Texturing a sphere in a Cg shader

Question

So I need to map a texture to a sphere from within a pixel/fragment shader in Cg.

What I have as "input" in every pass are the Cartesian coordinates x, y, z for the point on the sphere where I want the texture to be sampled. I then transform those coordinates into Spherical coordinates and use the angles Phi and Theta as U and V coordinates, respectively, like this:

u = atan2(y, z)
v = acos(x/sqrt(x*x + y*y + z*z))

I know that this simple mapping will produce seams at the poles of the sphere but at the moment, my problem is that the texture repeats several times across the sphere. What I want and need is that the whole texture gets wrapped around the sphere exactly once.

I've fiddled with the shader and searched around for hours but I can't find a solution. I think I need to apply some sort of scaling somewhere but where? Or maybe I'm totally on the wrong track, I'm very new to Cg and shader programming in general... Thanks for any help!

Answer 1

Since the results of inverse trigonometric functions are angles, they will be in [-Pi, Pi] for u and [0, Pi] for v (though you can't have searched for hours with at least basic knowledge of trigonometrics, as acquired from school). So you just have to scale them appropriately. u /= 2*Pi and v /= Pi should do, assuming you have GL_REPEAT (or the D3D equivalent) as texture coordinate wrapping mode (which your description sounds like).