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?