Algorithm for computing volume of union or intersection of n-dimensional convex polytopes given their facets? I've googled this problem somewhat pretty extensively, and all the relevant literature understandably deals with 2-d or 3-d cases, rather than the n-d case.

EDIT: Yes, ℝn. I've done many searches combining terms like union, intersection, volume, convex hulls, polytope, etc. I've come across papers like this and this. My math and CS background is weak, but I can tell from the latter paper that this is a difficult problem that I am after.

I appreciate both answers given, unless I misunderstand (probable), I'm not sure that they answer my question? The first answer is just about finding the volume of a polytope given its facets or vertices. I'm aware of algorithms to do so. The second answer may be more on track, but it still raises the question of how to determine IF two polytopes intersect, and where?

Thanks, everyone, for your help so far.
A standard approach is to decompose it into a bunch of triangles (well, the n-dimensional generalization of triangles), then compute the volume of each triangle and sum them up.  Have a look at https://mathoverflow.net/q/979 or https://scicomp.stackexchange.com/q/2881.  Be warned that this could take exponential time.

There are also algorithms for approximating the volume of such a polytope, if that is useful to you.