CODEWITHSUNDEEP
pythonplotlycolormapisosurface
dolun
dolun

Reputation: 91

Mapping the color scale of 3D isosurface on a scalar field

Let's say we have some 3D complex valued function f(x,y,z). Using Plotly, I'm trying to plot isosurfaces of the magnitude |f(x,y,z)| of such function. So far, everything is OK and my code seems to do well, please find below a working example on atomic orbitals functions :

import chart_studio.plotly as py
import plotly.graph_objs as go
import scipy.special as scispe
import numpy as np
import math

a=5.29e-11          # Bohr radius (m)

def orbital(n,l,m,r,theta,phi):         # Complex function I want to plot
    L=scispe.genlaguerre(n-l-1,2*l+1)   # Laguerre polynomial
    radial= (2/(n*a))**(3/2) * np.sqrt(math.factorial(n-l-1)/(2*n*math.factorial(n+l))) * np.exp(-2*r/n) * (2*r/n)**l * L(2*r/n)
    wavefunction = radial * scispe.sph_harm(m,l, phi, theta)
    return wavefunction

#Quantum numbers
n=2
l=1
m=0

goodspan = (3 * n**2 - l * (l+1))/2   #Plot span adpated to the mean electron position
x, y, z = np.mgrid[-goodspan:goodspan:40j, -goodspan:goodspan:40j, -goodspan:goodspan:40j]    #in units of a
r = np.sqrt(x**2 + y**2 + z**2)    #Function has to be evaluated in spherical coordinates
theta = np.arccos(z/r)
phi = np.arctan(y/x)

AO=orbital(n,l,m,r,theta,phi)

magnitude = abs(AO)         # Compute the magnitude of the function
phase = np.angle(AO)        # Compute the phase of the function

isoprob = np.amax(magnitude)/2    # Set value the isosurface

fig = go.Figure(data=go.Isosurface(
    x=x.flatten(),
    y=y.flatten(),
    z=z.flatten(),
    value=magnitude.flatten(),
    opacity=0.5,
    isomin=isoprob,
    isomax=isoprob,
    surface_count=1,
    caps=dict(x_show=True, y_show=True)
    ))
fig.show()

which gives me this : enter image description here

At this point, the color scale of the graph is attributed depending on the value of the magnitude |f(x,y,z)|, so that a single isosurface is always uniform in color.

Now, instead to have a color scale mapped on the magnitude |f(x,y,z)|, I would like it to be mapped on the value of the phase Ф(x,y,z) = arg(f(x,y,z)), so that the color of each point of a ploted isosurface tells us about the value of the field Ф(x,y,z) (which would be distributed on [-π,π] ideally) instead of |f(x,y,z)| in thsi point.

Basically, I would like to do this with Plotly instead of Mayavi if it's possible.

It seems to me that all of that has something to do with a special way to set the cmin and cmax parameters of the function Isosurface, but I can't figure out how to do this.

Upvotes: 4

Views: 1076

Answers (2)

Sep
Sep

Reputation: 382

Given @Jan Joswig's answer and the link they provided, the quick/compact way of doing it will be:

import plotly.graph_objects as go
from skimage import measure
import numpy as np
xyz_shape = vol.shape
verts, faces = measure.marching_cubes(vol, .5)[:2] # iso-surface at .5 level

x, y, z = verts.T
I, J, K = faces.T

fig = go.Figure(
    data=[go.Mesh3d(
        x=x,
        y=y,
        z=z,
        color='lightpink',
        opacity=0.50,
        i=I,
        j=J,
        k=K, )])
fig.show()

Upvotes: 1

Jan Joswig
Jan Joswig

Reputation: 733

As @gnodab mentioned in his comment, plotly isosurfaces do not really support colouring the surfaces by a fifth dimension (at least there is no obvious way to do it). I am also not sure if it might be possible to extract the data describing the isosurface somehow to be re-plotted as a regular surface.

In this post, however, they describe how to generate an isosurface with skimage.measure.marching_cubes_lewiner which is then plotted and coloured by a custom colorscale with plotly as 'mesh3d' trace. This might be what you want. If I find the time, I'll give that a try and edit my answer later.

Upvotes: 1

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