Abstract
A polyhedron is any set that can be obtained from the open halfspaces 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).
The research of all three authors was partly supported by the ESPRIT Basic Research Actions Program, under contract No. 7141 (project ALCOM II). The research of the second author was also partially supported by the BMFT (Förderungskennzeichen ITS 9103). The paper is based on the first author's master's thesis [Dob90].
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© 1993 Springer-Verlag Berlin Heidelberg
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Dobrindt, K., Mehlhorn, K., Yvinec, M. (1993). A complete and efficient algorithm for the intersection of a general and a convex polyhedron. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_258
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DOI: https://doi.org/10.1007/3-540-57155-8_258
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