On the complexity of halfspace volume queries

CCCG 2003info:eu-repo/semantics/publishe

On the Complexity of Halfspace Volume Queries

Given a polyhedron P in R d with n vertices, a halfspace volume query asks for the volume of P ∩ H for a given halfspace H. We show that, for d ≥ 3, such queries can require Ω(n) operations even if the polyhedron P is convex and can be preprocessed arbitrarily