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Front. Inform. Technol. Electron. Eng.  2010, Vol. 11 Issue (5): 356-364    DOI: 10.1631/jzus.C0910347
    
Triangular domain extension of linear Bernstein-like trigonometric polynomial basis
Wan-qiang Shen*, Guo-zhao Wang
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Triangular domain extension of linear Bernstein-like trigonometric polynomial basis
Wan-qiang Shen*, Guo-zhao Wang
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
 全文: PDF(286 KB)  
摘要： 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.
关键词： Computer aided geometric design (CAGD);  Free form modeling;  Trigonometric polynomial;  Basis function;  Bernstein basis;  Triangular domain    
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.
Key words: Computer aided geometric design (CAGD)    Free form modeling    Trigonometric polynomial    Basis function    Bernstein basis    Triangular domain
收稿日期: 2009-06-10 出版日期: 2010-04-28
CLC:  TP391.7  
基金资助: Project  supported  by  the  National  Natural  Science  Foundation  of  China (Nos. 60773179, 60933008, and 60970079), the National Basic
Research  Program  (973)  of  China  (No.  2004CB318000),  and  the China Hungary Joint Project (No. CHN21/2006)
通讯作者: Wan-qiang SHEN     E-mail: wq_shen@163.com
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Wan-qiang Shen, Guo-zhao Wang. Triangular domain extension of linear Bernstein-like trigonometric polynomial basis. Front. Inform. Technol. Electron. Eng., 2010, 11(5): 356-364.

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