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)


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.


Convex Hull Boundary Element Convex Polygon Domain Variable Regular Event 
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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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