need help tessellating a sphere

[imported_Tomato]

Posted on behalf of a friend:

"I am starting with an equilateral octahedron.

Then I break each triangle into 4 new triangles (picture a triaforce).

Then I normalize every point.

Then I repeat until I reach my desired resolution.

However I have the following problem:
1. the triangles aren't uniform. The triangles near where the original triangles touched are smaller than others.

help!?"

 

[Matthias99]

I'm not sure that it matters if the triangles are uniform in size. To do that, you'll need to approximate it with geometric figures rather than tesselating it, I think (unless you're VERY careful about how you do it).

This sounds like CS homework, and this approach sounds like a lot of work. Try calculating (x,y,z) surface points by taking the inverse cos and sin of the angles from -pi to +pi around the X, Y, and Z axes. Less work, more straightforward. However, I don't believe these will be uniform triangles, either, unless you space the ones near the 'poles' of the sphere proportionally further apart.

 

[imported_Tomato]

Originally posted by: Matthias99
I'm not sure that it matters if the triangles are uniform in size. To do that, you'll need to approximate it with geometric figures rather than tesselating it, I think (unless you're VERY careful about how you do it).

This sounds like CS homework, and this approach sounds like a lot of work. Try calculating (x,y,z) surface points by taking the inverse cos and sin of the angles from -pi to +pi around the X, Y, and Z axes. Less work, more straightforward. However, I don't believe these will be uniform triangles, either, unless you space the ones near the 'poles' of the sphere proportionally further apart.

Thanks so much for the suggestion, Matthias... I'll pass it along and hopefully it will save my friend a lot of time. I really appreciate it.