I have been working on a procedural spherical terrain generator for a few months which has a quadtree LOD system. The system splits the six faces of a quadrilateralized spherical cube into smaller "quads" or "patches" as the player approaches those faces. What I can't figure out is how to generate height maps for these patches. To generate the heights I am using a 3D ridged multi fractals algorithm. For now I can only displace the vertices of the patches directly using the output from the ridged multi fractals. I don't understand how I generate height maps that allow the vertices of a terrain patch to be mapped to pixels in the height map. The only thing I can think of is taking each vertex in a patch, plug that into the RMF and take that position and translate into u,v coordinates then determine the pixel position directly from the u,v coordinates and determine the grayscale color based on the height. I feel as if this is the right approach but there are a few other things that may further complicate my problem. First of all I intend to use "height maps" with a pixel resolution of 192x192 while the vertex "resolution" of each terrain patch is only 16x16 - meaning that I don't have any vertices to sample for the RMF for most of the pixels. The main reason the height map resolution is higher so that I can use it to generate a normal map (otherwise the height maps serve little purpose as I can just directly displace vertices as I currently am).

I am pretty much following this paper very closely. This is, essentially, the part I am having trouble with.

Using the cube-to-sphere mapping and the ridged multifractal algorithm previously described, a normalized height value ([0, 1]) is calculated. Using this height value, the terrain position is calculated and stored in the first three channels of the positionmap (RGB) – this will be used to calculate the normalmap. The fourth channel (A) is used to store the height value itself, to be used in the heightmap.

The steps in the first sentence are my primary problem. I don't understand how the pixel positions correspond to positions on the sphere and what positions are sampled for the RMF to generate the pixels if only vertices cannot be used.