3D Voxel Plot | Matplotlib | Cylindrical Coordinates

Introduction

In this lab, you will learn how to create a 3D voxel plot using cylindrical coordinates in Matplotlib. The plot will demonstrate how to use the x, y, and z parameters of .Axes3D.voxels to create a 3D voxel plot.

VM Tips

After the VM startup is done, click the top left corner to switch to the Notebook tab to access Jupyter Notebook for practice.

Sometimes, you may need to wait a few seconds for Jupyter Notebook to finish loading. The validation of operations cannot be automated because of limitations in Jupyter Notebook.

If you face issues during learning, feel free to ask Labby. Provide feedback after the session, and we will promptly resolve the problem for you.

Import Libraries

The first step is to import the necessary libraries for this lab. We will be using matplotlib.pyplot, numpy, and matplotlib.colors.

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.colors

Define Midpoints Function

Next, we define a midpoints function to calculate the midpoints of an array of coordinates. This function will be used later to calculate the midpoints of r, theta, and z.

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

Define Coordinates and RGB Values

In this step, we define the coordinates r, theta, and z, 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)

Create the 3D Voxel Plot

Now we create the 3D voxel plot using the ax.voxels function. We pass in x, y, z, and sphere as the parameters. We also add facecolors and edgecolors using the colors array we defined earlier.

ax = plt.figure().add_subplot(projection='3d')
ax.voxels(x, y, z, sphere,
          facecolors=colors,
          edgecolors=np.clip(2*colors - 0.5, 0, 1),  ## brighter
          linewidth=0.5)

Display the Plot

Finally, we display the plot using the plt.show() function.

plt.show()

Summary

In this lab, you learned how to create a 3D voxel plot using cylindrical coordinates in Matplotlib. You also learned how to define coordinates and RGB values and how to create a 3D voxel plot using the ax.voxels function.

Creating 3D Voxel Plots in Matplotlib