Title: Declarative modelling and transformation of a constrained geometric object

Authors: Mireille Moinet, Philippe Serre

Addresses: LISMMA Supmeca Paris, 3 rue Fernand Hainaut, 93407 saint Ouen cedex, France. ' LISMMA Supmeca Paris, 3 rue Fernand Hainaut, 93407 saint Ouen cedex, France

Abstract: 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.

Keywords: geometric constraints; non-Cartesian geometry; tensorial models; perturbation; declarative modelling; vectors.

DOI: 10.1504/IJPD.2011.042028

International Journal of Product Development, 2011 Vol.13 No.4, pp.344 - 361

Published online: 20 Aug 2011 *

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