General algorithm to cap an n-dimensional convex polyhedra

Question

I am looking for a way to cap an $n$-dimensional ($n$ > 3) polyhedra, that is to say:

Given an $n$ dimensional set of vertices and faces (including hyperplane equation), and an $n$ dimensional plane, output the set of points that are both inside the original polyhedron and "below" the plane.

I looked around and saw two interesting papers, both only handling 3-dimensional input. (one thesis, and one SIGGRAPH paper).

In my case, I suppose I could use the generic approach of using double description, i.e. enumerating the vertices of the polyhedron described by my original set of hyperplanes and the new plane equation, but it seems to me that I would do the work twice.

Is there another documented approach that I could use ?

Answer 1

Perhaps start here and work backward and forward in time using Google scholar:

Günther, Oliver, and Eugene Wong. "A dual approach to detect polyhedral intersections in arbitrary dimensions." BIT Numerical Mathematics 31.1 (1991): 2-14. PDF download.

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