均匀B样条曲线的一种表示形式

A New Representation of Uniform B-Spline Curve

在CAD中,由于B样条曲线的良好性质,使其广泛应用于设计自由曲线。本文对均匀B样条曲线进行了详细地讨论,指出由相邻的k个点P_(i-1),P_(i-2),…,P_(i+k-2)所构造的一段k阶均匀B样条曲线C_i可表示为sum from i=0 to k-1 BS_(j,k)(u)P_(j+i-1),(K-1≤u≤k)。并通过对BS_(j,k)(u)的讨论,得到了均匀B样条曲线的一种新的表示式。

In CAD,B-Spline Curve is applied to represent the free curve because of its better properties.ln this paper, the author discusses Uniform B-Spline Curve in detail, and points out that a Uniform B-Spline Curve formed by Points Pi-1,Pj-2,Pj＋k-2 can be expressed with∑j=0^k-BSj.k（u）Pj＋i-1,（k-1≤u≤k）Pi＋k2 In discussing BSj,k（u）,a new representation of Uniform B-Spline Curve is obtained.