#! /usr/bin/env python
"""
 This program plots the so-called deltoid curve, which is defined 
 parametrically by the equations:
         x = 2cos(theta) + cos(2theta),     y = 2sin(theta) - sin(2theta)

 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 rendering in lables
plt.rc('text', usetex=True)

# define parameters
thetaMin, thetaMax = 0, 2*np.pi
steps = 100

# Using the numpy vectorization, one can easily 
# create x & y arrays for plotting 
#
theta = np.linspace(thetaMin, thetaMax, steps)
x = 2*np.cos(theta) + np.cos(2*theta)
y = 2*np.sin(theta) - np.sin(2*theta)

# plot curve and decorate with latex equation
plt.plot(x, y)
plt.xlabel(r"$2cos(\theta) + cos(2\theta)$")
plt.ylabel(r"$2sin(\theta) - sin(2\theta)$")
plt.title("Deltroid curve")
plt.savefig("deltroid.png")
plt.show()