P-152: Virtual World Concept Update 12: Quadrilateralized spherical cubes

The approach I need to take to creating spherical terrain involves the creation of a “Quadrilateralized spherical cubes”. Essentially, a cube which is projected to a sphere.

I have been trying to create a sphere using the wrong equations. I have been getting very close to the solution, as can be seen in the first image, but this approach will not solve the problem. I can only have one value along the z-axis with the type of terrain I am using, and so creating a sphere or part of a sphere with conventional sphere equatiosn will produce distortions or invalid vertex point information whenever the sphere section curves back on itself.

I will need to use different equations to produce the Quad cube, however, this wil require being able to modify the X and Y axes of the terrain file in addition to the Z axis (height). The second two images show the results of modifying the Z-axis height only. This is very close to being correct, but I can never assemble these sections into a sphere without also modifying the other axes. T3D’s Terrain does not allow this, and so I have quite a lot of work to do to modify the terrain code.

UPDATE:
I found THIS website, which contains the equations necessary to create the quad cube. This is a vital resource.