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  1. import math
  2.  
  3. class Point:
  4.     def __init__(self, x,y):
  5.         self.x = x
  6.         self.y = y
  7.  
  8.     def magnitude(self):
  9.         return math.sqrt(self.x*self.x + self.y*self.y)
  10.  
  11.     def _applyVectorFunc(self, other, f):
  12.         return Point(f(self.x, other.x), f(self.y, other.y))
  13.     def _applyScalarFunc(self, a, f):
  14.         return self._applyVectorFunc(Point(a,a), f)
  15.  
  16.     def __add__(self, other):
  17.         return self._applyVectorFunc(other, lambda a,b: a+b)
  18.     def __sub__(self, other):
  19.         return self._applyVectorFunc(other, lambda a,b: a-b)
  20.     def __mul__(self, a):
  21.         return self._applyScalarFunc(a, lambda b,c: b*c)
  22.     def __div__(self, a):
  23.         return self._applyScalarFunc(a, lambda b,c: b/c)
  24.  
  25.     def __repr__(self):
  26.         return "Point({}, {})".format(self.x, self.y)
  27.  
  28. def dot_product(a,b):
  29.     return a.x * b.x + a.y * b.y
  30.  
  31. def angle_between(b,c):
  32.     return math.acos(dot_product(b,c) / (b.magnitude() * c.magnitude()))
  33.  
  34. def to_degrees(a):
  35.     return a * 360 / (2*math.pi)
  36.  
  37. def find_collision_point(target_pos, target_vel, interceptor_pos, interceptor_speed):
  38.     k = target_vel.magnitude() / interceptor_speed
  39.     c = (interceptor_pos - target_pos).magnitude()
  40.  
  41.     b_hat = target_vel
  42.     c_hat = interceptor_pos - target_pos
  43.  
  44.     CAB = angle_between(b_hat, c_hat)
  45.     ABC = math.asin(math.sin(CAB) * k)
  46.     ACB = (math.pi) - (CAB + ABC)
  47.  
  48.     j = c / math.sin(ACB)
  49.     a = j * math.sin(CAB)
  50.     b = j * math.sin(ABC)
  51.  
  52.  
  53.     t = b / target_vel.magnitude()
  54.     collision_pos = target_pos + (target_vel * t)
  55.  
  56.     print "Collision pos: {}".format(collision_pos)
  57.     print "Time: {}".format(t)
  58.  
  59.     print "Angle A: {}".format(to_degrees(CAB))
  60.     print "Angle B: {}".format(to_degrees(ABC))
  61.     print "Angle C: {}".format(to_degrees(ACB))
  62.  
  63.     print "a: {}".format(a)
  64.     print "b: {}".format(b)
  65.     print "c: {}".format(c)
  66.  
  67. target_pos = Point(120,40)
  68. target_vel = Point(5,2)
  69. interceptor_pos = Point(80,80)
  70. interceptor_speed = 10
  71.  
  72. find_collision_point(target_pos, target_vel, interceptor_pos, interceptor_speed)
Success #stdin #stdout 0.01s 7692KB
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stdin
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Standard input is empty
stdout
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Collision pos: Point(163.065368246, 57.2261472985)
Time: 8.61307364926
Angle A: 113.198590514
Angle B: 29.6680851288
Angle C: 37.1333243575
a: 86.1307364926
b: 46.3828210973
c: 56.5685424949
https://ideone.com/x1jVMn
language:
Python (cpython 2.7.16)
created:
10 years ago
visibility:
public

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