圆域B样条曲线插值问题的研究

A study on the interpolation problems of disk B-spline curves

基于B样条曲线的理论,给出了圆域B样条曲线的递归算法,并在此基础上,对于带有误差的测量数据,即由于误差的原因分布在平面上一系列的小区域内的测量数据,给出了利用圆域B样条曲线进行插值的算法.所得到的圆域B样条曲线具有局部性、连续性等良好性质,通过数值实验表明该算法是可行并且有效的.

In this paper,based on the interpolation theory of B-spline curves, we propose the recursive algorithm of disk B-spline curves. And based on this, for the data with error given by measuring, i. e. The measured data distributed in a set of areas because of the existence of error,we present an algorithm which interpolate them by disk B-spline curves. The disk B-spline curves we get have many good properties such as locality and continuity. At the end of this paper ,we present several numerical examples to show our algorithm to be feasible and effective.