Declarative modelling and transformation of a constrained geometric object

摘要

To establish the specifications and to solve 2D and 3D geometric problems defined by geometric constraints, we have developed a declarative model where objects and constraints are represented by a set of vectors. These vectors are not represented by their usual Cartesian coordinates but by their respective scalar products. Then, a metric tensor characterises the geometric object. To solve the problem, we have developed a model that transforms the object from its initial state to its final state.