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Non-overlapping Constraints between Convex Polytopes

  • Nicolas Beldiceanu
  • Qi Guo
  • Sven Thiel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2239)

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.

Keywords

Convex Hull Boundary Element Convex Polygon Domain Variable Regular Event 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Nicolas Beldiceanu
    • 1
  • Qi Guo
    • 2
  • Sven Thiel
    • 3
  1. 1.SICSUppsalaSweden
  2. 2.Department of MathematicsHarbin Institute of TechnologyHarbinChina
  3. 3.MPI für InformatikSaarbrückenGermany

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