superquad-toroids-1.irmf

/*{
  "author": "Glenn M. Lewis",
  "copyright": "Apache-2.0",
  "date": "2020-03-17",
  "irmf": "1.0",
  "materials": ["PLA"],
  "max": [5,5,5],
  "min": [-5,-5,-5],
  "notes": "Figure 10 from: https://authors.library.caltech.edu/9756.",
  "options": {},
  "title": "Superquadric toroids",
  "units": "mm",
  "version": "1.0"
}*/

float superquad(in float e1, in float e2, in float a4, in vec3 xyz) {
  xyz.xyz *= 2.5;
  float angle = -1.3;
  float c = cos(angle);
  float s = sin(angle);
  xyz.yz = mat2(c, - s, s, c) * xyz.yz;
  xyz = abs(xyz); // Due to GLSL 'pow' definition.
  float f = pow(pow(pow(xyz.x, 2.0 / e2) + pow(xyz.y, 2.0 / e2), e2 / 2.0) - a4, 2.0 / e1) + pow(xyz.z, 2.0 / e1);
  return f <= 1.0 ? 1.0 : 0.0;
}

void mainModel4(out vec4 materials, in vec3 xyz) {
  float u = 1.2;
  float v = 3.4;
  float a4 = 1.25;
  materials[0] =
  superquad(0.3, 0.3, a4, xyz - vec3(-v, 0, v))
  + superquad(0.3, 0.1, a4, xyz - vec3(-u, 0, v))
  + superquad(0.3, 1.0, a4, xyz - vec3(u, 0, v))
  + superquad(0.3, 3.0, a4, xyz - vec3(v, 0, v))
  + superquad(0.1, 0.3, a4, xyz - vec3(-v, 0, u))
  + superquad(0.1, 0.1, a4, xyz - vec3(-u, 0, u))
  + superquad(0.1, 1.0, a4, xyz - vec3(u, 0, u))
  + superquad(0.1, 3.0, a4, xyz - vec3(v, 0, u))
  + superquad(1.0, 0.3, a4, xyz - vec3(-v, 0, - u))
  + superquad(1.0, 0.1, a4, xyz - vec3(-u, 0, - u))
  + superquad(1.0, 1.0, a4, xyz - vec3(u, 0, - u))
  + superquad(1.0, 3.0, a4, xyz - vec3(v, 0, - u))
  + superquad(3.0, 0.3, a4, xyz - vec3(-v, 0, - v))
  + superquad(3.0, 0.1, a4, xyz - vec3(-u, 0, - v))
  + superquad(3.0, 1.0, a4, xyz - vec3(u, 0, - v))
  + superquad(3.0, 3.0, a4, xyz - vec3(v, 0, - v));
}