Percentage area overlap between circles in Python.

circle_overlap.py

#!/usr/bin/python

## Percentage area overlap between circles in Python. 
## Inspired by PHP code by JP Hastings-Spital:
##     https://gist.github.com/jphastings/316058

import math

def circle_overlap(centers_distance, radius1, radius2):
    # Make sure the larger circle is left-most (for convenience)
    R, r = max(radius1, radius2), min(radius1, radius2)

    # Special cases: no overlap and full overlap
    if centers_distance >= R + r:
        return 0.0      # 0% overlap
    elif R >= centers_distance + r:
        return 1.0      # 100% overlap

    # Else: partial overlap
    R2, r2 = R**2, r**2

    # Distance of cross-point from origin of larger circle
    x1 = (centers_distance**2 - R2 + r2 )/(2*centers_distance)
    # Distance of cross-point from origin of smaller circle
    x2 = abs(centers_distance - x1)

    y = math.sqrt(R2 - x1**2)

    # Area of smaller lens
    a1 = R2 * math.atan2(y, x1) - x1*y

    # Area of larger lens
    if x1 <= centers_distance:
        a2 = r2 * math.atan2(y, x2) - x2*y
    else:
        # Special case: if the cross-point is further away from the origin of
        # the first circle than the second circle is, then a2 needs to be the
        # large side of the circle, not the small one:
        a2 = math.pi * r2 - a2

    overlap_area = a1 + a2
    
    # Return the ratio between overlap area and smaller circle area
    return overlap_area / (math.pi * r2)