Mechanical steps for the natural-neighbor interpolation

[maistral]

TL;DR Summary

The 2D interpolation variant; without the abstractions please.

So I have a massive (I mean, 1000-point) three-column 2D data series (z = f(x,y)) and at some point, I need intermediate values. An option that I thought of is to fit the entire data series in a surface, which is somewhat out of the question due to the nature of the experiments I'm working with (I mean, repeatedly deriving empirical equations is somewhat inefficient).

Another method I thought of is bilinear/cubic interpolation, which temporarily solved my problems, until I saw this certain 'natural-neighbor interpolation' which presents itself as a more efficient and accurate alternative. So I began searching and searching for materials, and the best I could see was this:
https://www.powershow.com/view/1223a7-MDczZ/2D_Interpolation_methods_powerpoint_ppt_presentation
(The slides on natural-neighbor interpolation start at slide 21) While I understood the concept of the method thanks to the slides, I have no idea how to execute it. Thanks to Wiki I have an idea on how to form the circumcircles, but I have no idea on how to generate the triangles to begin with.

Can someone show me to a resource that mechanically shows the steps in doing the method? A code that I can study is much more preferrable, if it is possible. thanks!

 

[maistral]

Update:

I saw this thing: https://excel-works.com/manual/interpxyz and quite frankly this is what I wanted. Apparently it also uses the natural-neighbor interpolation scheme. I tried looking for things and I also saw this:http://xongrid.sourceforge.net/ which apparently demonstrates how it is done. I looked at the source code and it was incomprehensible

Does someone know of a resource that can teach how the interpolation method is done at its most basic form, then from there I will try and build it up myself. Thank you!

 

[math771]

Hi there,

I can definitely understand your frustration with trying to execute the natural-neighbor interpolation method. It can be daunting to try and implement a new technique without clear instructions or code to follow.

I did some digging and found a few resources that may be helpful for you in understanding and implementing this method:

1. This research paper (https://doi.org/10.1016/S0167-7055(03)00047-1) provides a detailed explanation of the natural-neighbor interpolation method, including the steps involved in generating the triangles and executing the method. It also includes some code examples that you may find useful.

2. This GitHub repository (https://github.com/alexis-mignon/python-natgrid) contains a Python implementation of the natural-neighbor interpolation method. You can take a look at the code and see how it is executed in practice.

3. This blog post (https://blog.mapbox.com/natural-neighbor-interpolation-for-continuous-data-8f9e87a7b8d7) walks through the steps of natural-neighbor interpolation using a real-world example and includes some code snippets to help you understand the process.

I hope these resources will be helpful for you in understanding and implementing the natural-neighbor interpolation method. Good luck!