How to create an even sphere with triangles in OpenGL?

Question

Is there a formula that generates a set of coordinates of triangles whose vertices are located on a sphere?

I am probably looking for something that does something similar to gluSphere. Yet, I need to color the different triangles in specfic colors so that it seems I can't use gluSphere.

Also: I do understand that gluSphere draws edges along lines with equal longitudes and lattitudes which entails the triangles being small at the poles compared to their size at the equator. Now, if such a formula would generate the triangles such that their difference in size is minimized, that would be great.

Answer 1

To calculate the normals and the uv map.

Fortunately there is an amazing trick for calculating the normals, on a sphere. If you think about it, the normals on a sphere are indeed nothing more than the direction from the centre of the sphere, to that point!! Furthermore, if you think it through, that means the normals literally equal the point! i.e., it's the same vector! - just don't forget to normalise the length, for the normal.

You can win bar bets on that one: "is there a shape where all the normals happen to be exactly ... equal to the vertices?" At first glance you'd think, that's impossible, no such coincidental shape could exist. But of course the answer is simply "a sphere with radius one!" Heh!

Regarding the UVs. It is relatively easy on a sphere, assuming you're projecting to 2D in the "obvious" manner, a "rectangle-style" map projection. In that case the u and v is basically just the longitude / latitude of any point, normalised to 0,1.

Hope it helps!

Here's the all-time-classic web page that beautifully explains how to build an icosphere .. http://blog.andreaskahler.com/2009/06/creating-icosphere-mesh-in-code.html

Answer 2

Start with a unit icosahedron. Then apply muliple homogenous subdivisions of the triangles, normalizing the resulting vertices distance to the origin.