1  import math
 2  
 3  
 4  def deg2rad(angle: float) -> float:
 5      return (angle % 360) / 180 * math.pi
 6  
 7  
 8  def rad2deg(angle: float) -> float:
 9      return (angle * 180 / math.pi) % 360
10  
11  
12  class Point:
13      def __init__(self, x: float, y: float):
14          self.x = x
15          self.y = y
16  
17      def __repr__(self) -> str:
18          return f"Point(x={self.x}, y={self.y})"
19  
20      def __iter__(self):
21          yield self.x
22          yield self.y
23  
24      def __add__(self, other):
25          assert isinstance(other, Point)
26          return Point(self.x + other.x, self.y + other.y)
27  
28      def __sub__(self, other):
29          assert isinstance(other, Point)
30          return Point(self.x - other.x, self.y - other.y)
31  
32      def __mul__(self, other):
33          assert isinstance(other, int) or isinstance(other, float)
34          return Point(self.x * other, self.y * other)
35  
36      def __truediv__(self, other):
37          assert isinstance(other, int) or isinstance(other, float)
38          return Point(self.x / other, self.y / other)
39  
40      def to_vector(self):
41          if not self.x: return Vector(-self.y, 0)
42          a = math.atan(self.y / self.x)
43          d = self.x / math.cos(a)
44          return Vector(d, rad2deg(a) + 90)
45  
46  
47  class Vector:
48      def __init__(self, distance: float, angle: float):
49          if distance < 0:
50              distance *= -1
51              angle += 180
52          self.distance = distance
53          self.angle = angle % 360
54  
55      def __repr__(self) -> str:
56          return f"Vector(distance={self.distance}, angle={self.angle})"
57  
58      def __add__(self, other):
59          assert isinstance(other, Vector)
60          return (self.to_point() + other.to_point()).to_vector()
61  
62      def __sub__(self, other):
63          assert isinstance(other, Vector)
64          return (self.to_point() - other.to_point()).to_vector()
65  
66      def __mul__(self, other):
67          assert isinstance(other, int) or isinstance(other, float)
68          return Point(self.distance * other, self.angle)
69  
70      def __truediv__(self, other):
71          assert isinstance(other, int) or isinstance(other, float)
72          return Point(self.distance / other, self.angle)
73  
74      def to_point(self):
75          return Point(
76              math.cos(deg2rad(self.angle - 90)) * self.distance,
77              math.sin(deg2rad(self.angle - 90)) * self.distance
78          )
79  
80      def copy(self):
81          return Vector(self.distance, self.angle)