vector.py

import math

class Vector:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self._magnitude = -1

    def get_magnitude(self):
        if self._magnitude == -1:
            self._magnitude = (self.x ** 2 + self.y ** 2) ** 0.5
        return self._magnitude

    def __add__(self, other):
        return Vector(self.x + other.x, self.y + other.y)
    
    def __sub__(self, other):
        return Vector(self.x - other.x, self.y - other.y)
    
    def __mul__(self, other):
        return Vector(self.x * other, self.y * other)
    
    def __truediv__(self, other):
        return Vector(self.x / other, self.y / other)
    
    def __floordiv__(self, other):
        return Vector(self.x // other, self.y // other)
    
    def dot(self, other):
        return self.x * other.x + self.y * other.y
    
    def normalize(self):
        return self / self.get_magnitude()
    
    def round(self):
        return Vector(round(self.x), round(self.y))
    
    def rotate(self, origin, rotation):
        dx = self.x - origin.x
        dy = self.y - origin.y
        cos = math.cos(rotation)
        sin = math.sin(rotation)
        return Vector(origin.x + dx * cos + dy * -1 * sin, origin.y + dx * sin + dy * cos)