How approximately do you need it?
A really crude way would be to just generate a bunch of random points inside box A, then compute the fraction of those points that also lie inside B.
real sphere2sphere(sphere c1, sphere c2) {
vec delta = c2.pos - c1.pos;
real cr = c1.rad + c2.rad;
real ds = dot(delta,delta);
if(ds > cr*cr) return 0; //not intersecting
elif(ds < eps) return min(volume(c1.rad),volume(c2.rad)); //special case equal position (stability)
else {
real d = sqrt(ds);
real x1 = 0.5*(d - (c2.rad*c2.rad - c1.rad*c1.rad)/d);
real x2 = d - x1;
if (x1<=-c1.rad) return volume(c1.rad); //total containment
elif(x2<=-c2.rad) return volume(c2.rad); //total containment
else return cap_volume(x1,c1.rad) + cap_volume(x2,c2.rad);
}
}
real cap_volume(real x, real r) {
real h = r-x;
return pi*h*h*(3*r-h)/3;
}
real volume(real r) return cap_volume(-r,r);
[quote name='quasar3d' timestamp='1321892893' post='4886249']
How approximately do you need it?
A really crude way would be to just generate a bunch of random points inside box A, then compute the fraction of those points that also lie inside B.
