Résolution de contraintes géométriques par rigidifications récursive et propagation d'intervalles

Abstract

Geometric constraint satisfaction problems (GCSPs) are ubiquitous in applications like CAD, robotics or molecular biology. They consist in searching positions, orientations and dimensions of geometric objects bound by geometric constraints. The goal of the thesis was to find an efficient and complete solving method for GCSPs. In the first part, we compare solving methods and decomposition techniques, and we choose Hoffmann et al's decomposition and interval solving methods. We define a general framework for the study of rigidity in GCSPs, a concept used in all the geometric decomposition methods. In the second part, we analyse Hoffmann et al's method, and the limits inherent to all the structural geometric approaches. We propose the degree of rigidity concept to overcome some of these limits. We introduce a new decomposition method, and its combination with interval solving techniques.