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.
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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.