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Generating texture coordinates along a sphere?

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I''m using tessellation to dynamically create an approximation of a sphere. All is well, except I can''t figure out how to generate texture coordinates that will map a 2D texture onto the sphere. Given an (x, y, z) point, I want to be able to find out the (s, t) coordinates that should be used for that point. Any suggestions?

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What I have so far is sort of a spherical coordinate conversion. It doesn''t look too far off, but it has problems with artifacts appearing near x=0.

What I''m doing right now goes something like this:

Given an x, y, and z
r = sqrt(x² + y² + z²)
s = atan(y / x)
t = acos(z / r)
textureCoordinate = (s / pi, t / pi)

If it weren''t for the artifacts that appear close to the YZ plane, this would be great.

Anyone have any suggestions? Anyone see where I''m going wrong?

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