Geometric constraint solving: The witness configuration method

Dominique Michelucci, Sebti Foufou

Research output: Contribution to journalArticlepeer-review


Geometric constraint solving is a key issue in CAD, CAM and PLM. The systems of geometric constraints are today studied and decomposed with graph-based methods, before their numerical resolution. However, graph-based methods can detect only the simplest (called structural) dependences between constraints; they cannot detect subtle dependences due to theorems. To overcome these limitations, this paper proposes a new method: the system is studied (with linear algebra tools) at a witness configuration, which is intuitively similar to the unknown one, and easy to compute.

Original languageEnglish (US)
Pages (from-to)284-299
Number of pages16
JournalCAD Computer Aided Design
Issue number4
StatePublished - Apr 2006


  • Constraints dependences
  • Decomposition and solving
  • Geometric constraints
  • Rigidity theory
  • The numerical probabilistic method

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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