Given a directed cycle in the plane I need to walk it and detect whether it is clockwise or counterclockwise.

My first idea is to gather the sum of the turn angles, where a "left" turn is a negative angle, and a "right" turn is a positive angle. If I go with this one, I need a good way to calculate the angle between two vectors, and also which sign this angle should have (+/-).

Even if I had the right tools to calculate the (+/-) angle I feel like this could be done simpler.c