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A complete and efficient algorithm for the intersection of a general convex polyhedron

MPS-Authors

Dobrindt,  K.
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Yvinec,  M.
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-93-140.pdf
(Any fulltext), 14MB

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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).