Drawing a sliced sphere

sphere.py

import matplotlib.pyplot as plt
from matplotlib import cm, colors
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from matplotlib.patches import FancyArrowPatch
from mpl_toolkits.mplot3d import proj3d

class Arrow3D(FancyArrowPatch):
    def __init__(self, xs, ys, zs, *args, **kwargs):
        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)
        self._verts3d = xs, ys, zs

    def draw(self, renderer):
        xs3d, ys3d, zs3d = self._verts3d
        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
        self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))
        FancyArrowPatch.draw(self, renderer)

plt.style.use('ggplot')

gg_blue=plt.rcParams['axes.color_cycle'][1]
gg_color=plt.rcParams['axes.color_cycle'][2]

# Create a sphere
r = 1
pi = np.pi
cos = np.cos
sin = np.sin
theta, phi = np.mgrid[0.0:pi:17j, pi/2:2.0*pi:25j]
theta1, phi1 = np.mgrid[pi/2:pi:9j, 0:pi/2:9j]

x = r*sin(theta)*cos(phi)
y = r*sin(theta)*sin(phi)
z = r*cos(theta)

x1 = r*sin(theta1)*cos(phi1)
y1 = r*sin(theta1)*sin(phi1)
z1 = r*cos(theta1)

theta_=np.pi/6
phi_=np.pi/3
xx=np.array([r*sin(theta_)*cos(phi_),r*sin(theta_)*cos(phi_),0])
yy=np.array([r*sin(theta_)*sin(phi_),r*sin(theta_)*sin(phi_),0])
zz=np.array([r*cos(theta_),0,0])

a_x = Arrow3D([0, 1.15], [0, 0], [0, 0], mutation_scale=20, lw=2, arrowstyle="-|>", color="k")
a_y = Arrow3D([0, 0], [0, 1.15], [0, 0], mutation_scale=20, lw=2, arrowstyle="-|>", color="k")
a_z = Arrow3D([0, 0], [0, 0], [0, 1.15], mutation_scale=20, lw=2, arrowstyle="-|>", color="k")
w_0 = Arrow3D([0, 0], [0, 0], [0, 1], mutation_scale=20, lw=2, arrowstyle="-|>", color="k")
w_f = Arrow3D([0, r*sin(theta_)*cos(phi_)], [0, r*sin(theta_)*sin(phi_)], [0, r*cos(theta_)], mutation_scale=20, lw=2, arrowstyle="-|>", color=gg_blue)

r_a = 0.2

angle_theta = Arrow3D([0, r_a*sin(theta_)*cos(phi_)], [0, r_a*sin(theta_)*sin(phi_)], [r_a, r_a*cos(theta_)], mutation_scale=20, lw=2, arrowstyle="-|>", color="k")
angle_phi = Arrow3D([0.5*r_a, r_a*sin(theta_)*cos(phi_)], [0, r_a*sin(theta_)*sin(phi_)], [0, 0], mutation_scale=20, lw=2, arrowstyle="-|>", color="k")

#Set colours and render
fig = plt.figure(figsize=(20, 20))
ax = fig.add_subplot(111, projection='3d')
ax.view_init(50,20)
ax.set_axis_bgcolor('white')

ax.plot(xx,yy,zz, linestyle='--', color='k', linewidth=0.5)

ax.plot_surface(x, y, z,  rstride=1, cstride=1, color=gg_color, alpha=0.5, linewidth=0.2)
ax.plot_surface(x1, y1, z1,  rstride=1, cstride=1, color=gg_color, alpha=0.5, linewidth=0.2)

ax.set_axis_off()
ax.text(0.2, 0.03, 0, "$\phi_0$", color='k',fontsize=20)
ax.text(0, 0.02, 0.2, "$\\theta_0$", color='k',fontsize=20)

ax.text(0, 0.02, 0.85, "$\Omega_0$", color='k',fontsize=20)
ax.text(r*sin(theta_)*cos(phi_), r*sin(theta_)*sin(phi_), r*cos(theta_), "$\Omega_f$", color=gg_blue,fontsize=20)

ax.add_artist(a_x)
ax.add_artist(a_y)
ax.add_artist(a_z)
ax.add_artist(w_0)
ax.add_artist(w_f)
ax.add_artist(angle_theta)
ax.add_artist(angle_phi)

ax.text(1.25, 0, 0, "$x$", color='k',fontsize=30)
ax.text(0, 1.15, 0, "$y$", color='k',fontsize=30)
ax.text(0, 0, 1.2, "$z$", color='k',fontsize=30)

ax.set_xlim([-1,1])
ax.set_ylim([-1,1])
ax.set_zlim([-1,1])
ax.set_aspect("equal")