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How do I generate a mesh gradient?

I want to create a mesh gradient from some random points and colours similar to https://csshero.org/mesher/ .

It's pretty trivial to interpolate between two colours using the method on https://www.alanzucconi.com/2016/01/06/colour-interpolation/ although the issue I have is I don't know how to interpolate between multiple colours in two dimensions like this. Any pseudo-code/python of how to interpolate between colours like this would be appreciated.

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