非单调插值方法 [英] Non-monotonic interpolation methods
问题描述
我目前正试图通过内插多个维度曲线（这只是涉及到使用的各个维度插值方法单独），和我有点困惑的PCHIP（分段三次埃尔米特插值多项式）。是否PCHIP只适用于单调的数据？我感兴趣的数据必然是不单调，所以我用的Catmull-Rom样条，但PCHIP似乎更适合我的数据，但现成的实现使用仅适用于严格递增/递减数据PCHIP IM的。我想已经写我自己的PCHIP插值算法（在Java），但我似乎无法在网络上的任何地方发现底层的算法。我想我的问题是
I'm currently trying to interpolate curves through multiple dimensions (which just involves using interpolation methods on each dimension individually), and I'm a bit confused about the PCHIP (piecewise cubic hermite interpolation polynomial). Does the PCHIP only apply to monotonic data? The data I am interested in is necessarily non-monotonic, so I used a Catmull-Rom spline, but the PCHIP seems to fit my data better, but the off the shelf implementation of the PCHIP im using only works for strictly increasing/decreasing data. I would like to have written my own PCHIP interpolation algorithm (in java), but I cant seem to find the underlying algorithm anywhere on the web. I guess my questions are
1）是否PCHIP适用于非单调数据？
1) Does the PCHIP apply to non-monotonic data?
2）如果没有，是否有任何其他的插值方法，它通过控制点通过，我可以使用？
2) If not, are there any other interpolation methods, which pass through the control points, that I could use?
3）有谁知道在哪里可以找到PCHIP背后的算法？
3) Does anyone know of where I can find the algorithm behind the PCHIP?
推荐答案
我不知道PCHIP作为一个既定的术语，但对我来说顾名思义的任意的的使用三次埃尔米特多项式插值，即较普通的词语，其中包括卡特莫尔-ROM等等的。从普通样条插值主要鉴别事实似乎是明确地计算切线。这两种可能对您的情况，因为两者会通过界定点，也不会施加单调性。维基百科有一些描述，并为您一些参考，如果这些是你心目中的概念。如果没有，你应该更具体的了解中，你读到这个词的背景下，作为这方面可能会提供一个更具体的定义。
I don't know PCHIP as an established term, but to me the name suggests any use of a cubic hermite polynomial for interpolation, i.e. a more general term which includes Catmull-Rom among others. The main distinguishing fact from common spline interpolation seems to be the explicitely computed tangents. Both might work for your situation, as both will pass through the defining points and neither will enforce monotonicity. Wikipedia has some descriptions and some references for you if these are the concepts you have in mind. If not, you should be more specific about the context in which you read about this term, as that context might provide a more specific definition.
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