Geometric construction by assembling solved subfigures

Among the expected contributions of Artificial Intelligence to Computer-Aided Design is the possibility of constructing a geometric object, the description of which is given by a system of topological and dimensional constraints. This paper presents the theoretical foundations of an original approach to formal geometric construction of rigid bodies in the Euclidian plane, based on invariance under displacements and relaxation of positional constraints. This general idea allows to explain in greater detail several methods proposed in the literature. One of the advantages of this approach is its ability to efficiently generalize and join together 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. Finally, some significant examples solved by this prototype are presented.