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

Dobrindt, Katrin; Mehlhorn, Kurt; Yvinec, Mariette

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

Dobrindt, K., Mehlhorn, K., & Yvinec, M. (1993). A Complete and Efficient Algorithm for the Intersection of a General and a Convex Polyhedron.

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Datensatz-Permalink: https://hdl.handle.net/11858/00-001M-0000-0014-ADD5-E Versions-Permalink: https://hdl.handle.net/11858/00-001M-0000-0014-ADD6-C

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Urheber:
Dobrindt, Katrin¹, Autor
Mehlhorn, Kurt², Autor
Yvinec, Mariette¹, Autor

Affiliations:
1Max Planck Society, ou_persistent13
2Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019

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Zusammenfassung: Un polyedre est tout ensemble qui peut etre obtenu a partir de demi-espaces par un nombre fini d{'}operations de complement et d{'}intersection. Nous proposons ici un algorithme complet et efficace pour construire l{'}intersection de deux polyedres dans l{'}espace tridimensionnel dont l{'}un est convexe. L{'}algoritme est efficace car son temps de calcul est, a un facteur logarithmique pres, borne par la taille des entrees plus la taille de la sortie. L{'}algorithme est complet dans le sens qu{'}il peut traiter toutes les entrees sans aucune hypothese de position generale. De plus, nous decrivons une nouvelle structure de donnees susceptible de representer tout polyedre dans l{'}espace (toutes les structures utilisees precedemment representent seulement des ensembles de polyedres qui ne sont pas stables pour les operations booleennes de base). 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 revious data structures is not closed under the basic boolean operations).