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Asked: 2026-06-08T12:12:40+00:00

I have two 2D rectangles, defined as an origin (x,y) a size (height, width)

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I have two 2D rectangles, defined as an origin (x,y) a size (height, width) and an angle of rotation (0-360°). I can guarantee that both rectangles are the same size.

I need to calculate the approximate area of intersection of these two rectangles.
Rectangle intersection

The calculation does not need to be exact, although it can be. I will be comparing the result with other areas of intersection to determine the largest area of intersection in a set of rectangles, so it only needs to be accurate relative to other computations of the same algorithm.

I thought about using the area of the bounding box of the intersected region, but I’m having trouble getting the vertices of the intersected region because of all of the different possible cases:
So many possible intersection shapes

I’m writing this program in Objective-C in the Cocoa framework, for what it’s worth, so if anyone knows any shortcuts using NSBezierPath or something you’re welcome to suggest that too.

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1 Answer

  1. Editorial Team

    A simple algorithm that will give an approximate answer is sampling.

    Divide one of your rectangles up into grids of small squares. For each intersection point, check if that point is inside the other rectangle. The number of points that lie inside the other rectangle will be a fairly good approximation to the area of the overlapping region. Increasing the density of points will increase the accuracy of the calculation, at the cost of performance.

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