i haven't ventured further into 3d than the calculation of 3d points in the frustrum for wireframe graphics, so i'm not sure what i'm missing to answer this on my own.

accordingly, i understand the concept of projection (apart from cartographic references, projection is the introductory topic for this 2 hour movie on visualisation of higher dimensions.. modeled in pov-ray, where i have experienced the application of height fields to spheres

i've been mulling over exactly how one would apply a height field to a sphere, and i think i must have the basic idea wrong.

being aware that points towards the upper and lower edges of a 2d height field are applied to increasingly smaller diameters, what i am visualising is the generation of standard 2d noise image, then translating this to the spherical height field by using an increasingly smaller width of pixels towards the upper and lower edges, using a sinusoidal 'lemon' shaped region of the source height field.

to reword for clarity, the output 'product' height field is sourced from a region of a temporary 'source' height field that is shaped like a lemon, with the points tangent to the top and bottom. amplitude is scaled/reduced for samples towards the top and bottom.

well.. the obvious issue with this method is that if you are using a method of interpolation using more than the immediate samples (eg. the preferred bicubic interpolation for perlin noise) you are up a very complex creek (eg. as one would have to wrap points of interpolation, requiring having to perform stages of intermediary interpolation..)

i feel certain that the predominant method must be more sensible than what i am envisioning, which seems to be lemon shaped.