ENH: spatial: implement alpha shapes

[pmla]

What does this implement/fix?

This implements alpha shapes in the scipy.spatial module.
https://en.wikipedia.org/wiki/Alpha_shape

Most of the work is done by the Delaunay class. The main additions are a stable calculation of the simplex circumcenters and calculation of the alpha intervals in which a facet is on the surface. The approach I have taken is to do the hard work once (calculation of circumradii and alpha intervals) which makes it cheap to test different alpha thresholds.

I would like to add a connected component analysis, so that a suitable alpha value can be chosen automagically, but this requires a fast disjoint-set data structure. We don't appear to have one in scipy. I can't find any reference to it on the SciPy github page or on the mailing list. Does anyone know if this has been discussed previously?
Edit: I have added a disjoint set data structure in cython. I might move more of the _calculate_connectivity_thresholds function into the cython module to get better performance.

Additional information

This PR is WIP for the purpose of collecting feedback. Comments are very welcome.

[tylerjereddy]

Cool, it may take me a bit to get around to reviewing this. I think I still need to go back to some of your previous enhancement PRs.

[pmla]

@tylerjereddy this needs some more work before it is ready for review.

I can now use the DisjointSet structure in scipy.cluster.hierarchy which will make the changeset here a lot smaller. Looking over it again it could use some polish too.

[ilayn]

I like this draft mode so converted to it but feel free to dismiss it

[pmla]

@ilayn I'm using pinv to solve a stack of least-squares problems. Is there a better way? I would use lstsq but it doesn't support stacks and looping is too slow.

[ilayn]

For now, I guess we have to live with it. pinv uses SVD so I am surprised that loop is slower. But it is what it is I guess.