Interactive Design of Cubic IPH Spline Curves

作     者：ZHANG Jingjing LI Xin ZHANG Jingjing;LI Xin

作者机构：School of Mathematical SciencesAnhui UniversityHefei 230026China University of Science and Technology of ChinaHefei 230026China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2023年第36卷第3期

页      面：1302-1318页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Science Foundation of China under Grant No.11801126 

主　　题：Bezier curve offsets pythagorean hodograph rational parameterization 

摘      要：Indirect Pythagorean hodographs(IPH)spline curves are a set of curves which have rational Pythagorean hodographs after reparameterization by a fractional quadratic *** this paper,the authors provide an algorithm to interactively design a cubic IPH spline curve from any given control *** method has the same friendly interface and properties as those for B-splines,meanwhile facilitates intuitive and efficient construction of open and closed IPH spline *** key idea is to solve the ratios of a set of auxiliary points associated with the edges and then construct a piecewise cubic IPH spline curve which has as high as possible continuity,i.e.,the absolute curvature value of the adjacent curve segments are the same.A very interesting observation is that for any open control polygon,a quadratic B-spline curve can have continuous absolute curvature by carefully choosing the knots as the function of the control points.