Using: [python] [numpy] [matplotlib] So I have a 3D array to create a scatter plot making an * n * n cube. Those points have different values of potential represented by colors.
size = 11
z = y = x = size
potential = np.zeros((z, y, x))
Positive = 10
Negative = -10
""" ------- Positive Polo --------- """
polox = poloy = poloz = [1,2]
polos=[polox,poloy,poloz]
polop = [list(x) for x in np.stack(np.meshgrid(*polos)).T.reshape(-1,len(polos))] # Positive polos list
for coord in polop:
potential[coord] = Positive
""" ------- Negative Polo --------- """
polo2x = polo2y = polo2z = [size-3,size-2]
polos2=[polo2x,polo2y,polo2z]
polon = [list(x) for x in np.stack(np.meshgrid(*polos2)).T.reshape(-1,len(polos2))] # Negative polos list
for coord in polon:
potential[coord] = Negative
I have 2 polos of values -10 and 10 at the start and the rest of the points are calculated like this: (the mean of the surrounding points, no diagonals):
for z in range(1,size):
for y in range(1,size):
for x in range(1,size):
if [z,y,x] in polop:
potential[z,y,x] = Positive # If positive polo, keeps potential
elif [z,y,x] in polon:
potential[z,y,x] = Negative # If negative polo, keeps potential
elif z!=size-1 and y!=size-1 and x!=size-1: # Sets the potential to the mean potential of neighbors
potential[z][y][x] = (potential[z][y][x+1] + potential[z][y][x-1] + potential[z][y+1][x] + potential[z][y-1][x] + potential[z+1][y][x] + potential[z-1][y][x]) / 6
And for the outer cells:
for z in range(0,size):
for y in range(0,size):
for x in range(0,size):
potential[z,y,0] = potential[z,y,2]
potential[z,0,x] = potential[z,2,x]
potential[0,y,x] = potential[2,y,x]
if z == size-1:
potential[size-1,y,x] = potential[size-3,y,x]
elif y == size-1:
potential[z,size-1,x] = potential[z,size-3,x]
elif x == size-1:
potential[z,y,size-1] = potential[z,y,size-3]
What I need is to show a surface connecting the points that have the same value interval 'same colors' (like from 0 to 2.5).
I know that there are a lot of questions like this, but I can't adapt to my code, it either doesn't show (such as this ) or it's not the same problem or it's not with python (as this one ), that's why I'm asking again. It can also be shown as a lot of subplots each with a surface.
Note: My 3D array is such that if I type print(potential[1,1,1]) it shows the value of that cell that, as you can see in the image below, is 10. And that's what I use to show the colors.
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
z,y,x = potential.nonzero()
cube = ax.scatter(x, y, z, zdir='z', c=potential[z,y,x], cmap=plt.cm.rainbow) # Plot the cube
cbar = fig.colorbar(cube, shrink=0.6, aspect=5) # Add a color bar which maps values to colors.
It would be beneficial for you to create a Minimum, Complete and Verifiable Example to make assistance easier.
It's still not clear to me how you mean to calculate your potential, nor how you mean to generate your surface, so I have included trivial functions.
The code below will generate a 3D Scatterplot of coloured points and a Surface with the average value of the colour.
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
def fn(x, y):
"""Custom fuction to determine the colour (potential?) of the point"""
return (x + y) / 2 # use average as a placeholder
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
size = 11 # range 0 to 10
# Make the 3D grid
X, Y, Z = np.meshgrid(np.arange(0, size, 1),
np.arange(0, size, 1),
np.arange(0, size, 1))
# calculate a colour for point(x,y,z)
zs = np.array([fn(x, y) for x, y in zip(np.ravel(X), np.ravel(Y))])
ZZ = zs.reshape(X.shape) # this is used below
# create the surface
xx, yy = np.meshgrid(np.arange(0, size, 1), np.arange(0, size, 1))
# Calcule the surface Z value, e.g. average of the colours calculated above
zzs = np.array([np.average(ZZ[x][y]) for x, y in zip(np.ravel(xx), np.ravel(yy))])
zz= zzs.reshape(xx.shape)
cube = ax.scatter(X, Y, Z, zdir='z', c=zs, cmap=plt.cm.rainbow)
surf = ax.plot_surface(xx, yy, zz, cmap=plt.cm.rainbow)
cbar = fig.colorbar(cube, shrink=0.6, aspect=5) # Add a color bar
plt.show()
The image generated will look something like this:
EDIT: With your additional code, I'm able to replicate your cube.
Then use the following code to generate a surface:
xx, yy = np.meshgrid(np.arange(0, size, 1), np.arange(0, size, 1))
#define potential range
min_p = 1.0
max_p = 4.0
zz = np.zeros((size, size))
for i in range(size): # X
for j in range(size): # Y
for k in range(size): # Z
p = potential[k,j,i]
if min_p < p < max_p:
zz[j][i] = p # stop at the first element to meet the conditions
break # break to use the first value in range
Then to plot this surface:
surf = ax.plot_surface(xx, yy, zz, cmap=plt.cm.rainbow)
Note: include vmin and vmax keyword args to keep the same scale, I've left those out so the surface deviations are more visible. I also set the alpha on the cube to 0.2 to make it easier to see the surface.
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