# How to find polygons overlap reign

I have an algorithmic problem.

I have a set of different polygons in the 2D space. Each polygon is represented according to its vertex representation (x and y coordinates) and may contain up to N different vertices.

Assuming I have a set of N polygons, then for a new polygon k, how do I determine whether or not k overlaps with each one of the N polynomials in the set AND what is the overlapping reign percentage?

This is a purely algorithmic question but I plan on writing the algorithm in parallel using the CUDA platform, therefore any highly parallel solution would be preferred.