107 lines
3.7 KiB
Python
107 lines
3.7 KiB
Python
from __future__ import division
|
|
from math import sqrt
|
|
from itertools import count
|
|
from pprint import pprint as pp
|
|
try:
|
|
from itertools import izip as zip
|
|
except:
|
|
pass
|
|
|
|
# Remove duplicates and sort, largest first.
|
|
circles = sorted(set([
|
|
# xcenter ycenter radius
|
|
(1.6417233788, 1.6121789534, 0.0848270516),
|
|
(-1.4944608174, 1.2077959613, 1.1039549836),
|
|
(0.6110294452, -0.6907087527, 0.9089162485),
|
|
(0.3844862411, 0.2923344616, 0.2375743054),
|
|
(-0.2495892950, -0.3832854473, 1.0845181219),
|
|
(1.7813504266, 1.6178237031, 0.8162655711),
|
|
(-0.1985249206, -0.8343333301, 0.0538864941),
|
|
(-1.7011985145, -0.1263820964, 0.4776976918),
|
|
(-0.4319462812, 1.4104420482, 0.7886291537),
|
|
(0.2178372997, -0.9499557344, 0.0357871187),
|
|
(-0.6294854565, -1.3078893852, 0.7653357688),
|
|
(1.7952608455, 0.6281269104, 0.2727652452),
|
|
(1.4168575317, 1.0683357171, 1.1016025378),
|
|
(1.4637371396, 0.9463877418, 1.1846214562),
|
|
(-0.5263668798, 1.7315156631, 1.4428514068),
|
|
(-1.2197352481, 0.9144146579, 1.0727263474),
|
|
(-0.1389358881, 0.1092805780, 0.7350208828),
|
|
(1.5293954595, 0.0030278255, 1.2472867347),
|
|
(-0.5258728625, 1.3782633069, 1.3495508831),
|
|
(-0.1403562064, 0.2437382535, 1.3804956588),
|
|
(0.8055826339, -0.0482092025, 0.3327165165),
|
|
(-0.6311979224, 0.7184578971, 0.2491045282),
|
|
(1.4685857879, -0.8347049536, 1.3670667538),
|
|
(-0.6855727502, 1.6465021616, 1.0593087096),
|
|
(0.0152957411, 0.0638919221, 0.9771215985),
|
|
]), key=lambda x: -x[-1])
|
|
|
|
def vdcgen(base=2):
|
|
'Van der Corput sequence generator'
|
|
for n in count():
|
|
vdc, denom = 0,1
|
|
while n:
|
|
denom *= base
|
|
n, remainder = divmod(n, base)
|
|
vdc += remainder / denom
|
|
yield vdc
|
|
|
|
def vdc_2d():
|
|
'Two dimensional Van der Corput sequence generator'
|
|
for x, y in zip(vdcgen(base=2), vdcgen(base=3)):
|
|
yield x, y
|
|
|
|
def bounding_box(circles):
|
|
'Return minx, maxx, miny, maxy'
|
|
return (min(x - r for x,y,r in circles),
|
|
max(x + r for x,y,r in circles),
|
|
min(y - r for x,y,r in circles),
|
|
max(y + r for x,y,r in circles)
|
|
)
|
|
def circle_is_in_circle(c1, c2):
|
|
x1, y1, r1 = c1
|
|
x2, y2, r2 = c2
|
|
return sqrt((x2 - x1)**2 + (y2 - y1)**2) <= r1 - r2
|
|
|
|
def remove_covered_circles(circles):
|
|
'Takes circles in decreasing radius order. Removes those covered by others'
|
|
covered = []
|
|
for i, c1 in enumerate(circles):
|
|
eliminate = [c2 for c2 in circles[i+1:]
|
|
if circle_is_in_circle(c1, c2)]
|
|
if eliminate: covered += [c1, eliminate]
|
|
for c in eliminate: circles.remove(c)
|
|
#pp(covered)
|
|
|
|
def main(circles):
|
|
print('Originally %i circles' % len(circles))
|
|
print('Bounding box: %r' % (bounding_box(circles),))
|
|
remove_covered_circles(circles)
|
|
print(' down to %i due to some being wholly covered by others' % len(circles))
|
|
minx, maxx, miny, maxy = bounding_box(circles)
|
|
# Shift to 0,0 and compute r**2 once
|
|
circles2 = [(x - minx, y - miny, r*r) for x, y, r in circles]
|
|
scalex, scaley = abs(maxx - minx), abs(maxy - miny)
|
|
pcount, inside, last = 0, 0, ''
|
|
for px, py in vdc_2d():
|
|
pcount += 1
|
|
px *= scalex; py *= scaley
|
|
if any((px-cx)**2 + (py-cy)**2 <= cr2 for cx, cy, cr2 in circles2):
|
|
inside += 1
|
|
if not pcount % 100000:
|
|
area = (inside/pcount) * scalex * scaley
|
|
print('Points: %8i, Area estimate: %r'
|
|
% (pcount, area))
|
|
# Hack to check if precision OK
|
|
this = '%.4f' % area
|
|
if this == last:
|
|
break
|
|
else:
|
|
last = this
|
|
print('The value has settled to %s' % this)
|
|
|
|
|
|
if __name__ == '__main__':
|
|
main(circles)
|