optpath.py

import numpy
from numpy import cos, sin, exp, log, pi, tan, arccos, arcsin, arctan
import matplotlib.pyplot as plt

# make a quadratic figure
plt.figure(figsize=(6, 6))

# generate 400 points between 0 and 1
t = numpy.linspace(0, 1, 40)
print 't = ', t

# plot the curve
# I think it is a circle?
# then go from 0 to 90 degrees
x = sin(t*pi/2)
y = cos(t*pi/2)

plt.plot(x, y, '-')


# if you want text, then place it like this
t_text = 60 / 180. * pi # at 60 degrees
x_text = sin(t_text)
y_text = cos(t_text)

plt.text(x_text, y_text, 'my text here')

# if you want arrows, then place them like this
x_start = 0
y_start = y_text
x_end = x_text
y_end = y_text
plt.arrow(x_start, y_start, x_end - x_start, y_end - y_start, length_includes_head=True)


# axes labels
plt.ylabel('y')
plt.xlabel('x')
# store to file
plt.savefig('optpath_cartoon.png')
plt.savefig('optpath_cartoon.pdf', bbox_inches='tight')
plt.close()

# now the second plot:

# for every possible W we want to compute the formula
# W is between 0 and 1 in y
W_y = y
# it is always 0 in x
W_x = numpy.zeros_like(W_y)

A_t = t
A_x = x
A_y = y

F_x = 0.5
F_y = 0

# compute distance between W and A
WA = ((W_x - A_x)**2 + (W_y - A_y)**2)**0.5
print WA
# compute distance between A and F
AF = ...
print AF

OP = WA + AF
plt.plot(W_y, OP)
plt.savefig('optpath.pdf', bbox_inches='tight')
plt.savefig('optpath.png', bbox_inches='tight')
plt.close()