三次Catmull-Rom样条保广义凸插值的充要条件  

Sufficient and Necessary Conditions of Cubic Catmull-Rom Spline Preserving Generalized Convex Interpolation

作　　者：王子睿 章仁江[1] 金曼莎 Wang Zirui;Zhang Renjiang;Jin Mansha(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018)

机构地区：[1]浙江工商大学统计与数学学院,杭州310018

出　　处：《计算机辅助设计与图形学学报》2021年第11期1765-1772,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61772025);浙江省自然科学基金(LY20F020004)。

摘　　要：对于任意给定的有序点列,利用三次Catmull-Rom样条基函数构造通过该点列的曲线,导出三次Catmull-Rom样条曲线保凸插值的充要条件;进而利用广义凸的概念,导出三次Catmull-Rom样条参数曲线保广义凸插值的充要条件.当所给点列满足保广义凸插值的充要条件时,三次Catmull-Rom样条参数曲线是自动保广义凸的且是G^(1)连续的.采用自行构造的实例佐证了方法的有效性和理论的正确性.For any given sequence of points, the expression of cubic Catmull-Rom spline basis function is used to construct a curve through those points, and the sufficient and necessary conditions of cubic Catmull-Rom spline preserving convex interpolation are derived. Furthermore, by using the concept of generalized convexity, the sufficient and necessary conditions of the cubic parameter Catmull-Rom spline preserving generalized convex interpolation are derived. When the given sequence of points satisfies the sufficient and necessary conditions for preserving generalized convex interpolation obtained, the cubic parameter Catmull-Rom spline curve of the interpolating points is an automatically preserving generalized convex and G^(1) continuous curve. The validity of the method and the correctness of the theory are proved by some constructed examples.

关 键 词：CATMULL-ROM样条 保凸 插值曲线 G^(1)连续 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]