import matplotlib.pyplot as plt
import numpy as np

def height(x, y, r = [1, 1]):
    return - r[0] * np.log(abs(x)) - r[1] * np.log(abs(y))

fig, ax = plt.subplots(subplot_kw={'projection': '3d', 'computed_zorder': False})

x = np.arange(-0.5, 1.5, 0.01)
y = np.arange(-1, 1, 0.01)
X, Y = np.meshgrid(x, y)
z = X + 1j*Y
ax.plot_surface(X, Y, height(z, 1 - z), zorder=0)

ax.scatter(0.5, 0, height(1/2, 1/2), color='red')

theta = np.arange(0, 2 * np.pi, 0.01)
r = 1/10
z = r*np.e**(1j*theta)
x = np.real(z)
y = np.imag(z)
ax.plot(x, y, height(z, 1 - z), c='red')

r = 1/5
z = r*np.e**(1j*theta)
x = np.real(z)
y = np.imag(z)
ax.plot(x, y, height(z, 1 - z), c='red')

r = 1/2
z = r*np.e**(1j*theta)
x = np.real(z)
y = np.imag(z)
ax.plot(x, y, height(z, 1 - z), c='red')

ax.set_zlim([0, 3])
fig.set_figwidth(10)
fig.set_figheight(10)
plt.tight_layout()

plt.savefig("height_of_binomial_different_v.png")