保形三次B样条插值算法

An Algorithm for Constructing Shape Preserving Cubic Spline Interpolation

给定空间有序点列{Vi}ni=0,构造了一条三次B样条插值曲线,该曲线上的所有3n+1个deBoor点由点列{Vi}ni=0直接计算产生。对于平面有序点列{Vi}ni=0,导出了该三次B样条插值曲线保形的一种算法,该算法中所有的deBoor点由点列{Vi}ni=0直接计算产生,避免了求解矢量方程。

For a set of ordered space data points{Vi}ni=0, 3n+1 deBoor points are defined, which consists of all Vi together with 2 additional points between each consecutive pair of data points,The resulting cubic Bspline curve interpolates all Vi . For a set of ordered planar data points{Vi}ni=0, an algorithm is derived, which constructs shape preserving cubic Bspline interpolation. In this algorithm, all deBoor points are determined by asset of appropriate parameters λi,,there is no need to solve a set of vector equations.