Abstract
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 [7] 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.
Partly supported by the IST Program of the EU under contract number IST-1999-14186, (ALCOM-FT).
Currently at: Department of Mathematics, Uppsala University, SE-75237 Uppsala, Sweden.
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Beldiceanu, N., Guo, Q., Thiel, S. (2001). Non-overlapping Constraints between Convex Polytopes. In: Walsh, T. (eds) Principles and Practice of Constraint Programming — CP 2001. CP 2001. Lecture Notes in Computer Science, vol 2239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45578-7_27
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DOI: https://doi.org/10.1007/3-540-45578-7_27
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