Qualitative Study of Geometric Constraints

Modelling by geometric constraints is a promising method in the eld of CAD/CAM. However, this process, closely related to computer programming, is also prone error. A geometric constraints based modeller should help the end user to nd his mistakes , or, better, not to commit ones by watching the building process. The well known main cause of errors with these methods is the speciication of redundant constraints, and sometimes connicting constraints. It's also important to detect under-constrained parts of the system involving indecisiveness. This paper alludes to some usual numerical and probabilistic tools that could be used for this goal. There's also a decomposition method of constraints systems using tools of the graph theory. Since these two approaches have their own advantages it's worth combining them. All these methods will be studied rst for systems of equations and then extended to the more speciic case, but also more interesting for modelling, of systems of constraints.