In Python, given a N_1 x N_2 x N_3 matrix containing either 0s or 1s, I would be looking for a way to display the data in 3D as a N_1 x N_2 x N_3 volume with volumic pixels (voxels) at the location of 1s.

For example, if the coordinates of 1s were [[1, 1, 1], [4, 1, 2], [3, 4, 1]], the desired output would look like this

It seems that the mplot3D module of matplotlib could have the potential to achieve this, but I haven't found any example of this kind of plot. Would anyone be aware of simple solution to tackle this issue?

Thanks a lot in advance for your help.

A. Using voxels

From matplotlib 2.1 on, there is a Axes3D.voxels function available, which pretty much does what's asked for here. It is however not very easily customized to different sizes, positions or colors.

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
N1 = 10
N2 = 10
N3 = 10
ma = np.random.choice([0,1], size=(N1,N2,N3), p=[0.99, 0.01])

fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect('equal')

ax.voxels(ma, edgecolor="k")

plt.show()

To place the voxels at different positions, see How to scale the voxel-dimensions with Matplotlib?.

B. Using Poly3DCollection

Manually creating the voxels may make the process a little bit more transparent and allows for any kind of customizations of the sizes, positions and colors of the voxels. Another advantage is that here we create a single Poly3DCollection instead of many, making this solution faster than the inbuild voxels.

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection

def cuboid_data(o, size=(1,1,1)):
    X = [[[0, 1, 0], [0, 0, 0], [1, 0, 0], [1, 1, 0]],
         [[0, 0, 0], [0, 0, 1], [1, 0, 1], [1, 0, 0]],
         [[1, 0, 1], [1, 0, 0], [1, 1, 0], [1, 1, 1]],
         [[0, 0, 1], [0, 0, 0], [0, 1, 0], [0, 1, 1]],
         [[0, 1, 0], [0, 1, 1], [1, 1, 1], [1, 1, 0]],
         [[0, 1, 1], [0, 0, 1], [1, 0, 1], [1, 1, 1]]]
    X = np.array(X).astype(float)
    for i in range(3):
        X[:,:,i] *= size[i]
    X += np.array(o)
    return X

def plotCubeAt(positions,sizes=None,colors=None, **kwargs):
    if not isinstance(colors,(list,np.ndarray)): colors=["C0"]*len(positions)
    if not isinstance(sizes,(list,np.ndarray)): sizes=[(1,1,1)]*len(positions)
    g = []
    for p,s,c in zip(positions,sizes,colors):
        g.append( cuboid_data(p, size=s) )
    return Poly3DCollection(np.concatenate(g),  
                            facecolors=np.repeat(colors,6, axis=0), **kwargs)

N1 = 10
N2 = 10
N3 = 10
ma = np.random.choice([0,1], size=(N1,N2,N3), p=[0.99, 0.01])
x,y,z = np.indices((N1,N2,N3))-.5
positions = np.c_[x[ma==1],y[ma==1],z[ma==1]]
colors= np.random.rand(len(positions),3)

fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect('equal')

pc = plotCubeAt(positions, colors=colors,edgecolor="k")
ax.add_collection3d(pc)

ax.set_xlim([0,10])
ax.set_ylim([0,10])
ax.set_zlim([0,10])
#plotMatrix(ax, ma)
#ax.voxels(ma, edgecolor="k")

plt.show()

C. Using plot_surface

Adapting a code from this answer (which is partly based on this answer), one can easily plot cuboids as surface plots.

One then can iterate over the input array and upon finding a 1 plot a cuboid at the position corresponding to the array indices.

The advantage here is that you get nice shading on the surfaces, adding to the 3D effect. A disadvantage may be that the cubes may not behave physical in some cases, e.g. they might overlap for certain viewing angles.

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt

def cuboid_data(pos, size=(1,1,1)):
    # code taken from
    # https://stackoverflow.com/a/35978146/4124317
    # suppose axis direction: x: to left; y: to inside; z: to upper
    # get the (left, outside, bottom) point
    o = [a - b / 2 for a, b in zip(pos, size)]
    # get the length, width, and height
    l, w, h = size
    x = [[o[0], o[0] + l, o[0] + l, o[0], o[0]],  
         [o[0], o[0] + l, o[0] + l, o[0], o[0]],  
         [o[0], o[0] + l, o[0] + l, o[0], o[0]],  
         [o[0], o[0] + l, o[0] + l, o[0], o[0]]]  
    y = [[o[1], o[1], o[1] + w, o[1] + w, o[1]],  
         [o[1], o[1], o[1] + w, o[1] + w, o[1]],  
         [o[1], o[1], o[1], o[1], o[1]],          
         [o[1] + w, o[1] + w, o[1] + w, o[1] + w, o[1] + w]]   
    z = [[o[2], o[2], o[2], o[2], o[2]],                       
         [o[2] + h, o[2] + h, o[2] + h, o[2] + h, o[2] + h],   
         [o[2], o[2], o[2] + h, o[2] + h, o[2]],               
         [o[2], o[2], o[2] + h, o[2] + h, o[2]]]               
    return np.array(x), np.array(y), np.array(z)

def plotCubeAt(pos=(0,0,0),ax=None):
    # Plotting a cube element at position pos
    if ax !=None:
        X, Y, Z = cuboid_data( pos )
        ax.plot_surface(X, Y, Z, color='b', rstride=1, cstride=1, alpha=1)

def plotMatrix(ax, matrix):
    # plot a Matrix 
    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            for k in range(matrix.shape[2]):
                if matrix[i,j,k] == 1:
                    # to have the 
                    plotCubeAt(pos=(i-0.5,j-0.5,k-0.5), ax=ax)            

N1 = 10
N2 = 10
N3 = 10
ma = np.random.choice([0,1], size=(N1,N2,N3), p=[0.99, 0.01])

fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect('equal')

plotMatrix(ax, ma)

plt.show()