Area of intersection between circle and rectangle

Question

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

Answer 1

Perhaps you can use the answer to this question, where the area of intersection between a circle and a triangle is asked. Split your rectangle into two triangles and use the algorithms described there.

Another way is to draw a line between the two intersection points, this splits your area into a polygon (3 or 4 edges) and a circular segment, for both you should be able to find libraries easier or do the calculations yourself.