The union of convex polyhedra in three dimensions

Boris Aronov; Micha Sharir; Boaz Tagansky

doi:10.1137/S0097539793250755

The union of convex polyhedra in three dimensions

Boris Aronov^*
, Micha Sharir
, Boaz Tagansky

^*Corresponding author for this work

School of Computer Science and AI

Dept. of Comp. and Info. Science
New York University
New York University
School of Mathematical Sciences
Tel Aviv University

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k³ + kn log k). This bound is almost tight in the worst case, as there exist collections of polyhedra with Ω(k³ + knα(k)) union complexity. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k³ + kn log k log n) expected time.

Original language	English
Pages (from-to)	1670-1688
Number of pages	19
Journal	SIAM Journal on Computing
Volume	26
Issue number	6
DOIs	https://doi.org/10.1137/S0097539793250755
State	Published - Dec 1997

Keywords

Combinatorial complexity
Combinatorial geometry
Computational geometry
Convex polyhedra
Geometric algorithms
Randomized algorithms

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10.1137/S0097539793250755

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The union of convex polyhedra in three dimensions

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Keywords

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