3D Contour plot from data using Mayavi / Python

Question

I would like to do a 3D contour plot using Mayavi in exactly the same way as the third figure on this page (a hydrogen electron cloud model) :

http://www.sethanil.com/py

Answer 1

You can use delaunay3d filter to create cells from points. Then you can create an iso_surface() for the output UnstructuredGrid of delaunay3d. If you want ImageData, you can use image_data_probe filter.

import numpy as np
from tvtk.api import tvtk
from mayavi import mlab

points = np.random.normal(0, 1, (1000, 3))
ug = tvtk.UnstructuredGrid(points=points)
ug.point_data.scalars = np.sqrt(np.sum(points**2, axis=1))
ug.point_data.scalars.name = "value"
ds = mlab.pipeline.add_dataset(ug)
delaunay = mlab.pipeline.delaunay3d(ds)
iso = mlab.pipeline.iso_surface(delaunay)
iso.actor.property.opacity = 0.1
iso.contour.number_of_contours = 10
mlab.show()

Answer 2

The trick is to interpolate over a grid before you plot - I'd use scipy for this. Below R is a (500,3) array of XYZ values and V is the "magnitude" at each XYZ point.

from scipy.interpolate import griddata
import numpy as np

# Create some test data, 3D gaussian, 200 points
dx, pts = 2, 100j

N = 500
R = np.random.random((N,3))*2*dx - dx
V = np.exp(-( (R**2).sum(axis=1)) )

# Create the grid to interpolate on
X,Y,Z = np.mgrid[-dx:dx:pts, -dx:dx:pts, -dx:dx:pts]

# Interpolate the data
F = griddata(R, V, (X,Y,Z))

From here it's a snap to display our data:

from mayavi.mlab import *
contour3d(F,contours=8,opacity=.2 )

This gives a nice (lumpy) Gaussian.

Take a look at the docs for griddata, note that you can change the interpolation method. If you have more points (both on the interpolated grid, and on the data set), the interpolation gets better and better represents the underlying function you're trying to illustrate. Here is the above example at 10K points and a finer grid: