Issue with intersection region of multiple spherical caps #292
Description
Hello. I am a PhD student working on a project that requires computing the intersection region of arbitrarily many spherical caps on the unit sphere. While I was using spherical_geometry to compute the intersection region of five particular circles, I noticed that its area seemed unusually small, and I ran some experiments to see why this was the case. I found that, if I fed the circles into the .intersection() function in a different order, that I obtained a completely different result that was several orders of magnitude larger than the previous one:
from spherical_geometry.polygon import SphericalPolygon
#Data containing centers and radii on the unit circle in degrees
circle_data = [{'lat': 40.5785, 'long': -122.4005, 'radius': 126.08093425137112},
{'lat': -33.5605, 'long': -70.5815, 'radius': 90.64909777330483},
{'lat': 38.9005, 'long': -77.0505, 'radius': 92.53797630605003},
{'lat': 45.0905, 'long': 7.6575, 'radius': 108.34122674041656},
{'lat': -25.7795, 'long': -56.4515, 'radius': 73.960984449381}]
#Generate the circles as SphericalPolygon objects
#Pair them with their radii for later sorting
circles = []
for entry in circle_data:
circle = SphericalPolygon.from_cone(lat = entry['lat'], lon = entry['long'], radius = entry['radius'], degrees = True, steps = 64)
circles.append((circle, entry['radius']))
#Compute the intersection area of all seven circles
unsorted_intersection_region = circles[0][0]
for circle in circles[1:]:
unsorted_intersection_region = unsorted_intersection_region.intersection(circle[0])
#Outputs 0.004884172524381114
print(f"Area of unsorted circles: {unsorted_intersection_region.area()}")
#Sort the circles by their radii
#Recompute their mutual intersection area
circles.sort(key = lambda x: x[1])
sorted_intersection_region = circles[0][0]
for circle in circles[1:]:
sorted_intersection_region = sorted_intersection_region.intersection(circle[0])
#Outputs 2.423151795846394
print(f"Area of sorted circles: {sorted_intersection_region.area()}")
I'm not sure what could be causing this. All but one of these spherical caps are larger than half the unit sphere, but in previous tests this has not been a problem. Is there a way to fix this particular bug and ensure that the intersection region is accurate?