Numerical decomposition of geometric constraints

Geometric constraint solving is a key issue in CAD/CAM. Since Owen’s seminal paper, solvers typically use graph based decomposition methods. However, these methods become difficult to implement in 3D and are misled by geometric theorems. We extend the Numerical Probabilistic Method (NPM), well known in rigidity theory, to more general kinds of constraints and show that NPM can also decompose a system into rigid subsystems. Classical NPM studies the structure of the Jacobian at a random (or generic) configuration. The variant we are proposing does not consider a random configuration, but a configuration similar to the unknown one. Similar means the configuration fulfills the same set of incidence constraints, such as collinearities and coplanarities. Jurzak’s prover is used to find a similar configuration. CR Categories: I.6.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems

• Type: Conference
• Year: 2005
• Where: SMA
• Authors: Sebti Foufou, Dominique Michelucci, Jean-Paul Jurzak
• Keywords: Graph Based Decomposition, Numerical Probabilistic Method, Owen’s Seminal Paper, SMA 2005