Python 3.8.5 : A sphere in Cartesian coordinates - part 001.

I like the equation of a sphere of radius R centered at the origin is given in Cartesian coordinates:

x*x + y*y + z*z = r*r

It is one of the first elements that helped me better understand mathematics and later the dynamics and theory of electromagnetic fields.

I did not find a graphical representation using python as accurately as possible without eliminating the discretion of the range from -1 and 1 and radius * radius = 1.

The main reason is the plot_surface from matplotlib python package.

This is output of my script:

[mythcat@desk ~]$ python sphere_xyz.py 
[-1.         -0.91666667 -0.83333333 -0.75       -0.66666667 -0.58333333
 -0.5        -0.41666667 -0.33333333 -0.25       -0.16666667 -0.08333333
  0.          0.08333333  0.16666667  0.25        0.33333333  0.41666667
  0.5         0.58333333  0.66666667  0.75        0.83333333  0.91666667
  1.        ]
sphere_xyz.py:7: RuntimeWarning: invalid value encountered in sqrt
  return np.sqrt(1-x**2 - y**2)
sphere_xyz.py:18: UserWarning: Z contains NaN values. This may result in rendering artifacts.
  surface1 = ax.plot_surface(X2, Y2, -Z2,rstride=1, cstride=1, linewidth=0,antialiased=True)
sphere_xyz.py:19: UserWarning: Z contains NaN values. This may result in rendering artifacts.
  surface2 = ax.plot_surface(X2, Y2, Z2,rstride=1, cstride=1, linewidth=0,antialiased=True)

The image result is this:

The source code is this:

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.colors import LightSource

#@np.vectorize
def solve_Z2(x,y):
    return np.sqrt(1-x**2 - y**2)

fig = plt.figure()
ax = fig.gca(projection='3d')

xrange2 = np.linspace(-1.0, 1.0, 25)
yrange2 = np.linspace(-1.0, 1.0, 25)
print(xrange2)
X2, Y2 = np.meshgrid(xrange2, yrange2)
Z2 = solve_Z2(X2, Y2)

surface1 = ax.plot_surface(X2, Y2, -Z2,rstride=1, cstride=1, linewidth=0,antialiased=True)
surface2 = ax.plot_surface(X2, Y2, Z2,rstride=1, cstride=1, linewidth=0,antialiased=True)

plt.show()