Circle-Circle: Area of Intersection

While working on my remake of the popular web game Agar.io, I originally calculated the intersection between two cells as the distance between their two center points (accounting for their respective radii); this is an inaccurate calculation. The actual area of intersection between two circles is much more complicated than a Euclidean vector distance. Rather, it involves calculating several points around the area of intersection, then their two common sectors, to eventually find the sum of two segments, which is the common area among the two circles in question. This was an interesting project on its own, due to the unique trigonometry and geometry involved, and I hope to implement this algorithm for finding intersections into my Agar.io remake in the future!