Geometric construction by assembling solved subfigures
Artificial Intelligence
Numerical decomposition of geometric constraints
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Dealing with redundancy and inconsistency in constructive geometric constraint solving
Advances in Engineering Software
Interrogating witnesses for geometric constraint solving
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Using the witness method to detect rigid subsystems of geometric constraints in CAD
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
When interval analysis helps inter-block backtracking
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Interrogating witnesses for geometric constraint solving
Information and Computation
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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 over-rigid) subGCSPs.