Best way to plot a 3D matrix in python

Question

I am trying to visualize 3D data. This is a full 3D matrix: each (x,y,z) coordinate has a value, unlike a surface or a collection of individual data vectors. The way I am trying to do this is to plot an opaque cube, where each edge of the cube shows the sum of the data over the orthogonal dimension.

Some example data -- basically, a blob centered at (3,5,7):

import numpy as np
(x,y,z) = np.mgrid[0:10,0:10, 0:10]
data = np.exp(-((x-3)**2 + (y-5)**2 + (z-7)**2)**(0.5))
edge_yz = np.sum(data,axis=0)
edge_xz = np.sum(data,axis=1)
edge_xy = np.sum(data,axis=2)

So the idea would be here to generate a 3D plot that showed a cube; each surface of the cube would show the appropriate 2D matrix edge_*. This would be like plotting 3 4-sided polygons at the appropriate 3D positions (or 6 if you did the back sides of the cube as well) except that each polygon is actually a matrix of values to be plotted in color.

My best approximation at the moment is to compute larger matrices that contained skewed versions of edge, and concatenate these into a single, larger 2D matrix, and imshow() that larger matrix. Seems pretty clumsy, and does a lot of work that some engine in matplotlib or m3plot or something I'm sure already does. It also only works to view a static image at a single view angle, but that's not something I need to overcome at the moment.

Is there a good way to plot these cube edges in a true 3D plot using an existing python tool? Is there a better way to plot a 3D matrix?

Answer 1

Falko's suggestion to use contourf works with a bit of finagling. It's a bit limited since at least my version of contourf has a few bugs where it sometimes renders one of the planes in front of other planes it should be behind, but for now only plotting either the three front or three back sides of the cube will do:

import numpy as np
import math
import matplotlib.pyplot as plot
import mpl_toolkits.mplot3d.axes3d as axes3d

def cube_marginals(cube, normalize=False):
    c_fcn = np.mean if normalize else np.sum
    xy = c_fcn(cube, axis=0)
    xz = c_fcn(cube, axis=1)
    yz = c_fcn(cube, axis=2)
    return(xy,xz,yz)

def plotcube(cube,x=None,y=None,z=None,normalize=False,plot_front=False):
    """Use contourf to plot cube marginals"""
    (Z,Y,X) = cube.shape
    (xy,xz,yz) = cube_marginals(cube,normalize=normalize)
    if x == None: x = np.arange(X)
    if y == None: y = np.arange(Y)
    if z == None: z = np.arange(Z)

    fig = plot.figure()
    ax = fig.gca(projection='3d')

    # draw edge marginal surfaces
    offsets = (Z-1,0,X-1) if plot_front else (0, Y-1, 0)
    cset = ax.contourf(x[None,:].repeat(Y,axis=0), y[:,None].repeat(X,axis=1), xy, zdir='z', offset=offsets[0], cmap=plot.cm.coolwarm, alpha=0.75)
    cset = ax.contourf(x[None,:].repeat(Z,axis=0), xz, z[:,None].repeat(X,axis=1), zdir='y', offset=offsets[1], cmap=plot.cm.coolwarm, alpha=0.75)
    cset = ax.contourf(yz, y[None,:].repeat(Z,axis=0), z[:,None].repeat(Y,axis=1), zdir='x', offset=offsets[2], cmap=plot.cm.coolwarm, alpha=0.75)

    # draw wire cube to aid visualization
    ax.plot([0,X-1,X-1,0,0],[0,0,Y-1,Y-1,0],[0,0,0,0,0],'k-')
    ax.plot([0,X-1,X-1,0,0],[0,0,Y-1,Y-1,0],[Z-1,Z-1,Z-1,Z-1,Z-1],'k-')
    ax.plot([0,0],[0,0],[0,Z-1],'k-')
    ax.plot([X-1,X-1],[0,0],[0,Z-1],'k-')
    ax.plot([X-1,X-1],[Y-1,Y-1],[0,Z-1],'k-')
    ax.plot([0,0],[Y-1,Y-1],[0,Z-1],'k-')

    ax.set_xlabel('X')
    ax.set_ylabel('Y')
    ax.set_zlabel('Z')
    plot.show()

plot_front=True plot_front=False Other data (not shown)