# Algebraic decomposition of non-convex polyhedra

Edelsbrunner H. 1995. Algebraic decomposition of non-convex polyhedra. FOCS: Foundations of Computer Science, 248–257.

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Abstract

Any arbitrary polyhedron P contained as a subset within Rd can be written as algebraic sum of simple terms, each an integer multiple of the intersection of d or fewer half-spaces defined by facets of P. P can be non-convex and can have holes of any kind. Among the consequences of this result are a short boolean formula for P, a fast parallel algorithm for point classification, and a new proof of the Gram-Sommerville angle relation.

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Date Published

1995-10-01

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248 - 257

Conference

FOCS: Foundations of Computer Science

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### Cite this

Edelsbrunner H. Algebraic decomposition of non-convex polyhedra. In: IEEE; 1995:248-257.

Edelsbrunner, H. (1995). Algebraic decomposition of non-convex polyhedra (pp. 248–257). Presented at the FOCS: Foundations of Computer Science, IEEE.

Edelsbrunner, Herbert. “Algebraic Decomposition of Non-Convex Polyhedra,” 248–57. IEEE, 1995.

H. Edelsbrunner, “Algebraic decomposition of non-convex polyhedra,” presented at the FOCS: Foundations of Computer Science, 1995, pp. 248–257.

Edelsbrunner, Herbert.

*Algebraic Decomposition of Non-Convex Polyhedra*. IEEE, 1995, pp. 248–57.