#! /usr/bin/env python
"""
 Spiral.py is a program which make a polar plot of r = theta^2
   i.e. the Galilean spiral

 Paul Eugenio
 Florida State University
 PHZ4151C
 29 Jan 2019
"""

from __future__ import division, print_function
import matplotlib.pyplot as plt
import numpy as np

# use latex 
plt.rc('text', usetex=True)

# define parameters
thetaMin, thetaMax = 0, 10*np.pi
steps = 1000


# use numpy vectorization to generate plotting values
theta = np.linspace(thetaMin, thetaMax, steps)
r = theta*theta
x = r*np.cos(theta)
y = r*np.sin(theta)

# plot curve and decorate with latex equation
plt.plot(x, y)
plt.plot(x, y)
plt.xlabel(r"$r(\theta)$")
plt.ylabel(r"$\theta^2$")
plt.title("Galilean spiral")
plt.savefig("spiral.png")
plt.show()