广义B样条曲线节点插入算法及其应用

Knot Insertion Algorithm of Generalized B-splines and Its Application

通过研究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,并以多项式B样条为例,将样条曲线的求值算法和节点插入算法推广到曲面。最后给出了相应算例。数值实验表明,求值算法和节点插入算法对样条曲线和样条曲面均准确、有效。利用广义B样条曲线在2个方向上取不同类型的样条曲线,构造了特殊曲面。

A new representation to B-splines and the concept of generalized B-spline are introduced in this paper by considering the null space of a second order constant coefficient differential operator and the unique solution to an initial-value problem. The evaluation algorithm and knot insertion algorithm for generalized B-splines are also presented, and they are extended to sur- faces by taking polynomial spline surface for example. At last, numerical examples show that the algorithms are valid to both curves and surfaces. On the other hand, the tensor product surfaces can be constructed by using different kinds of the splines and it is easy to construct some special surfaces.