Search results for "rigidity theory"
showing 2 items of 2 documents
Geometric constraint solving: The witness configuration method
2006
Geometric constraint solving is a key issue in CAD, CAM and PLM. The systems of geometric constraints are today studied and decomposed with graph-based methods, before their numerical resolution. However, graph-based methods can detect only the simplest (called structural) dependences between constraints; they cannot detect subtle dependences due to theorems. To overcome these limitations, this paper proposes a new method: the system is studied (with linear algebra tools) at a witness configuration, which is intuitively similar to the unknown one, and easy to compute.
Using the witness method to detect rigid subsystems of geometric constraints in CAD
2010
International audience; This paper deals with the resolution of geometric constraint systems encountered in CAD-CAM. The main results are that the witness method can be used to detect that a constraint system is over-constrained and that the computation of the maximal rigid subsystems of a system leads to a powerful decomposition method. In a first step, we recall the theoretical framework of the witness method in geometric constraint solving and extend this method to generate a witness. We show then that it can be used to incrementally detect over-constrainedness. We give an algorithm to efficiently identify all maximal rigid parts of a geometric constraint system. We introduce the algorit…