B样条曲面的求值和节点插入算法研究

Evaluation algorithm and knot insertion algorithm for B-spline surfaces

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,介绍了其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.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.

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 it is extended to surfaces by taking polynomial spline surface for example. The numerical examples showed that the algorithms are valid to both curves and surfaces.