摘要
样条函数的变差缩减方法（简称Ｖ·Ｄ逼近）是利用Ｂ样条构造曲线的一种十分有效的方法。这种方法具有模拟被逼近曲线几何形态的特点、且计算简单、特别适用于自由形式的曲线和曲面的设计。古典的Ｂｅｒｎｓｔｅｉｎ多项式逼近是Ｖ·Ｄ逼近的特例。而Ｖ·Ｄ逼近的理论基础是Ｂ样条所具有的Ｖ·Ｄ的性质。本文采用与以往证明方法不同的途径、对Ｂ样条的Ｖ·Ｄ性质给出了一种纯代数的证明，该证明简单、自然。
The variation contraction method of spline-function (V.D approximation)is a very effective one in forming curves by B-spline. The method is characterized by immitating the geometric form of curves approximated and is simple in calculation. It especially applies to the curves of free form and the design of the surface. The classaicl Bernstein multinormial approximation is a special example among V.D approximations. The theoretical base of V.D approximation is the V. D property of B-spline. In this paper we provide a pure algebra identification for the V. D property of B-spline in a way different from those used in the past. And this identification is simple and natural.
关键词
B样条
变差缩减
配置方阵
全正性
广义零点
B-spline variation contraction allocation square matrix perfect positive propertygeneralized zero
