如何对未描述函数的N点进行插值 [英] How to interpolate N points that do not describe a function

问题描述

假设我有 n 个点，还假设该点具有顺序，并且不一定要使这些点起作用.我想知道如果这些点没有描述函数怎么对它们进行插值?例如，这将是原始点:

Suppose i have n points, also suppose that this points have an order, and not necessary this points make a function. I'm wondering how to interpolate them if the points do not describe a function? For example this will be the original points:

我希望这个结果:

请注意，仅使用样条线不起作用，因为这些点不起作用，而使用Bezier曲线也不起作用，因为它们不对点进行插值(仅通过点).我该怎么做呢?有针对这个的算法吗?

Note that only using splines do not works because the points do not make a function, and also using Bezier curves do not works because them do not interpolate the points (only pass near of them). How can i do for get this? Is there an algorithm for that?

只是一个更新.由于我作为参考接受的答案的链接已关闭，因此我将分享我根据该文章撰写的文章，以帮助其他人解决此问题.

Just an update. Since the accepted answer’s link that I took as a reference is down, I’m going to share an article I wrote based on that for helping others with this issue.

插入2D点，有用WPF中的Bezier曲线

推荐答案

1. 样条线种类很多，例如， Catmull-Rom样条线适用在这里.

通过贝塞尔曲线进行插值的简单而有趣的方法是Maxim提出的.Shemanarev

Simple and interesting method for interpolation by Bezier curves has been proposed by Maxim Shemanarev

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