Compile with Asymptote.
Note that the problem of opacity is still not implemented in Asymptote at present.
Compile at http://asymptote.ualberta.ca/
Specially, if you have a powerful computer, you will learn 3D Asymptote easily, otherwise you will get a common error in Asymptote is out of memory, :-). Sob!
// settings.render=10;
size(8cm);
import three;
currentprojection=orthographic((1,0.5,0.35));
currentlight=nolight;
// See three.asy
// Line 2012: restricted path3 unitsquare3=O--X--X+Y--Y--cycle;
path3 p1=unitsquare3;
path3 p2=shift(1/3*(X+Y))*scale3(1/3)*p1;
// transform3 t=scale(1.25,1,1);
surface s=surface(reverse(p1)^^p2,planar=true);
surface[] S={s,rotate(90,O,X)*s,rotate(-90,O,Y)*s
,shift(Z)*s,rotate(90,X,X+Y)*s,rotate(-90,Y,X+Y)*s};
path3[] p3=p1^^p2;
path3[][] P={p3,rotate(90,O,X)*p3,rotate(-90,O,Y)*p3
,shift(Z)*p3,rotate(90,X,X+Y)*p3,rotate(-90,Y,X+Y)*p3};
draw(S,white);
for (int i=0; i<P.length; ++i){
draw(P[i][0],0.8bp+red);
draw(P[i][1],0.8bp+blue);
}
surface s0=scale3(1/3)*unitcube;
transform3[] T={identity4,shift(1/3*X),shift(2/3*X)
,shift(1/3*Y),shift(2/3*Y),shift(1/3*X+2/3*Y)
,shift(2/3*X+1/3*Y),shift(2/3*(X+Y))};
for (transform3 i : T) draw(i*s0,white);
for (transform3 i : T) draw(shift(2/3*Z)*i*s0,white);
transform3 tt(real r)
{
return rotate(r,1/2*(X+Y),1/2*(X+Y)+(0,0,1));
}
for (int i : new int[]{0,90,180,270})
{
draw(tt(i)*shift(1/3*Z)*s0,white);
}
draw(shift(1/3*(X+Y))*scale(1/3,1/3,1)*unitcube,invisible,0.8bp+blue);
draw(shift(1/3*(Z+Y))*scale(1,1/3,1/3)*unitcube,invisible,0.8bp+blue);
draw(shift(1/3*(X+Z))*scale(1/3,1,1/3)*unitcube,invisible,0.8bp+blue);
Animation:
import three;
import graph3;
currentprojection=orthographic((1,0.5,0.35));
currentlight=nolight;
size(8cm,0);
string[] files;
int numberofframes=72;
for (int i=0; i <= numberofframes; ++i)
{
files[i]="T"+(string) i;
picture pic;
// See three.asy
// Line 2012: restricted path3 unitsquare3=O--X--X+Y--Y--cycle;
path3 p1=unitsquare3;
path3 p2=shift(1/3*(X+Y))*scale3(1/3)*p1;
transform3 t=rotate(i*5,Z);
surface s=surface(reverse(p1)^^p2,planar=true);
surface[] S={s,rotate(90,O,X)*s,rotate(-90,O,Y)*s
,shift(Z)*s,rotate(90,X,X+Y)*s,rotate(-90,Y,X+Y)*s};
path3[] p3=p1^^p2;
path3[][] P={p3,rotate(90,O,X)*p3,rotate(-90,O,Y)*p3
,shift(Z)*p3,rotate(90,X,X+Y)*p3,rotate(-90,Y,X+Y)*p3};
draw(pic,t*S,white);
for (int i=0; i<P.length; ++i){
draw(pic,t*P[i][0],0.8bp+red);
draw(pic,t*P[i][1],0.8bp+blue);
}
surface s0=scale3(1/3)*unitcube;
transform3[] T={identity4,shift(1/3*X),shift(2/3*X)
,shift(1/3*Y),shift(2/3*Y),shift(1/3*X+2/3*Y)
,shift(2/3*X+1/3*Y),shift(2/3*(X+Y))};
for (transform3 i : T) draw(pic,t*i*s0,white);
for (transform3 i : T) draw(pic,t*shift(2/3*Z)*i*s0,white);
transform3 tt(real r)
{
return rotate(r,1/2*(X+Y),1/2*(X+Y)+(0,0,1));
}
for (int i : new int[]{0,90,180,270})
{
draw(pic,t*tt(i)*shift(1/3*Z)*s0,white);
}
draw(pic,t*shift(1/3*(X+Y))*scale(1/3,1/3,1)*unitcube,invisible,0.8bp+blue);
draw(pic,t*shift(1/3*(Z+Y))*scale(1,1/3,1/3)*unitcube,invisible,0.8bp+blue);
draw(pic,t*shift(1/3*(X+Z))*scale(1/3,1,1/3)*unitcube,invisible,0.8bp+blue);
xaxis3(pic,"$x$",-.5,2,Arrow3);
yaxis3(pic,"$y$",-2,2,Arrow3);
zaxis3(pic,"$z$",-.5,2,Arrow3);
add(pic);
shipout(files[i],bbox(invisible));
erase();
}
\mengerspongecommand you'll find there.