Significant progress has been accomplished during the past decades about geometric constraint solving, in particular thanks to its applications in industrial fields like CAD and robotics. In order to tackle problems of industrial size, many solving methods use, as a preprocessing, decomposition techniques that transform a large geometric constraint system into a set of smaller ones.In this paper, we propose a survey of the decomposition techniques for geometric constraint problems a . We classify them into four categories according to their modus operandi, establishing some similarities between methods that are traditionally separated. We summarize the advantages and limitations of the different approaches, and point out key issues for meeting industrial requirements such as generality and reliability.

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Handling geometric objects described declaratively by a system of geometric constraints is an important issue in CAD. But until now, this requires the effective geometric construction of the objects. This paper presents an original approach to formal geometric constructions in the Euclidian plane, based on invariance under displacements and relaxation of positional constraints. This approach allows to efficiently generalize and join different methods for local solving. The paper also describes the main features of a powerful and extensible operational prototype based on these ideas, which can be viewed as a simple multi-agent system with a blackboard.

Decomposition of constraint systems is a key component of geometric constraint solving in CAD. On the other hand, some authors have introduced the notion of reparameterization which aims at helping the solving of indecomposable systems by replacing some geometric constraints by other ones. In previous works, the minimal change of the initial system is a main criterion. We propose to marry these two ingredients, decomposition and reparameterization, in a method able to reparameterize and to decompose a constraint system according to this reparameterization. As a result, we do not aim at minimizing the number of added constraints during the reparameterization, but we want to decompose the system such that each component owns a minimal number of such added constraints.