//
// "Generalized Distance Functions" by Akleman and Chen.
// see the Paper at https://www.viz.tamu.edu/faculty/ergun/research/implicitmodeling/papers/sm99.pdf
//
// This set of constants is used to construct a large variety of geometric primitives.
// Indices are shifted by 1 compared to the paper because we start counting at Zero.
// Some of those are slow whenever a driver decides to not unroll the loop,
// which seems to happen for fIcosahedron und fTruncatedIcosahedron on nvidia 350.12 at least.
// Specialized implementations can well be faster in all cases.
//

const vec3 GDFVectors[19] = vec3[](
	normalize(vec3(1, 0, 0)),
	normalize(vec3(0, 1, 0)),
	normalize(vec3(0, 0, 1)),

	normalize(vec3(1, 1, 1 )),
	normalize(vec3(-1, 1, 1)),
	normalize(vec3(1, -1, 1)),
	normalize(vec3(1, 1, -1)),

	normalize(vec3(0, 1, PHI+1)),
	normalize(vec3(0, -1, PHI+1)),
	normalize(vec3(PHI+1, 0, 1)),
	normalize(vec3(-PHI-1, 0, 1)),
	normalize(vec3(1, PHI+1, 0)),
	normalize(vec3(-1, PHI+1, 0)),

	normalize(vec3(0, PHI, 1)),
	normalize(vec3(0, -PHI, 1)),
	normalize(vec3(1, 0, PHI)),
	normalize(vec3(-1, 0, PHI)),
	normalize(vec3(PHI, 1, 0)),
	normalize(vec3(-PHI, 1, 0))
);

// Version with variable exponent.
// This is slow and does not produce correct distances, but allows for bulging of objects.
float fGDF(vec3 p, float r, float e, int begin, int end) {
	float d = 0;
	for (int i = begin; i <= end; ++i)
		d += pow(abs(dot(p, GDFVectors[i])), e);
	return pow(d, 1/e) - r;
}

// Version with without exponent, creates objects with sharp edges and flat faces
float fGDF(vec3 p, float r, int begin, int end) {
	float d = 0;
	for (int i = begin; i <= end; ++i)
		d = max(d, abs(dot(p, GDFVectors[i])));
	return d - r;
}

// Primitives follow:

float fOctahedron(vec3 p, float r, float e) {
	return fGDF(p, r, e, 3, 6);
}

float fDodecahedron(vec3 p, float r, float e) {
	return fGDF(p, r, e, 13, 18);
}

float fIcosahedron(vec3 p, float r, float e) {
	return fGDF(p, r, e, 3, 12);
}

float fTruncatedOctahedron(vec3 p, float r, float e) {
	return fGDF(p, r, e, 0, 6);
}

float fTruncatedIcosahedron(vec3 p, float r, float e) {
	return fGDF(p, r, e, 3, 18);
}

float fOctahedron(vec3 p, float r) {
	return fGDF(p, r, 3, 6);
}

float fDodecahedron(vec3 p, float r) {
	return fGDF(p, r, 13, 18);
}

float fIcosahedron(vec3 p, float r) {
	return fGDF(p, r, 3, 12);
}

float fTruncatedOctahedron(vec3 p, float r) {
	return fGDF(p, r, 0, 6);
}

float fTruncatedIcosahedron(vec3 p, float r) {
	return fGDF(p, r, 3, 18);
}