How to compute the overlapping ratio of two rotated rectangles?

Question

Given two rectangles, and we know the position of four corners, widths, heights, angles. How to compute the overlapping ratio of these two rectangles? Can you please help me out?

Answer 1

A convenient way is by the Sutherland-Hodgman polygon clipping algorithm. It works by clipping one of the polygons with the four supporting lines (half-planes) of the other. In the end you get the intersection polygon (at worst an octagon) and find its area by the polygon area formula.

You'll make clipping easier by counter-rotating the polygons around the origin so that one of them becomes axis parallel. This won't change the area.

Note that this approach generalizes easily to two general convex polygons, taking O(N.M) operations. G.T. Toussaint, using the Rotating Caliper principle, reduced the workload to O(N+M), and B. Chazelle & D. P. Dobkin showed that a nonempty intersection can be detected in O(Log(N+M)) operations. This shows that there is probably a little room for improvement for the S-H clipping approach, even though N=M=4 is a tiny problem.

Answer 2

Use rotatedRectangleIntersection function to get contour and use contourArea function to get area and find the ratios

https://docs.opencv.org/3.0-beta/modules/imgproc/doc/structural_analysis_and_shape_descriptors.html#rotatedrectangleintersection