CHARACTERISATION OF RATIONAL AND NURBS DEVELOPABLE SURFACES IN COMPUTER AIDED DESIGN

作     者：Leonardo Fernandez-Jambrina Leonardo Fernández-Jambrina

作者机构：ETSI NavalesUniversidad Politecnica de Madrid28040-MadridSpain 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2021年第39卷第4期

页      面：556-573页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：This work is partially supported by the Spanish Ministerio de Economia y Competitividad through research grant TRA2015-67788-P. 

主　　题：NURBS Bezier Rational Spline NURBS Developable surfaces 

摘      要：In this paper we provide a characterisation of rational developable surfaces in terms of the blossoms of the bounding curves and three rational functions∧,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∧,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∧,M,ν.The results are readily extended to rational spline developable surfaces.