摘要
规范B基即最优规范的全正基,因其具有凸包性、仿射不变性、最优保形性、端点插值性及B-算法等重要性质,在CAGD中起着重要的作用.本文讨论了各种规范B基曲面,包括C-Bézier曲面、H-C-Bézier曲面、C-B-Bézier曲面和H-B-Bézier曲面,并给出了摆线柱面、旋转摆线面、悬链面等超越曲面的规范B基曲面表示.
Normalized B-basis, namely optimal normalized totally positive basis, plays an important role in CAGD, for it possesses positive properties such as variation diminishing, convex-hull, affine invariance, tangency to the control polygon at the endpoints and B-algorithm. The widely used basis functions in CAGD, such as Bernstein, B-spline and NURBS basis, are all normalized B-basis. Using normalized B-basis, C-Bézier surface, H-Bézier surface, and H-C-Bézier surface model are constructed and discussed, and then some transcendental surfaces are represented such as cycloidal cylindrical surface, cycloidal surface of revolution and catenoid of revolution.
出处
《纯粹数学与应用数学》
CSCD
北大核心
2005年第2期192-196,共5页
Pure and Applied Mathematics
关键词
规范B基
超越曲面
函数空间
CAGD
normalized B-basis, transcendental surfaces, functional space, CAGD
