CHARACTERISATION OF RATIONAL AND NURBS DEVELOPABLE SURFACES IN COMPUTER AIDED DESIGN  

作　　者：Leonardo Fernandez-Jambrina 

机构地区：[1]ETSI Navales,Universidad Politecnica de Madrid,28040-Madrid,Spain

出　　处：《Journal of Computational Mathematics》2021年第4期556-573,共18页计算数学（英文）

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

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.

关 键 词：NURBS BEZIER RATIONAL SPLINE NURBS Developable surfaces 

分 类 号：O17[理学—数学]