Sorting a list of vertices of a polygon clockwise

Question

Please note that I'm a beginner with polygons and spatial representation.

This is what I have:

I'm working on a C# project, and I have list of vertices (defined by a latitude / longitude), representing a closed polygon. The polygon can be convex or concave, and it can't have any "holes". These vertices are adjacent but can be clockwise, or anti-clockwise.

This is what I'd like:

I'd like to know how to determine if this list is clockwise or counter-clockwise, then sort the vertices in order to they were clockwise. I'm able to do the sort algorithm by myself, but I have no idea how to determine it the given list of vertices are CW or CCW.

Answer 1

Here's the solution: https://en.wikipedia.org/wiki/Curve_orientation#Orientation_of_a_simple_polygon

Works also for concave polygons, as pointed out in the "practical considerations" section (basically the middle point for the test needs to be the topmost and leftmost point).