Paper by Erik D. Demaine

Erik D. Demaine, Jeff Erickson, and Stefan Langerman, “On the Complexity of Halfspace Volume Queries”, in Proceedings of the 15th Canadian Conference on Computational Geometry (CCCG 2003), Halifax, Nova Scotia, Canada, August 11–13, 2003, pages 159–160.

Given a polyhedron P in Rd with n vertices, a halfspace volume query asks for the volume of P intersect 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.

The paper is 2 pages.

The paper is available in PostScript (96k), gzipped PostScript (40k), and PDF (80k).
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Last updated May 16, 2024 by Erik Demaine.