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Possible Duplicate:
Generate a random direction within a cone

A point on a unit sphere $(x,y,z)$ and an maximal angular separation $\theta$ defines a patch with an area of $\Omega = 2 \pi (1-\cos \theta)$ steradians. How can I uniformly sample over that patch?

Currently I'm generating points on the sphere and rejecting all those not within the allowed region. Can I do this without rejection?

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    @joriki and others - I'm voting to close my own question as the new and updated answers on the other question are more than enough. Thank you all!2012-10-02

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