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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.

Formal resolution of geometrical constraint systems by assembling