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An optimal algorithm for intersecting three-dimensional convex polyhedra

Bernard Chazelle

Open publisher page 32 citations

Abstract

A linear algorithm for intersecting two convex polyhedra in 3-space is described. The algorithm is quite simple; it does not require any complicated data structure and should be practical. A number of optimal algorithms for other problems are obtained directly from this result. These include intersecting several polytopes at once or computing the convex hull of their union, merging Voronoi diagrams in the plane in linear time, and computing three-dimensional convex hulls in linear expected time.>

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What this paper is about

A linear algorithm for intersecting two convex polyhedra in 3-space is described. The algorithm is quite simple; it does not require any complicated data structure and should be practical. A number of optimal algorithms for other problems are obtained directly from this result. These include intersecting several polytopes at once or computing the convex hull of their union, merging Voronoi diagrams in the plane in linear time, and computing three-dimensional convex hulls in linear expected time.>

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OpenAlex reports 32 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A linear algorithm for intersecting two convex polyhedra in 3-space is described. The algorithm is quite simple; it does not require any complicated data structure and should be practical. A number of optimal algorithms for other problems are obtained directly from this result. These include intersecting several polytopes at once or computing the convex hull of their union, merging Voronoi diagrams in the plane in linear time, and computing three-dimensional convex hulls in linear expected time.>

Key concepts: Polyhedron, Convex hull, Convex polytope, Polytope, Voronoi diagram, Regular polygon, Output-sensitive algorithm, Combinatorics

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