Affiliation:
1. Laboratoire d'Ingénierie des Systèmes Mécaniques et des MAtériaux, Supméca, 3 rue Fernand Hainaut, 93407 Saint-Ouen cedex, France
Abstract
In preliminary project phases, designers generally prefer to express their ideas via 2D or 3D sketches. The scientific problem covered in this paper is that of the analysis of the consistency of a 3D geometric specification. Since traditional geometric Cartesian modelling does not permit easy analysis of consistency, we will present two non-Cartesian modellings: either by exclusively using points, and Cayley-Menger determinants will enable the relations between mutual distances to be written, or by using points and vectors, and Gram determinants will enable the relations between scalar products to be written. Finally, we will present the advantages of these two modellings in order to analyse the overall consistency of a specification.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science
Reference10 articles.
1. Constraint-based functional design verification for conceptual design
2. H. Lamure and D. Michelucci, Geometric Constraint Solving and Applications (Springer-Verlag, 1998) pp. 134–145.
3. Algorithms in Invariant Theory
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