Is there any Python library/function in order to print in 3D the function "weight"
weight(x,y,z) = x**(y*z) + y**(x*z) + z**(x*y)
with Python and Matplotlib ?
Here is already an interesting link How to plot a 3D density map in python with matplotlib but it shows a density instead of a weight for distributed coordinates X Y Z, for example from -5 to +5 with regular steps 0.1 (where solutions for the weight exists in real numbers).
I am just playing around with some math functions and wanted to show this for teaching purpose, no immediate use identified.
Update 1: achievement so far with plotly
"""
release May22 2020
https://plotly.com/python/3d-volume-plots/
"""
import plotly.graph_objects as go
import numpy as np
#X, Y, Z = np.mgrid[-5:5:40j, -5:5:40j, -5:5:40j]
X, Y, Z = np.mgrid[ 0.01:2:40j, 0.01:2:40j, 0.01:2:40j]
#
# pascal dagsi surfaces
#vol=(X**(Y*Z)) + (Y**(X*Z)) + (Z**(X*Y))
#vol=(X**(Y+Z)) + (Y**(X+Z)) + (Z**(X+Y))
#vol=(X**(Y+Z)) * (Y**(X+Z)) * (Z**(X+Y))
vol=(X**(Y*Z)) * (Y**(X*Z)) * (Z**(X*Y))
fig = go.Figure(data=go.Volume(
x=X.flatten(),
y=Y.flatten(),
z=Z.flatten(),
value=vol.flatten(),
opacity=0.1,
isomin=0.02,
isomax=100,
surface_count=22,
caps=dict(x_show=False, y_show=False, z_show=False)
))
#
fig.show()
Update 2: other variant (iso surface)
"""
release May22 2020
https://plotly.com/python/3d-isosurface-plots/
"""
import plotly.graph_objects as go
import numpy as np
#X, Y, Z = np.mgrid[-5:5:40j, -5:5:40j, -5:5:40j]
#X, Y, Z = np.mgrid[ 0.1:5:40j, 0.1:5:40j, 0.1:5:40j]
X, Y, Z = np.mgrid[ 0.01:2:40j, 0.01:2:40j, 0.01:2:40j]
#
# pascal dagsi surfaces
#values=(X**(Y*Z)) + (Y**(X*Z)) + (Z**(X*Y))
#values=(X**(Y+Z)) + (Y**(X+Z)) + (Z**(X+Y))
#values=(X**(Y+Z)) * (Y**(X+Z)) * (Z**(X+Y))
values=(X**(Y*Z)) * (Y**(X*Z)) * (Z**(X*Y))
fig = go.Figure(data=go.Isosurface(
x=X.flatten(),
y=Y.flatten(),
z=Z.flatten(),
value=values.flatten(),
opacity=0.2,
isomin=0.5,
isomax=25,
surface_count=10,
caps=dict(x_show=False, y_show=False)
))
#
fig.show()
Update 3: mayavi works
"""
release May22 2020
pascal dagsi surfaces
"""
import numpy as np
from mayavi import mlab
#
x, y, z = np.ogrid[ 0.01:2:40j, 0.01:2:40j, 0.01:2:40j]
#
#s=(x**(y*z)) + (y**(x*z)) + (z**(x*y))
#s=(x**(y+z)) + (y**(x+z)) + (z**(x+y))
#s=(x**(y+z)) * (y**(x+z)) * (z**(x+y))
s=(x**(y*z)) * (y**(x*z)) * (z**(x*y))
src = mlab.pipeline.scalar_field(s)
mlab.pipeline.iso_surface(src, contours=[0.1, 0.2, 0.5, 1, 11, 1001, 100001], opacity=0.2,colormap='magma',vmin=0.01,vmax=0.99)
mlab.axes()
mlab.show()
