@Article{JCM-33-6,
author = {Zhu, Yuanpeng and Xuli, Han},
title = {New Trigonometric Basis Possessing Exponential Shape Parameters},
journal = {Journal of Computational Mathematics},
year = {2015},
volume = {33},
number = {6},
pages = {642--684},
abstract = {<p style="text-align: justify;">Four new trigonometric Bernstein-like basis functions with two exponential shape parameters are constructed, based on which a class of trigonometric Bézier-like curves, analogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an ellipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cubic Bézier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape parameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be $C^2$ ∩ $FC^3$ continuous for a non-uniform knot vector, and $C^3$ or $C^5$ continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for $G^1$ continuous joining two trigonometric Bézier-like patches over triangular domain are deduced.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1509-m4414},
url = {https://global-sci.com/article/84618/new-trigonometric-basis-possessing-exponential-shape-parameters}
}