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To the OP: There are also several other tools for scattered data approximation/interpolation developed in the last few decades, both mesh-based and mesh-free. Linear interpolation using barycentric coordinates on a triangulation is fast (and might be the most practical method for this particular use case), but nowhere near as good a result as you can get via other methods.

See e.g. http://scribblethink.org/Courses/ScatteredInterpolation/scat...

Not sure if that applies for my purposes, since I'm not actually using linear interpolation barycentric coordinates (I don't think that's possible). The barycentric coordinates supply the gradient within themselves.

I may have to read further, though. That's a lot of math.

What you’re calling a gradient is also known as linear interpolation.

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