A New Approach to Transform a Constrained Geometric Object

This chapter presents a geometric declarative model where objects and constraints are represented by a set of vectors in order to establish the specifications and to solve 2D and 3D problems. In this declarative model, vectors are not defined by their usual Cartesian coordinates but by their respective scalar products. Then a metric tensor characterizes the geometric object. To solve the problem, a new method based on the point displacement gives the final object satisfying all the specifications asked by the designer.

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