Thin-plate splines

Starting a ‘feather in my cap’ list for this one…

Wikipedia explains Thin‐plate splines like this:

I have to tell someone… (I’m very tempted to write this on facebook but it would just come across as a humblebrag), I implemented thin‐plate spline interpolation on my landscape. It’s not only the gold standard for interpolating sparse points in a data set, but more importantly I believed the math behind it to be far beyond my ken (just look at Wikipedia’s explaination above!)

It feels like a real achievement, accomplishing something you thought was well beyond your ability. I still assume the math behind deriving the TPS equations is beyond my ken — it looks like goobledegook to me, but understanding and using it is not… not any more. This is helped by the interpolation being conceptually simpler than I assumed (math people/notation make concepts impenetrable, but there are lecture slides and other people’s blogs breaking each part down), and I’m also helped by there being a simple way to avoid the crazy computational complexity of TPS: You just compute it for small sections and naively stitch those together — the academic papers on techniques for how to blend patches together were also difficult and offputting, but I noticed some open‐source GIS software just wasn’t bothering with any of that, and if that’s good enough for GIS software…