An extension of Bernstein-Bézier surface over the triangular domain
An extension of Bernstein-Bézier surface over the triangular domain
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DOI：
10.1080/10020070612331343269
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发表时间：
2007-03
期刊：
影响因子：
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通讯作者：
Cao Juan;Guozhao Wang
中科院分区：
文献类型：
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作者：
Cao Juan;Guozhao Wang
摘要本文给出了一组n次单参数拟Bernstein多项式，它是Bernstein多项式在三角域上的推广。利用所提出的多项式作为基函数，构造了一类具有形状参数的形状调节曲面，即拟b - b参数曲面。这些曲面与B-B参数曲面共享许多特性。特别地，当形状参数等于1时，它们退化为B-B参数曲面。通过改变形状参数的值，可以得到固定控制网下的不同曲面。**国家自然科学基金（no . 0）资助；国家重点基础研究计划项目（批准号：2004CB318000）
Abstract 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. ** Supported by National Natural Science Foundation of China (Grant N0. 60473130) and National Program on Key Basic Research Project (Grant No. 2004CB318000)