CLC number: TP391.7; O29
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2010-04-09
Cited: 4
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Wan-qiang Shen, Guo-zhao Wang. Triangular domain extension of linear Bernstein-like trigonometric polynomial basis[J]. Journal of Zhejiang University Science C, 2010, 11(5): 356-364.
@article{title="Triangular domain extension of linear Bernstein-like trigonometric polynomial basis",
author="Wan-qiang Shen, Guo-zhao Wang",
journal="Journal of Zhejiang University Science C",
volume="11",
number="5",
pages="356-364",
year="2010",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.C0910347"
}
%0 Journal Article
%T Triangular domain extension of linear Bernstein-like trigonometric polynomial basis
%A Wan-qiang Shen
%A Guo-zhao Wang
%J Journal of Zhejiang University SCIENCE C
%V 11
%N 5
%P 356-364
%@ 1869-1951
%D 2010
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.C0910347
TY - JOUR
T1 - Triangular domain extension of linear Bernstein-like trigonometric polynomial basis
A1 - Wan-qiang Shen
A1 - Guo-zhao Wang
J0 - Journal of Zhejiang University Science C
VL - 11
IS - 5
SP - 356
EP - 364
%@ 1869-1951
Y1 - 2010
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.C0910347
Abstract: In computer aided geometric design (CAGD), the Bernstein-Bézier system for polynomial space including the triangular domain is an important tool for modeling free form shapes. The Bernstein-like bases for other spaces (trigonometric polynomial, hyperbolic polynomial, or blended space) has also been studied. However, none of them was extended to the triangular domain. In this paper, we extend the linear trigonometric polynomial basis to the triangular domain and obtain a new Bernstein-like basis, which is linearly independent and satisfies positivity, partition of unity, symmetry, and boundary representation. We prove some properties of the corresponding surfaces, including differentiation, subdivision, convex hull, and so forth. Some applications are shown.
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