How to plot a 3D function with colors given spacing 2D input - matplotlib

Question

Let's assume I have 3 arrays defined as:
v1=np.linspace(1,100)
v2=np.linspace(1,100)
v3=np.linspace(1,100)   
Then I have a function that takes those 3 values and gives me the desired output, let's assume it is like:
f = (v1 + v2*10)/v3
I want to plot that function on a 3D plot with axis v1,v2,v3 and color it's surface depending on its value.
More than the best way to plot it, I was also interested in how to scroll all the values in the in vectors and build the function point by point.
I have been trying with for loops inside other for loops but I am always getting one error.
MANY THANKS
I tried this but i'm always getting a line instead of a surface
import mpl_toolkits.mplot3d.axes3d as axes3d
import sympy
from sympy import symbols, Function
# Parameters I use in the function
L = 132
alpha = 45*math.pi/180
beta = 0
s,t = symbols('s,t')
z = Function('z')(s,t)
figure = plt.figure(figsize=(8,8))
ax = figure.add_subplot(1, 1, 1, projection='3d')
# experiment with various range of data in x and y
x1 = np.linspace(-40,-40,100)
y1 = np.linspace(-40,40,100)
x,y = np.meshgrid(x1,y1)
# My function Z
c1=math.cos(beta)**2
c2=math.cos(alpha)**2
s1=math.sin(alpha)**2
den = math.sqrt((c1*c2)+s1)
z=L*((math.cos(beta)/den)-1)+(s*(math.sin(alpha)))+(t*(1-math.cos(alpha)))
ax.plot_surface(x,y,z,cmap='rainbow')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
plt.show()

Answer 1

In this example I'm going to show you how to achieve your goal. Specifically, I use Numpy because it supports vectorized operations, hence I avoid for loops.
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import Normalize
import matplotlib.cm as cm
# Parameters I use in the function
L = 132
alpha = 45*np.pi/180
beta = 0
figure = plt.figure()
ax = figure.add_subplot(1, 1, 1, projection='3d')
# experiment with various range of data in x and y
x1 = np.linspace(-40,40,100)
y1 = np.linspace(-40,40,100)
x,y = np.meshgrid(x1,y1)
# My function Z
c1=np.cos(beta)**2
c2=np.cos(alpha)**2
s1=np.sin(alpha)**2
den = np.sqrt((c1*c2)+s1)
z=L*((np.cos(beta)/den)-1)+(x*(np.sin(alpha)))+(y*(1-np.cos(alpha)))
# compute the color values according to some other function
color_values = np.sqrt(x**2 + y**2 + z**2)
# normalize color values between 0 and 1
norm = Normalize(vmin=color_values.min(), vmax=color_values.max())
norm_color_values = norm(color_values)
# chose a colormap and create colors starting from the normalized values
cmap = cm.rainbow
colors = cmap(norm_color_values)
surf = ax.plot_surface(x,y,z,facecolors=colors)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
# add a colorbar
figure.colorbar(cm.ScalarMappable(norm=norm, cmap=cmap), label="radius")
plt.show()