Solving Constraints Between Lines in Euclidean Geometry

  • Philippe Balbiani
  • Khalil Challita
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3192)


We consider constraints satisfaction problems between lines in Euclidean geometry. Our language of constraints is based on the binary relation of parallelism. Our main results state that (1) solving constraints between lines in dimension 2 can be done in polynomial time whereas (2) solving constraints between lines in dimension 3 is NP-hard.


Spatial reasoning Constraint satisfaction problems Euclidean geometry 


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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Philippe Balbiani
    • 1
  • Khalil Challita
    • 1
  1. 1.Irit-CNRSUniversité Paul SabatierToulouse Cedex 4France

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