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I’m looking for a fast way to determine the area of intersection between a rectangle and a circle (I need to do millions of these calculations).
A specific property is that in all cases the circle and rectangle always have 2 points of intersection.
Given 2 points of intersection:
0 vertices is inside the circle: The area of a circular segment
1 vertex is inside the circle: The sum of the areas of a circular segment and a triangle.
2 vertices are inside the circle: The sum of the area of two triangles and a circular segment
3 vertices are inside the circle: The area of the rectangle minus the area of a triangle plus the area of a circular segment
To calculate these areas:
Most of the points you’ll need to use can be found by finding the intersection of a line and a circle
The areas you need to compute can be found by computing the area of a circular segment and computing the area of a triangle.
You can determine if a vertex is inside the circle by calculating if its distance from the center is less than the radius.