How to find the number of revolutions of a polygon boundary around a point?

Question

C++ / C#

In computer graphics, there is a "non-zero number of turns" rule. It is used to determine whether a point belongs to a polygon.
Total. We have a polygon defined by an array of vertices (vectror or double arrX[n] double arrY[n] etc.) defined in any way. We need to create a function to which we pass an array of points, a test point, and it should return the number of turns or a ready answer, whether the point belongs to the polygon or not.