"""
Ex. 9.6 from "A primer on..."
Extend a class for a point in 2D with a
subclass that represents the point
both in Cartesian and polar coordinates. 
"""
from math import cos, sin, sqrt, pi

class Point:
    def __init__(self, x, y):
        self.x, self.y = x, y

    def __str__(self):
        return f'({self.x:g}, {self.y:g})'



class PolarPoint(Point):
    def __init__(self, r, theta):
        self.r = r
        self.theta = theta
        x = r * cos(theta)
        y = r * sin(theta)
        super().__init__(x,y)

    def __str__(self):
        cart = super().__str__()
        polar = f'({self.r:g}, {self.theta:g})'
        return f'Cartesian: {cart}, polar: {polar}'


def test_PolarPoint():
    """
    r,theta = (1,pi/2) -> x,y = (0,1)
    r,theta = (2,pi/4) -> x,y = (sqrt(2),sqrt(2))
    """
    tol = 1e-10

    points_polar = [(1,pi/2),(2,pi/4)]
    points_cart = [(0,1),(sqrt(2),sqrt(2))]

    for p, x in zip(points_polar,points_cart):
        pp = PolarPoint(p[0],p[1])
        assert abs(pp.r-p[0]) < tol
        assert abs(pp.theta-p[1]) < tol
        assert abs(pp.x-x[0]) < tol
        assert abs(pp.y-x[1]) < tol

if __name__ == "__main__":
    test_PolarPoint()

    p = Point(1.0, 2.5) 
    print(p) 

    p2 = PolarPoint(1.0, 0.5)
    print(p2)

"""
Terminal> python PolarPoint.py 
(1, 2.5)
Cartesian: (0.877583, 0.479426), polar: (1, 0.5)
"""