While optimizing a ray tracer I was trying to improve data locality for the intersection datastructure using a Morton space filling curve, except that my 3D space is not cubic (eg. 512x512x256). All sides are a power of two, but not all sides are the same length.

I have been unable to find any examples for non square Morton curves where the sides are a power of two. If it matters I can guarantee that the x/y axis are the same size with only the z axis being a different length.

Note how the width is 2x height, but it could also be 3x or 4x or any other. I have been unable to find a way how to do this.

Ideally the solution would be fast as the Morton code has to be calculated a lot. So my question is: How do I generate a space filling morton curve for non-cubic spaces? This is specifically for the GPU (Cuda).

The conditions on the dimensions are:
x, y, z are a power of two
x == y
x, y >= z
Or if easier
x, y > z