Geometric transformation of a constrained object using a non-Cartesian method. (1st January 2014)

• Record Type: Journal Article
• Authors: Moinet, Mireille; Serré, Philippe
• Is Part Of: International journal of product development. Volume 19:Number 1/2/3(2014)
• Page Start: 156
• Page End: 172
• Publication Date: 2014-01-01
• Subjects: geometric constraint -- non-Cartesian geometry -- tensorial model -- perturbation -- declarative modelling; New products -- Periodicals; Technological innovations -- Periodicals; Research, Industrial -- Periodicals; 658.57505
• Languages: English
• ISSNs: 1477-9056

Abstract

This paper presents a new approach to transform a constrained geometric object. The geometric model is based on the vectorisation of the object's shape. Thus, elementary geometric entities and constraints are represented by a set of vectors or bivectors in order to establish the object specifications. The metric tensor is the mathematical tool used to define the vector space generated by the set of vectors and bivectors. The transformation of the initial object is realised thanks to a transformation matrix associated with a connection matrix. Based on the point of displacements of the initial object, this new method gives the final object satisfying the geometric specifications required by the designer.