B样条曲线降阶新方法

New Algorithm for Degree Reduction of B Spline Curves

首先导出了 B样条曲线退化的条件 ,然后根据 B样条升阶恒等式提出了 B样条曲线降阶的新算法 .最后 ,对结果进行了简要的误差分析 .如果结合节点插入技术 ,还可以将降阶后的误差限定在给定的容差之内 .实践表明 ,该算法容易实现、效率高、逼近效果好 .

In this paper, a degeneration condition of B spline curves is derived, and a new algorithm for degree reduction of B spline curves is proposed by using the identical matrix equation for B spline degree raising. In fact, the algorithm is not only very efficient but also easy to implement. In addition, an approximation error is analyzed briefly. With the technique for inserting knots into B spline curves, the error after degree reduction can be easily limited within a given tolerance.