改进的保形二次样条插值

李道伦; 卢德唐; 董玉德; 孔祥言

doi:10.11834/jig.200504103

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改进的保形二次样条插值
An Improved Method on Shape Preserving Quadratic Spline Interpolation
2005年10卷第4期页码：516
纸质出版：2005
DOI： 10.11834/jig.200504103
稿件说明：

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李道伦, 卢德唐, 董玉德, 孔祥言. 改进的保形二次样条插值[J]. 中国图象图形学报, 2005,10(4):516. DOI： 10.11834/jig.200504103.

An Improved Method on Shape Preserving Quadratic Spline Interpolation[J]. Journal of Image and Graphics, 2005, 10(4): 516. DOI： 10.11834/jig.200504103.

摘要

Schumaker给出的保形二次样条插值，对不满足单调性条件的子区间，采用人机交互确定节点斜率的方法，使插值函数具有严格的保单调性。在仔细研究不满足单调性条件原因的基础上，提出了新的无需人机交互的保形样条插值方法。新方法首先找出不满足单调性条件的子区间，然后利用加密点调整相邻节点的斜率值，使之满足单调性条件，最后利用Schumaker的方法构造出严格保单调、保凸凹的C^1连续的二次样条插值。此样条插值方法在计算机辅助设计等中有实际的应用价值。

Abstract

The shape-preserving quadratic spline interpolations introduced by Schumaker need users to adjust the slopes to satisfy monotone condition

We study carefully the reasons of requiring users to adjust the slopes and introduce a new method that does not need the users to adjust the slopes. The new method first finds out the intervals that do not satisfy monotone conditions

then chooses additional split points that are given suitable slopes to satisfying monotone conditions

at last constructs shape preserving polynomial interpolation based on the method of Schumaker. Examples are given to illustrate the efficiency of the interpolation.