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June 24, 2006 21:54 WSPC/Guidelines schreck˙mathis International Journal of Computational Geometry Applications c World Scientific Publishing Company GEOMETRICAL CONSTRAINT SYSTEM DECOMPOSITION: A MULTI-GROUP APPROACH Pascal SCHRECK and Pascal MATHIS LSIIT, Universit´e Louis Pasteur, Strasbourg∗ Since they help to specify the shape of real objects, geometric constraint systems en- countered in CAD domain are often invariant by isometries. But other transformation groups can be considered to improve the solving process. More precisely, using different transformation groups leads to a new approach of decomposition which generalize in some sense the classical approaches. This paper presents a method able to perform such a multi-group decomposition. 1. Introduction One of the main goals of technical drawing consists in specifying material objects with the help of dimensions which have to be respected in order to let a mechanism run or which are used to machine a mechanical part. Like for all types of specifi- cations, it is wished that only one geometric object is described by a dimensioned sketch. A dimensioned sketch is said well-constrained if there is a finite number of solutions for the underlying constraint system. But the exact meaning of these words “a finite number of solutions” has to be clarified. Indeed, since a dimensioned sketch represents a mechanical part, the corre-