A New Structural Rigidity for Geometric Constraint Systems

The structural rigidity property, a generalization of Laman's theorem which characterizes rigid bar frameworks in 2D, is generally considered a good heuristic to detect rigidities in a geometric constraint satisfaction problem (GCSP). The gap between rigidity and structural rigidity essentially resides in the fact that structural rigidity is not a geometric property. In this article, we propose a new de nition of structural rigidity which takes into account geometric aspects of rigidity. We also propose a new ow-based algorithm for identifying GCSPs verifying our new de nition. This algorithm works on a geometric constraint network introduced by Ho mann et al.