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:
42              return Vector(-self.y, 0)
43          a = math.atan(self.y / self.x)
44          d = self.x / math.cos(a)
45          return Vector(d, rad2deg(a) + 90)
46  
47  
48  class Vector:
49      def __init__(self, distance: float, angle: float):
50          if distance < 0:
51              distance *= -1
52              angle += 180
53          self.distance = distance
54          self.angle = angle % 360
55  
56      def __repr__(self) -> str:
57          return f"Vector(distance={self.distance}, angle={self.angle})"
58  
59      def __add__(self, other):
60          assert isinstance(other, Vector)
61          return (self.to_point() + other.to_point()).to_vector()
62  
63      def __sub__(self, other):
64          assert isinstance(other, Vector)
65          return (self.to_point() - other.to_point()).to_vector()
66  
67      def __mul__(self, other):
68          assert isinstance(other, int) or isinstance(other, float)
69          return Point(self.distance * other, self.angle)
70  
71      def __truediv__(self, other):
72          assert isinstance(other, int) or isinstance(other, float)
73          return Point(self.distance / other, self.angle)
74  
75      def to_point(self):
76          return Point(
77              math.cos(deg2rad(self.angle - 90)) * self.distance,
78              math.sin(deg2rad(self.angle - 90)) * self.distance
79          )