Title: Mathematical theory of dimensioning and parameterising product geometry

Authors: Vijay Srinivasan

Addresses: IBM Corporation and Columbia University, New York, NY, USA

Abstract: The classic art of dimensioning a drawing and the modern art of parameterising a product geometric model in a computer aided system have a lot in common. As industry moved into the information age, this commonality became apparent and the need to find a unified mathematical theory assumed greater urgency. This paper presents the results of nearly two decades of work towards such a theory. It is based exclusively on congruence theorems, some of which are known since the days of Euclid and others which were proved only recently. These results are being incorporated into national and international standards that deal with product lifecycle management.

Keywords: dimensioning; parameterising; product geometry; geometric modelling; congruence theorems; symmetry; relative positioning; constraints; solids; PLM standards; product lifecycle management.

DOI: 10.1504/IJPLM.2005.007346

International Journal of Product Lifecycle Management, 2005 Vol.1 No.1, pp.70 - 85

Published online: 07 Jul 2005 *

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