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  1. import random
  2. random.seed(42) #reproducible results
  3.  
  4. def rp():
  5.     """Choose a random point uniformly in the unit circle"""
  6.     while True:
  7.         x = random.uniform(-1, 1)
  8.         y = random.uniform(-1, 1)
  9.         if x*x + y*y < 1:
  10.             return (x, y)
  11.  
  12. def ccw(a, b):
  13.     """Compute a 2x2 determinant to decide orientation of angle between
  14.        two points as seen from the origin."""
  15.     return a[0]*b[1] - a[1]*b[0]
  16.  
  17. containsCenter = 0
  18. areaWithCenter = 0
  19. numTotal = 250000 # higher means more time but more precision as well
  20. for i in xrange(numTotal):
  21.     p1 = rp()
  22.     p2 = rp()
  23.     p3 = rp()
  24.     c12 = ccw(p1, p2)
  25.     c23 = ccw(p2, p3)
  26.     c31 = ccw(p3, p1)
  27.     if c12*c23 > 0 and c23*c31 > 0 and c31*c12 > 0:
  28.         containsCenter += 1
  29.         areaWithCenter += abs(c12*c23*c31) # shoelace formula
  30.  
  31. areaWithCenter = areaWithCenter/containsCenter
  32. containsCenter = float(containsCenter)/numTotal
  33. print(containsCenter)
  34. print(areaWithCenter)
  35.  
Success #stdin #stdout 2.46s 10544KB
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0.250156
0.0297397699519
https://ideone.com/Sd0aQO
language:
Python (cpython 2.7.16)
created:
12 years ago
visibility:
public

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