A particle-spring approach to geometric constraints solving

Simon Thierry (1)

1 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

Current iterative methods, such as continuation or Newton-Raphson, work only on systems for which the corresponding matrix is a square one. The geometric constraint systems need thus either to have no degrees of freedom, or to be a system the software can anchor, i.e. a rigid system. In this article, we propose a new iterative numerical approach which can handle both rigid and under-rigid geometric constraint systems. It is based on the translation of the system under the form of a particle-spring system where particles correspond to the geometric entities and the springs to the constraints. We show that consistently over-constrained systems are also solved. We show that our approach is promising by giving results of a prototype implementation. We propose tracks for enhancements of the approach which could tackle its drawbacks (mainly stability).

Mots clés: geometric constraints solving; mass-spring system; numerical iterative computation

Domaines: Modélisation et simulation

Simon Thierry. A particle-spring approach to geometric constraints solving. Symposium on Applied Computing, 2011, TaiChung, Taiwan. pp.1100-1105, ⟨10.1145/1982185.1982428⟩. ⟨hal-00691697⟩