circle_overlap_area.py

# Calculates the overlap area between two circles of radii r1 and r2 with
# center points d apart.
def circle_overlap_area(r1, r2, d):
    try:
        # Expression from http://mathworld.wolfram.com/Circle-CircleIntersection.html
        return r2**2 * acos((d**2+r2**2-r1**2)/(2*d*r2))+r1**2*acos((d**2-r2**2+r1**2)/(2*d*r1)) - 1/2*sqrt((-d+r2+r1)*(d+r2-r1)*(d-r2+r1)*(d+r2+r1))
    except:
        # A few possible cases if there's a math domain error...
        if r1 == r2 and d == 0:
            # Identical circle radii and center points
            # Intersection area rea will be the area of either circle
            return pi * (r1**2)
        elif d+min(r1,r2) < max(r1,r2):
            # Smaller circle is completely contained within the larger circle
            # Intersection area is the area of the smaller circle
            return pi * (min(r1,r2)**2)
        elif d > r1+r2:
            # The circles don't overlap at all
            # Intersection area must be 0
            return 0.0
        else:
            # Undefined case
            return None