Detecting All Dependences in Systems of Geometric Constraints Using the Witness Method

  • Dominique Michelucci
  • Sebti Foufou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4869)


In geometric constraints solving, the detection of dependences and the decomposition of the system into smaller subsystems are two important steps that characterize any solving process, but nowadays solvers, which are graph-based in most of the cases, fail to detect dependences due to geometric theorems and to decompose such systems. In this paper, we discuss why detecting all dependences between constraints is a hard problem and propose to use the witness method published recently to detect both structural and non structural dependences. We study various examples of constraints systems and show the promising results of the witness method in subtle dependences detection and systems decomposition.


Structural Dependence Geometric Constraint Gradient Vector Cartesian Frame Geometric Theorem 
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 2007

Authors and Affiliations

  • Dominique Michelucci
    • 1
  • Sebti Foufou
    • 1
  1. 1.LE2I UMR CNRS 5158, UFR Sciences, Université de Bourgogne, BP 47870, 21078 Dijon CedexFrance

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