So I'm entering an argument over fictional evidence, which is already a losing move, but who cares.

Taking the convex hull of the observations is obviously the right thing to do!

If you asked a mathematician for the simplest function from a point set in the plane to a point set in the plane, they'd flip a coin and say either the constant function that's always the empty set or the constant function that's always the plane. But that's silly, because those functions don't use your evidence.

(Other constant functions are out, because there's no way to pick between them.)

So if you asked a mathematician for the next simplest function from a point set in the plane to a point set in the plane, they'd say the identity function. That's not silly, but if you want a theory that's not just a recapitulation of your evidence, it won't help you.

(Projections or other ways of taking subsets are out because there's no natural way to pick individual points out.)

(Things like the mean are out because of measure-theoretic difficulties.)

So if you asked a mathematician for the next simplest function from a point set in the plane to a point set in the plane, they'd say the convex hull. It has all sorts of nice properties (idempotent, nondecreasing, etc.) and just sort of feels like the right thing to do with a point set.

On the other hand, sticking line segments between the points (and in a hard to specify order) is a few more "next"s down the list and only makes sense for finite point sets with pretty special geometry anyways.