Faster Sphere Indexing

SphereIndexing.hlsl

float3 PositionToOctahedron(float3 position)
{
	// Normalize input position to unit sphere to simplify required ops
	float3 P = normalize(position);

	// Get octant index
	float3 side = P >= 0 ? 1 : 0;
	float octant_index = side.x + side.y * 2 + side.z * 4;

	// Project onto octahedron face, then onto each x/y plane
	float2 uv = abs(P.xy) * (1 / dot(1, abs(P)));

	return float3(uv, octant_index);
}


uint GetTriangleIndex(float3 uv_face, const uint3 constants)
{
	// Scale with subdivision count
	float2 uv = uv_face.xy * constants.x;

	// Split into integer/fractionals
	uint2 uv_i = uint2(uv);
	float2 uv_f = uv - uv_i;
	
	// Triangle pairs are grouped so double and offset using diagonal sidedness
	uv_i.x *= 2;
	uv_i.x = (uv_f.x + uv_f.y > 1) ? uv_i.x + 1 : uv_i.x;

	// Map to linear index on a grid
	uint face_index = (uint)uv_face.z;
	return face_index * constants.z + uv_i.y * constants.y + uv_i.x;
}