[SciPy-Dev] Adding alpha complexes/filtrations to scipy.spatial?

[Hamilton, Wesley]

These are the same as alpha shapes: alpha complexes are alpha shapes, and an alpha filtration is a collection of alpha shapes corresponding to varying alpha.

The situation I've had to use these for is in studying protein structure (which is one of the original applications for this stuff), though I'm sure there are other uses (like for scikit image?).

In practice, these constructions can work in any dimension, but geometrically I think the intuition changes drastically above 3 dimensions. In terms of computational complexity, I think the worst bit is in computing determinants for the in-circle radius and center, but again for small dimensions it isn't terrible. I'd also be happy to look into more optimal (if applicable) implementations for this construction, including reaching out to, say, Edelsbrunner and other experts.

I can also share the code somewhere, or if anyone wants to discuss via direct email, then that would also be great. I admit I'm relatively new to software development (and git, etc.), but I'm hoping this code can be implemented and useful to others!

Best,
Wesley
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