Curve construction based on four αβ-Bernstein-like basis functions

Release time:2016-04-25

Affiliation of Author(s):中南大学数学与统计学院

Journal:Journal of Computational and Applied Mathematics

Key Words:Said–Ball basis; Bernstein basis; Quasi Extended Chebyshev space; B-spline curve; Shape paramete

Abstract:Four new αβαβ-Bernstein-like basis functions with two exponential shape parameters, are constructed in this paper, which include the cubic Said–Ball basis functions and the cubic Bernstein basis functions. Within the general framework of Quasi Extended Chebyshev space, we prove that the proposed αβαβ-Bernstein-like basis is an optimal normalized totally positive basis. In order to compute the corresponding αβαβ-Bézier-like curves stably and efficiently, a new corner cutting algorithm is developed. Necessary and sufficient conditions are derived for the planar αβαβ-Bézier-like curve having sing

Co-author:Yuanpeng Zhu, Xuli Han, Shengjun Liu*

Indexed by:Unit Twenty Basic Research

Document Type:J

Volume:273

Issue:2015

Page Number:160-181

Translation or Not:no

Date of Publication:2015-01-01

Links to published journals:http://www.sciencedirect.com/science/article/pii/S0377042714002878