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CLC number: TP391.7; O29

On-line Access: 2010-04-28

Received: 2009-06-10

Revision Accepted: 2009-10-10

Crosschecked: 2010-04-09

Cited: 4

Clicked: 5746

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Journal of Zhejiang University SCIENCE C 2010 Vol.11 No.5 P.356-364

http://doi.org/10.1631/jzus.C0910347


Triangular domain extension of linear Bernstein-like trigonometric polynomial basis


Author(s):  Wan-qiang Shen, Guo-zhao Wang

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   wq_shen@163.com

Key Words:  Computer aided geometric design (CAGD), Free form modeling, Trigonometric polynomial, Basis function, Bernstein basis, Triangular domain


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.

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author="Wan-qiang Shen, Guo-zhao Wang",
journal="Journal of Zhejiang University Science C",
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pages="356-364",
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doi="10.1631/jzus.C0910347"
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%T Triangular domain extension of linear Bernstein-like trigonometric polynomial basis
%A Wan-qiang Shen
%A Guo-zhao Wang
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%DOI 10.1631/jzus.C0910347

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T1 - Triangular domain extension of linear Bernstein-like trigonometric polynomial basis
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EP - 364
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PB - Zhejiang University Press & Springer
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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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

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