Texture pinching

[granthutchison]

Short for "geodetic sphere" - it models a sphere as a network of triangles, with a max of six (and min of five) meeting at any vertex, like the domes by Buckminster Fuller. This contrasts with the other usual method of modelling a sphere, which builds in parallels of latitude and meridians of longitude - you end up with many more triangles converging on the poles.
I'd guess that an isosphere is a reference to an icosahedron - twenty equilateral triangles, five to each vertex, and effectively the simplest possible geodetic sphere.

Grant

[chris]

I think that geosphere means sphere geometry generated by icosohedral subdivision; such geometry has the nice quality of not producing degenerate triangles around the poles. However, Celestia instead uses spheres composed of sections aligned with lines of latitude and longitude. The reason for this is that icoshedral subdivision spheres won't work with planet texture maps that are split into multiple subtextures, so you'd give up high resolution texture support by using them.

--Chris

[granthutchison]

I think that geosphere means sphere geometry generated by icosohedral subdivision...

Yes ... that has the end result I describe above. You interpolate rows of triangles between the original pentagonal arrays surrounding each vertex of the icosahedron. There's a theorem by Euler which shows that you can subdivide indefinitely, with every vertex surrounded by six triangles, except that there must always be 12 vertices with the pentagonal symmetry of the original icosahedron. If you sit down with a soccer ball and some numbered adhesive labels, you'll find that there are exactly 12 pentagons separated in all directions by bands of hexagons. Divide the pentagons and hexagons into their component triangles, and you have an early generation of geosphere.

Grant