Algorithmes pour la détection de rigidité dans les systèmes de contraintes géométriques

The structural rigidity property, a generalization of Laman’s theorem which characterizes rigid bar frameworks in 2D, is generally considered a good approximation of rigidity in geometric constraint satisfaction problems (GCSPs). However, it may fail even on simple GCSPs because it does not take geometric properties into account. In this paper, we question the flow-based algorithm used by Hoffmann et al. to identify rigid subGCSPs. We show that this algorithm may fail because of the structural rigidity, but also by design. We introduce a new flow-based algorithm which uses Jermann et al.’s characterization of rigidity. We show that this algorithm is correct in 2D and 3D, and can be used to tackle the major issues related to rigidity: deciding whether a GCSP is rigid or not and identifying rigid (or overrigid) subGCSPs.