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#### A Complete and Efficient Algorithm for the Intersection of a General and a Convex Polyhedron

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MPI-I-93-140.pdf

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##### Citation

Dobrindt, K., Mehlhorn, K., & Yvinec, M.(1993). *A Complete
and Efficient Algorithm for the Intersection of a General and a Convex Polyhedron* (MPI-I-93-140). Saarbrücken:
Max-Planck-Institut für Informatik.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-B755-E

##### Abstract

A polyhedron is any set that can be obtained from the open half\-spaces by a

finite number of set complement and set intersection operations. We give an

efficient and complete algorithm for intersecting two three--dimensional

polyhedra, one of which is convex. The algorithm is efficient in the sense

that its running time is bounded by the size of the inputs plus the size of

the output times a logarithmic factor. The algorithm is complete in the sense

that it can handle all inputs and requires no general position assumption. We

also describe a novel data structure that can represent all three--dimensional

polyhedra (the set of polyhedra representable by all previous data structures

is not closed under the basic boolean operations).

finite number of set complement and set intersection operations. We give an

efficient and complete algorithm for intersecting two three--dimensional

polyhedra, one of which is convex. The algorithm is efficient in the sense

that its running time is bounded by the size of the inputs plus the size of

the output times a logarithmic factor. The algorithm is complete in the sense

that it can handle all inputs and requires no general position assumption. We

also describe a novel data structure that can represent all three--dimensional

polyhedra (the set of polyhedra representable by all previous data structures

is not closed under the basic boolean operations).