I have a pointed polyhedral cone $C$ in $\mathbb{R}^{N+1}$, with the vertex at the origin. Cone $C$ is known to be the intersection of $2 (^{N+1}_{\; \;2})$ closed half-spaces.
Furthermore, there is a set $S$ (bounded away from the origin. I need to estimate what "fraction" of the generating rays of $C$ meets $S$, in the sense of a suitable $N$-dimensional volume defined on the unit sphere in $\mathbb{R}^{N+1}$.
I suspect, one way to do this is by clever sampling on the sphere (actually, can't think of any others at the moment). The challenge is that the sampling should be confined to the intersection of the sphere and $C$. Are there known methods? Many thanks.
