uniform sampling of sphere/simplex intersection

[aupetit]

Hello,

I look for a method to sample uniformly (in order to perform
an integration) the intersection region
between a k-ball and a k-simplex in the k euclidean space.

I already know a method to sample uniformly
a k-simplex or a k-ball, and I could use
the accept-reject approach to sample in their
intersection, but I need a more efficient way to do that
especially when the intersection volume is small.

Do you have some hints?
Do you know some paper adressing this problem?

Thank you

Michaël
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