曲线拟合平面上未分类的点 [英] Curve fitting unsorted points on a plane

问题描述

问题：如果曲线不是单值，你如何拟合平面上的点？

Question: How do you fit a curve to points on a plane if they aren't single valued?

对于所示的例子，如何拟合曲线（像黑色一样）到嘈杂的蓝色数据？它类似于样条曲线平滑，但我不知道数据的顺序。

For the example shown, how would one fit a curve (like the black one) to the noisy blue data? It's similar to spline smoothing, but I don't know the order of the data.

Matlab是首选，但伪代码很好。或指向这个问题的正确术语的指针会很棒。

Matlab would be preferred, but pseudocode is fine. Or a pointer to what the correct terminology for this problem is would be great.

谢谢

推荐答案

查看本文：通过多项式参数保持形状的最小二乘逼近样条曲线，它似乎呈现 a 解决方案。另外，请参阅最后的参考书目。

Check this article: Shape-preserving least-squares approximation by polynomial parametric spline curves, it seems to present a solution. Also, see the bibliography at the end.

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