from math import cos, sin, pi, sqrt

class Point:
    def __init__(self, x, y):
        self.x, self.y = x, y
    def __str__(self):
        return '(%g, %g)'% (self.x, self.y)



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

    def __str__(self):
        return '(x,y)= (%g,%g), (r,theta) = (%g,%g)' %(self.x,self.y,self.r,self.theta)



#example use case
"""
origo = PolarPoint(0,pi)
p1 = PolarPoint(1,pi/2)
print(origo)
print(p1)
"""

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-14

    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])
        max_error = max(abs(pp.r-p[0]),abs(pp.theta-p[1]),abs(pp.x-x[0]),abs(pp.y-x[1]))
        msg = 'Something wrong with point %s' %str(pp)
        assert max_error < tol, msg


if __name__ == '__main__':
    test_PolarPoint()