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Percentage area overlap between circles in Python.
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#!/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) |
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