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'''

=======================================================

3D voxel / volumetric plot with cylindrical coordinates

=======================================================

Demonstrates using the ``x, y, z`` arguments of ``ax.voxels``.

'''

import matplotlib.pyplot as plt

import matplotlib.colors

import numpy as np

from mpl_toolkits.mplot3d import Axes3D

def midpoints(x):

sl = ()

for i in range(x.ndim):

x = (x[sl + np.index_exp[:-1]] + x[sl + np.index_exp[1:]]) / 2.0

sl += np.index_exp[:]

return x

# prepare some coordinates, and attach rgb values to each

r, theta, z = np.mgrid[0:1:11j, 0:np.pi*2:25j, -0.5:0.5:11j]

x = r*np.cos(theta)

y = r*np.sin(theta)

rc, thetac, zc = midpoints(r), midpoints(theta), midpoints(z)

# define a wobbly torus about [0.7, *, 0]

sphere = (rc - 0.7)**2 + (zc + 0.2*np.cos(thetac*2))**2 < 0.2**2

# combine the color components

hsv = np.zeros(sphere.shape + (3,))

hsv[..., 0] = thetac / (np.pi*2)

hsv[..., 1] = rc

hsv[..., 2] = zc + 0.5

colors = matplotlib.colors.hsv_to_rgb(hsv)

# and plot everything

fig = plt.figure()

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

ax.voxels(x, y, z, sphere,

facecolors=colors,

edgecolors=np.clip(2*colors - 0.5, 0, 1), # brighter

linewidth=0.5)

plt.show()

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