Validity of algorithm for creation of a non self-intersecting polygon

Question

As an extension and partial answer to my thread I wrote a simple algorithm that given a set of points(with xy coordinates) can form a non self-intersecting polygon.

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Answer 1

I would prove it slightly differently by setting the "divider line" as a connection between left-most and right-most points, rather than parallel to x axis. It could happen that there are no points below or above the parallel-to-x line and that could cause trouble to your proof.

Also, connection (5) could lead to some self-intersections with the connections generated in point (6)

There is also a special case when all points are colinear and your polygon is degraded to a line.

We assume that the set V of vertices is finite ;)

Other than that - I believe your claim is true.