Characterisation of Rational and NURBS Developable Surfaces in Computer Aided Design

Characterisation of Rational and NURBS Developable Surfaces in Computer Aided Design

Year:    2021

Author:    Leonardo Fernández-Jambrina

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 4 : pp. 556–573

Abstract

In this paper we provide a characterisation of rational developable surfaces in terms of the blossoms of the bounding curves and three rational functions $Λ, M, ν.$ Properties of developable surfaces are revised in this framework. In particular, a closed algebraic formula for the edge of regression of the surface is obtained in terms of the functions $Λ, M, ν,$ which are closely related to the ones that appear in the standard decomposition of the derivative of the parametrisation of one of the bounding curves in terms of the director vector of the rulings and its derivative. It is also shown that all rational developable surfaces can be described as the set of developable surfaces which can be constructed with a constant $Λ, M, ν .$ The results are readily extended to rational spline developable surfaces.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2003-m2019-0226

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 4 : pp. 556–573

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    NURBS Bézier Rational Spline Developable surfaces.

Author Details

Leonardo Fernández-Jambrina