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tl;dr
Can you explain the Dau Genton test in terms a median grandmother could understand?

Background:
So I am looking for an "in.chull" for multivariate, concave hull, and I was going through "spatstat" and ran into something called Dau Genton test. I was unfamiliar with it, and googled, but most of the descriptions are very technical and very spatial statistics focused.

Can you explain it in terms a median grandmother would understand? What was the motivation? How does it work? When not to use it? Does it have a "super-power"?

References:

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