基于最佳平方逼近的B样条曲线降阶

提出了一种基于带约束的最佳平方逼近的B样条曲线降阶的方法.首先讨论了降阶后曲线控制顶点个数以及节点向量的取法、保端点的B样条曲线降阶方法,并把带约束的最佳平方逼近技术引入到B样条曲线的降阶,即误差大的区域施加较大的权函数以降低最大误差.为满足给定误差限制下的降阶,提出了对原曲线插入节点的准则,即对不满足误差限制的区域插入节点.并用实例对新方法和基于扰动约束技术的降阶方法进行了比较.

Degree Reduction of B-Spline Curves Based on Least Squares Approximation

A method for reducing the degree of B-spline curves based on constrained least squares approximation is presented, which preserves endpoints of the B-spline curves. To make the degree reduced B-spline curve has better approximation, and its number of the control points and the knot vector are also discussed. It is presented that the method based on constrained least squares approximation, which adds a weight function to the object function for reducing the error of approximation. Furthermore, for the interval whose error is larger than the given tolerance, a method of knot insertion is presented so that the degree reduction is controlled under the tolerance. The new method is compared with the existing ones via examples.