triaxial hexatorus

more playing with geometry...

wrt method described here

 

// uv given on [0..1), remap to [-pi,pi) to simplify equations below

u = u * 2.0*Math.PI - Math.PI;

v = v * 2.0*Math.PI - Math.PI;

// evaluate

double sqrtTwo = Math.sqrt(2.0);

double twoThirdsPi = Math.PI * 2.0 / 3.0;

double x = Math.sin(u) / (sqrtTwo + Math.cos(v));

double y = Math.sin(u+twoThirdsPi) / (sqrtTwo + Math.cos(v+twoThirdsPi));

double z = Math.cos(u-twoThirdsPi) / (sqrtTwo + Math.cos(v-twoThirdsPi));

return new WB_Point(x,y,z);

 

Done