,0),(0.5,0.5,0),P33+(-0.5,0,0)},
{P30,P30+(0,0.5,0),P33+(0,-0.5,0),P33}
};

triple[][][] P1={
{
{PXY,PXY+(0,0.5,0),P03+(0,-0.5,0),P03},
{PXY+(0.5,0,0),(-0.5,-0.5,-2),(-0.5,0.5,-2),P03+(0.5,0,0)},
{P30+(-0.5,0,0),(0.5,-0.5,-2),(0.5,0.5,-2),P33+(-0.5,0,0)},
{P30,P30+(0,0.5,0),P33+(0,-0.5,0),P33}
},
{
{P00,P00+(-0.5,0.5,-1),P03+(0,-0.5,1),P03},
{P00+(0.5,-0.5,-1),(-0.5,-0.5,-2),(-0.5,0.5,-2),P03+(0.5,0,1)},
{P30+(-0.5,0,1),(0.5,-0.5,-2),(0.5,0.5,-2),P33+(-0.5,0,1)},
{P30,P30+(0,0.5,1),P33+(0,-0.5,1),P33}
},
{
{P00,P00+(-0.5,0.5,-1),P03+(0,-0.5,1),P03},
{P00+(0.5,-0.5,-1),(-0.5,-0.5,-2),(-0.5,0.5,2),P03+(0.5,0,1)},
{P30+(-0.5,0,1),(0.5,-0.5,-2),(0.5,0.5,-2),P33+(-0.5,0,1)},
{P30,P30+(0,0.5,1),P33+(0,-0.5,1),P33}
},
{
{P00,P00+(-0.5,0.5,-1),P03+(0,-0.5,1),P03},
{P00+(0.5,-0.5,-1),(-0.5,-0.5,-2),(-0.5,-0.5,2),P03+(0.5,0,1)},
{P30+(-0.5,0,1),(0.5,-0.5,-2),(0.5,0.5,-2),P33+(-0.5,0,1)},
{P30,P30+(0,0.5,1),P33+(0,-0.5,1),P33}
}
};

triple[][] interp(triple[][] a, triple[][] b, real x)
{
triple[][] c;
for (int i=0; i < a.length; ++i) {
triple [] t;
for (int j=0; j < a[i].length; ++j) {
t.push(interp(a[i][j],b[i][j],x));
}
c.push(t);
}
return c;
}

int n=20;
real step=1/n;

for (int i=0; i < P1.length; ++i) {
for (int j=0; j <= n; ++j) {
save();
triple[][] P=interp(P0,P1[i],j*step);
surface s=surface(P);
draw(s,15,15,yellow,meshpen=grey);
draw(sequence(new path3(int i){
return s.s[i].external();},s.s.length), bp+red);

dot("P[0][0]",P[0][0], align=N, black);
dot("P[0][3]",P[0][3], black);
dot("P[3][3]",P[3][3], align=S, black);
dot("P[3][0]",P[3][0], align=W, black);

draw(Label("P[0][1]",align=SW,EndPoint),P[0][0]--P[0][1], Arrow3);
draw(Label("P[1][0]",align=SE,EndPoint),P[0][0]--P[1][0], Arrow3);

draw(Label("P[0][2]",align=E,EndPoint),P[0][3]--P[0][2], Arrow3);
draw(Label("P[1][3]",align=W,EndPoint),P[0][3]--P[1][3], Arrow3);

draw(Label("P[2][3]",align=NE,EndPoint),P[3][3]--P[2][3], Arrow3);
draw(Label("P[3][2]",align=NW,EndPoint),P[3][3]--P[3][2], Arrow3);

draw(Label("P[3][1]",align=NE,EndPoint),P[3][0]--P[3][1], Arrow3);
draw(Label("P[2][0]", align=W,EndPoint),P[3][0]--P[2][0], Arrow3);

dot("P[1][1]",P[1][1], align=N);
dot("P[1][2]",P[1][2], align=E);
dot("P[2][2]",P[2][2], align=N);
dot("P[2][1]",P[2][1], align=W);