Using the witness method to detect rigid subsystems of geometric constraints in CAD

Dominique Michelucci (1) , Simon Thierry (2) , Pascal Schreck (2) , Christoph Fünfzig (1) , Jean-David Génevaux (2)

1 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]
2 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

This paper deals with the resolution of geometric constraint systems encountered in CAD-CAM. The main results are that the witness method can be used to detect that a constraint system is over-constrained and that the computation of the maximal rigid subsystems of a system leads to a powerful decomposition method. In a first step, we recall the theoretical framework of the witness method in geometric constraint solving and extend this method to generate a witness. We show then that it can be used to incrementally detect over-constrainedness. We give an algorithm to efficiently identify all maximal rigid parts of a geometric constraint system. We introduce the algorithm of W-decomposition to identify all rigid subsystems: it manages to decompose systems which were not decomposable by classical combinatorial methods.

Mots clés: Jacobian matrix; W-decomposition; geometric constraints solving; rigidity theory; witness configuration

Domaines: Modélisation et simulation

Dominique Michelucci, Simon Thierry, Pascal Schreck, Christoph Fünfzig, Jean-David Génevaux. Using the witness method to detect rigid subsystems of geometric constraints in CAD. Symposium on Solid and Physical Modeling, 2010, Haïfa, Israel. pp.91-100, ⟨10.1145/1839778.1839791⟩. ⟨hal-00691703⟩