Mastering Data Visualization with Matplotlib in Python

Chapter 6: 3D Plotting and Specialized Visualizations

🔹 1. Introduction

In this chapter, we will explore how to create 3D plots and other specialized visualizations using Matplotlib. 3D plots are essential when working with data that has three dimensions or more. Matplotlib provides support for 3D plotting using the Axes3D module, which can create 3D scatter plots, surface plots, contour plots, and more.

In addition to 3D plots, we will also cover some other specialized visualizations that can help you present complex data, such as polar plots, heatmaps, and violin plots.

By the end of this chapter, you will be able to:

• Create 3D scatter plots, surface plots, and contour plots
• Use polar coordinates to visualize circular data
• Create violin plots to visualize data distributions
• Plot heatmaps for visualizing matrices of data
• Customize and fine-tune 3D visualizations to suit your needs

🔹 2. Creating 3D Plots in Matplotlib

Matplotlib provides the Axes3D class for creating 3D plots. These plots are useful for visualizing relationships between three variables, such as 3D scatter plots or surface plots.

✅ Creating a 3D Scatter Plot

A 3D scatter plot allows you to visualize the relationship between three continuous variables by displaying data points in a three-dimensional space.

from mpl_toolkits.mplot3d import Axes3D

import matplotlib.pyplot as plt

import numpy as np

# Generate 3D data

x = np.linspace(-5, 5, 100)

y = np.linspace(-5, 5, 100)

z = np.sin(np.sqrt(x**2 + y**2))

# Create a 3D plot

fig = plt.figure()

ax = fig.add_subplot(111, projection='3d')

# Scatter plot

ax.scatter(x, y, z, color='r')

# Set labels

ax.set_xlabel('X')

ax.set_ylabel('Y')

ax.set_zlabel('Z')

plt.show()

In this example:

• ax.scatter(x, y, z, color='r') creates the 3D scatter plot.
• The projection='3d' parameter enables 3D plotting.

✅ Creating a 3D Surface Plot

A 3D surface plot is useful for visualizing a 3D surface formed by the relationship between three variables.

# Create a 3D surface plot

fig = plt.figure()

ax = fig.add_subplot(111, projection='3d')

# Surface plot

X = np.linspace(-5, 5, 100)

Y = np.linspace(-5, 5, 100)

X, Y = np.meshgrid(X, Y)

Z = np.sin(np.sqrt(X**2 + Y**2))

ax.plot_surface(X, Y, Z, cmap='viridis')

# Set labels

ax.set_xlabel('X')

ax.set_ylabel('Y')

ax.set_zlabel('Z')

plt.show()

Here:

• np.meshgrid() creates a 2D grid for X and Y values.
• ax.plot_surface(X, Y, Z, cmap='viridis') creates the 3D surface plot with the Viridis colormap.

🔹 3. Creating Contour Plots in 3D

A contour plot displays level curves of a 3D surface, showing the values of a function on a 2D plane.

✅ Creating a 3D Contour Plot

# Create a 3D contour plot

fig = plt.figure()

ax = fig.add_subplot(111, projection='3d')

# Contour plot

X = np.linspace(-5, 5, 100)

Y = np.linspace(-5, 5, 100)

X, Y = np.meshgrid(X, Y)

Z = np.sin(np.sqrt(X**2 + Y**2))

ax.contour3D(X, Y, Z, 50, cmap='inferno')

# Set labels

ax.set_xlabel('X')

ax.set_ylabel('Y')

ax.set_zlabel('Z')

plt.show()

• ax.contour3D(X, Y, Z, 50, cmap='inferno') generates a 3D contour plot, where 50 is the number of contour levels.

🔹 4. Polar Plots

Polar plots are used for visualizing data in polar coordinates (angles and radii), which is useful when analyzing data related to circular motion or periodic functions.

✅ Creating a Basic Polar Plot

# Data for plotting

angles = np.linspace(0, 2 * np.pi, 100)

radii = np.sin(angles)  # Radius based on sine function

# Create a polar plot

fig = plt.figure()

ax = fig.add_subplot(111, projection='polar')

ax.plot(angles, radii)

plt.title('Polar Plot of Sine Function')

plt.show()

In this example:

• ax = fig.add_subplot(111, projection='polar') creates a polar plot.
• The angles are the angular positions, and the radii are the radial distances.

🔹 5. Heatmaps

Heatmaps are used to represent matrix-like data visually, where the values are represented by colors.

✅ Creating a Heatmap

Heatmaps are especially useful for visualizing correlations or the density of values across a 2D grid.

# Create a 2D data matrix for the heatmap

data = np.random.rand(10, 10)

# Create a heatmap

plt.imshow(data, cmap='hot', interpolation='nearest')

plt.colorbar()  # Add a color bar

plt.title('Heatmap Example')

plt.show()

In this example:

• plt.imshow() displays a 2D matrix as an image.
• cmap='hot' applies the hot colormap to the heatmap.

🔹 6. Violin Plots

Violin plots are used to display the distribution of data, similar to a box plot, but with a rotated kernel density plot.

✅ Creating a Violin Plot

import seaborn as sns

# Create sample data

data = np.random.normal(0, 1, 100)

# Create a violin plot

sns.violinplot(data=data)

plt.title('Violin Plot')

plt.show()

• Violin plots provide insights into the distribution of data, allowing you to see the data’s distribution and density at different value ranges.

🔹 7. Summary Table