import matplotlib.pyplot as plt
import numpy as np

def chicken_egg ( B, L, w, x ):
#
#    real B, the maximum breadth of the egg (y direction);
#
#    real L, the maximum length of the egg (x direction).
#
#    real w: the x-distance between the location of the maximum
#    breadth and the midpoint of the egg's length (x=0).
#
#    real x(*): sample points between -L/2 and +L/2.
#
#  Output:
#
#    real y(*): the height of the egg at each x value.
#
  import numpy as np

  top = L**2 - 4.0 * x**2
  bot =  L**2 + 8.0 * w * x + 4.0 * w**2
  y = 0.5 * B * np.sqrt ( top / bot )

  return y

n = 81
B = 1.0
L = 1.5
w = 0.25
x = np.linspace ( -L/2.0, +L/2.0, n )
y = chicken_egg ( B, L, w, x )

plt.plot ( x, y, 'r-', linewidth = 3 )
plt.plot ( x, -y, 'g-', linewidth = 3 )
plt.axis ( 'equal' )
plt.grid ( True )
plt.title ( 'Chicken egg' )
filename = 'chicken_egg.png'
plt.savefig ( filename )
print ( '  Graphics saved as "' + filename + '"' )
plt.show ( )