New cubic rational basis with tension shape parameters  

作　　者：ZHU Yuan-peng HAN Xu-li 

机构地区：[1]School of Mathematical Sciences, University of Science and Technology of China [2]School of Mathematics and Statistics, Central South University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2015年第3期273-298,共26页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(60970097 and 11271376);Postdoctoral Science Foundation of China(2015M571931);Graduate Students Scientific Research Innovation Project of Hunan Province(CX2012B111)

摘　　要：By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.

关 键 词：Bernstein basis Said-Ball basis tension shape parameter totally positive property B-spline basis Bernstein-Bezier basis 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]