On the Complexity of Halfspace Volume Queries

Given a polyhedron P in Rd 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.

• Type: Conference
• Year: 2003
• Where: CCCG
• Authors: Erik D. Demaine, Jeff Erickson, Stefan Langerman
• Keywords: CCCG 2003, CCCG 2007, Halfspace H, Halfspace Volume Query, Polyhedron