#!/usr/bin/python
# -*- coding: utf8 -*-

import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
from math import *

code_website = 'http://commons.wikimedia.org/wiki/User:Geek3/mplwp'
try:
    import mplwp
except ImportError, er:
    print 'ImportError:', er
    print 'You need to download mplwp.py from', code_website
    exit(1)

name = 'mplwp_Euler_spiral.svg'
fig = mplwp.fig_standard(mpl)

xlim = -1.45,1.45; fig.gca().set_xlim(xlim)
ylim = -1,1; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

from scipy.special import fresnel
t = np.linspace(-6, 6, 10001)

fx = lambda x: sqrt(pi/2) * fresnel(sqrt(2/pi)*x)[1]
fy = lambda x: sqrt(pi/2) * fresnel(sqrt(2/pi)*x)[0]
x = [fx(tt) for tt in t]
y = [fy(tt) for tt in t]
plt.plot(x, y, label='x=C,   y=S')

plt.plot([-sqrt(pi/8), sqrt(pi/8)], [-sqrt(pi/8), sqrt(pi/8)],
    linestyle='none', marker='o', markersize=32, markeredgecolor='none',
    markerfacecolor=fig.gca().lines[-1].get_color())

plt.legend(loc='upper left').get_frame().set_alpha(0.9)

plt.savefig(name)
mplwp.postprocess(name)