有理Bézier三角曲面片低阶导矢界的估计

基于Bézier三角曲面的de Casteljau算法,同时运用一些恒等式和基本不等式,给出了两类有理Bézier三角曲面片低阶导矢的上界.第一类上界是用控制顶点凸包直径表示的,在一阶偏导的情况下,它是对已有上界的改进;在二阶偏导情况下,当最大权因子与最小权因子比值大于2时,它也是对已有上界的改进.第二类上界是用相邻控制顶点间距离的最大值来表示的.

Bound Estimations on Lower Derivatives of Rational Triangular Bézier Surfaces

Based on the de Casteljau algorithm for triangular patches, also using some existing identities and elementary inequalities, this paper presents two kinds of new magnitude upper bounds on the lower derivatives of rational triangular Bézier surfaces. The first one, which is obtained by exploiting the diameter of the convex hull of the control net, is always stronger than the known one in case of the first derivative. For the second derivative, the first kind is an improvement on the existing one when the ratio of the maximum weight to the minimum weight is greater than 2; the second kind is characterized as being represented by the maximum distance of adjacent control points.