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triangular domain extension of linear Bernstein-like trigonometric polynomial basis

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Journal of Zhejiang University-Science C(Computers and Electronics) 2010年第5期11卷 356-364页

作者： Wan-qiang SHEN Guo-zhao WANG Department of Mathematics Zhejiang University Hangzhou 310027 China

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 *** Bernstein-like bases for other spaces(trigonometric polynomial,hyperbolic polynomial,or blended space) has also been ***,none of them was extended to the triangular *** 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 *** prove some properties of the corresponding surfaces,including differentiation,subdivision,convex hull,and so *** applications are shown.

关键词： Computer aided geometric design(CAGD) Free form modeling Trigonometric polynomial Basis function Bernstein basis triangular domain

ORTHOGONAL PIECE-WISE POLYNOMIALS BASIS ON AN ARBITRARY triangular domain AND ITS APPLICATIONS

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Journal of Computational Mathematics 2001年第1期19卷 55-66页

作者： Jia-chang Sun. (Parallel Computing Division, Institute of Software, Chinese Academy of Sciences, Beijing 100080, China) 中科院软件所北京 00080

Presents a way to construct orthogonal piece-wise polynomials on an arbitrary triangular domain via barycentric coordinates. Solution of a boundary value problem for Laplace equation; Methodology; Results and discussion.

关键词： orthogonal piece-wise polynomials triangular domain eigen-decomposition

An extension of Bernstein-Bezier surface over the triangular domain

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Progress in Natural Science:Materials International 2007年第3期17卷 352-357页

作者： CAO Juan and WANG Guozhao (Institute of Image Processing and Computer Graphic, Department of Mathematics, Zhejiang University, Hangzhou 310027, China) [a]Deparfrnent of Mathematics Institute of Image Processing and Computer Graphic Zheiang University Hangzhou China

In this paper, a set of quasi-Bernstein polynomials of degree n with one parameter is presented, which is an extension of the Bernstein polynomials over the triangular domain. Using the presented polynomials as basis functions, we construct a class of shape adjusting surfaces defined over the triangular domain with a shape parameter, namely, quasi-B-B parametric surfaces. These surfaces share many properties with the B-B parametric surfaces. In particular, when shape parameters equal 1, they degenerate to be the B-B parametric surfaces. By changing the value of the shape parameter, we can get different surfaces under the fixed control net.

关键词： triangular domain shape parameter Bezier surfaces.

DUAL FUNCTIONALS OF SAID-BZIER TYPE GENERALIZED BALL BASES OVER TRIANGLE domain AND THEIR APPLICATION

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Applied Mathematics(A Journal of Chinese Universities) 2006年第1期21卷 96-106页

作者： Wu Hongyi Dept. of Math Hefei Univ. of Technology Hefei 230009 China.

A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several intermediate surfaces. To convert different bases and surfaces,the dual functionals of bases are presented. As an application of dual functionals,the subdivision formulas for surfaces are established.

关键词： Bézier basis Said-Bézier type generalized Ball (SBGB) basis triangular domain dual functional ,subdivision formula.