These are python bindings to Bernd Gärtners miniball software.
You can install miniball with:
pip install MiniballCppThere are wheels available for most platforms.
There is also a package for Arch Linux (that is not maintained by me!): https://aur.archlinux.org/packages/python-miniball/.
import math
import random
import miniball
P = [(random.uniform(0, 100), random.uniform(0, 100)) for i in range(10000)]
mb = miniball.Miniball(P)
print('Center', mb.center())
print('Radius', math.sqrt(mb.squared_radius()))This algorithm has some numerical challenges worth mentioning. The result may deviate from the optimal result by 10 times the machine epsilon and sometimes even more:
P = [(642123.5528970208, 5424489.146461355),
(651592.349934072, 5424969.380667617),
(642591.1068130962, 5425775.320365907),
(646380.0282527813, 5418648.987550308),
(648098.891235107, 5426586.3920675),
(650011.5835629451, 5426132.820254512),
(650297.6960375579, 5419125.777007122),
(645249.2122321032, 5421055.739722816),
(645333.9125837489, 5426228.852409409)]
mb = miniball.Miniball(P)
if not mb.is_valid():
print('Possibly invalid!')
print('Relative error', mb.relative_error())If this is a problem for you, shifting the input towards (0,0) may help:
minx = min(P, key=lambda p: p[0])[0]
miny = min(P, key=lambda p: p[1])[1]
P = [(p[0] - minx, p[1] - miny) for p in P]
mb = miniball.Miniball(P)
if not mb.is_valid():
print('Possibly invalid!')
print('Relative error', mb.relative_error())