4阶三角多项式空间中的T-Bézier基在三角域上的推广

J4 ›› 2013, Vol. 48 ›› Issue (3): 31-36.

4阶三角多项式空间中的T-Bézier基在三角域上的推广

陈素根1,苏本跃2,汪志华1

1. 安庆师范学院数学与计算科学学院, 安徽安庆 246133; 2. 安庆师范学院计算机与信息学院, 安徽安庆 246133

收稿日期:2012-09-10 出版日期:2013-03-20 发布日期:2013-03-14
作者简介:陈素根(1982- ),男,硕士,讲师,研究方向为计算机辅助几何设计与图形学.Email:chensugen@126.com
基金资助:
安徽省高等学校省级自然科学研究项目(KJ2012B088,KJ2012B089);安徽省教育厅自然科学基金重点项目(KJ2009A123);安庆师范学院青年科研基金项目(KJ201017,KJ201018)

The triangular domain extension of T-Bézier basis for 4-order trigonometric polynomial space

CHEN Su-gen1, SU Ben-yue2, WANG Zhi-hua1

1.School of Mathematics ＆ Computational Science, Anqing Teachers College, Anqing 246133, Anhui, China;
2. School of Computer ＆ Information, Anqing Teachers College, Anqing 246133, Anhui, China

Received:2012-09-10 Online:2013-03-20 Published:2013-03-14

摘要/Abstract

摘要：

由于T-Bézier曲线曲面是张量积形式的,为了进一步研究非多项式空间中的T-Bézier基,完善其关于三角域部分的理论,将4阶T-Bézier基推广到三角域上,构造了满足非负性、规范性、对称性、边界性质和线性无关性的基函数,并证明了三角域上相应曲面的一些性质,最后给出了一些应用。

关键词: 计算机辅助几何设计;T-Bézier基函数;三角多项式;三角域

Abstract:

The T-Bézier curve surfaces are all tensor form. In order to further study T-Bézier basis in non-polynomial space and perfect the theory of triangular domain, a kind of trigonometric basis for trigonometric polynomial space of order 4 over triangular domain was proposed. The constructed basis over triangular domain was proved to have nice properties such as positivity, partition of unity, symmetry, boundary representation and linear independence and so on. Some properties of the corresponding surface are also proved. Finally, some applications of the proposed T-Bézier surface are shown.

Key words: computer aided geometric design; T-Bézier basis; trigonometric polynomial; triangular domain

陈素根1,苏本跃2,汪志华1. 4阶三角多项式空间中的T-Bézier基在三角域上的推广[J]. J4, 2013, 48(3): 31-36.

CHEN Su-gen1, SU Ben-yue2, WANG Zhi-hua1. The triangular domain extension of T-Bézier basis for 4-order trigonometric polynomial space[J]. J4, 2013, 48(3): 31-36.

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