Interactive Design of Cubic IPH Spline Curves  

作　　者：ZHANG Jingjing LI Xin 

机构地区：[1]School of Mathematical Sciences,Anhui University,Hefei 230026,China [2]University of Science and Technology of China,Hefei 230026,China

出　　处：《Journal of Systems Science & Complexity》2023年第3期1302-1318,共17页系统科学与复杂性学报（英文版）

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

摘　　要：Indirect Pythagorean hodographs(IPH)spline curves are a set of curves which have rational Pythagorean hodographs after reparameterization by a fractional quadratic transformation.In this paper,the authors provide an algorithm to interactively design a cubic IPH spline curve from any given control polygon.The 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 curves.The 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.

关 键 词：Bezier curve OFFSETS pythagorean hodograph rational parameterization 

分 类 号：O186.11[理学—数学]