Starver; If I remember right, Spore solved this problem by storing all the surfaces of the planets on cubes, and sort of inflating them into spheres. Not a perfect solution as you get different kinds of distortion, but it's not as obvious.
Well, that makes me happier about the icosahedral idea, seeing as it's going to be less noticably distorted about the vertex[1] than a cube.
The 'only' complication being that there's a lot more trigonometry involved to make it accurate (and the "golden ratio" factor of (1+root(5))/2 being just the start of a long line of non-integer mathematics involved), and upon deciding the conventions when it comes to triangle and sub-triangle orientation and thus how a target lat/lon (range) converts to the arbitrary level of subtriangles.
I did originally consider a cylindrical approach (two circular projections based around the poles meeting a one-way-wrapping equatorial projection), each of which I could ensure contained no distortion artefacts, relative to the form of local geometry they use, but I didn't like idea of having to fudge the interface between so that it wasn't overly obvious. Making it triangle-against-triangle at all levels means it doesn't suffer from that problem.
Anyway, I'm digressing from the reason behind this thread. Heavily. Apologies.
[1] If I wasn't further subdividing the triangles, anyway, to eventually make it beyond geodesic with subtly non-equilateral triangles[2], it would be 300 degrees around the icosahedral vertex, as opposed to 270 around the cube.
[2] Which, in the end, just lets me defines a planar mesh that at a local level is semi-Euclidean without so much complication regarding polar singularities and mapping to/from the extreme upper and lower edges of a planar map. I can far easier handle triangles (and its four sub-triangles, defined by the lines linking the midpoints of its sides).
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Topic: How realistic worldgen really is (Read 42331 times)