Non-overlapping Constraints between Convex Polytopes
This paper deals with non-overlapping constraints between convex polytopes. Non-overlapping detection between fixed objects is a fundamental geometric primitive that arises in many applications. However from a constraint perspective it is natural to extend the previous problem to a non-overlapping constraint between two objects for which both positions are not yet fixed. A first contribution is to present theorems for convex polytopes which allow coming up with general necessary conditions for non-overlapping. These theorems can be seen as a generalization of the notion of compulsory part which was introduced in 1984 by Lahrichi and Gondran  for managing nonoverlapping constraint between rectangles. Finally, a second contribution is to derive from the previous theorems efficient filtering algorithms for two special cases: the non-overlapping constraint between two convex polygons as well as the non-overlapping constraint between d-dimensional boxes.
KeywordsConvex Hull Boundary Element Convex Polygon Domain Variable Regular Event
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- 2.Beldiceanu, N.: Sweep as a generic pruning technique. In TRICS: Technique foR Implementing Constraint programming, CP2000, Singapore, 2000.Google Scholar
- 3.Beldiceanu, N., Guo, Q., Thiel, S.: Non-overlapping Constraint between Convex Polytopes. SICS technical report T2001-12, (May 2001).Google Scholar
- 4.Berger, M.: Geometry II, Chapter 12. Springer-Verlag, 1980.Google Scholar
- 5.de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry-Algorithms and Applications. Springer, 1997.Google Scholar
- 6.Chamard, A., Deces, F., Fischler, A.: A Workshop Scheduler System written in CHIP. 2nd Conf Practical Applications of Prolog, London, April 1994.Google Scholar
- 7.Lahrichi, A., Gondran, M.: Thórie des parties obligatoires et dćoupes à deux dimensions. Research report HI/4762-02 from EDF (Électricité de France), (23 pages), 1984. In French.Google Scholar
- 8.Preparata F.P., Shamos M.I.: Computational Geometry. An Introduction. Springer-Verlag, 1985.Google Scholar
- 10.Van Hentenryck, P.: Constraint Satisfaction in Logic Programming. The MIT Press, 1989.Google Scholar