广义B样条曲线及其节点插入算法
Generalized B-Splines and Knot Insertion Algorithm
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摘要: 通过二阶常系数微分算子的零空间及其初值问题解的唯一性,引入了广义B样条曲线的概念,给出了B样条曲线的一种统一表示形式,介绍了该样条的求值算法及节点插入算法,并对其凸包性质和变差缩减性质作了分析,最后给出了相应算例。数值实验表明:该算法对任意样条都适用,且结果准确、有效。Abstract: A new representation to splines is introduced and the concept of generalized Bsplines is presented by considering the null space of a second order constant coefficient differential operator and the(unique) solution to an initial-value problem;it shows the evaluation algorithm and knot insertion algorithm for generalized B-splines and analyses convex-hull property and variation-diminishing result.At last,some examples show that the algorithm is valid to all kinds of splines.