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#### A complete and efficient algorithm for the intersection of a general 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 convex polyhedron* (MPI-I-93-140). Saarbrücken: Max-Planck-Institut
für Informatik.

Cite as: http://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).