一类非端点插值B样条曲线降阶的方法

A Class of Degree Reduction Methods for B-Spline Curves

降阶算法是B样条曲线和曲面设计的一个基本算法,它广泛应用于组合曲线,蒙皮或扫描曲面等设计中.Piegl与Tiller曾给出B样条曲线的降阶方法.本文给出了解决更一般的非端点插值B样条曲线降阶的方法.新的方法主要是通过对现有的节点插入方法进行分析,给出了一种端点插值递推公式,并利用此公式对Piegl与Tiller降阶方法加以改进,使之能够解决非端点插值均匀及非均匀B样条曲线的降阶问题.

Degree reduction is a common technique in curve and surface design. It is frequently used in geometric design of the composite curves and the sweeping and skinning surfaces. There were some problems in the degree reduction by the Piegl and Tiller algorithm. In this paper, a class of new methods of knot insertion （include endpoint interpolating） is established. The methods can be used to all uniform and non-uniform curves.