A 3D Scatter Plot is a mathematical diagram that visualizes data points in three dimensions, allowing us to observe relationships between three variables of a dataset. Matplotlib provides a built-in toolkit called mplot3d, which enables three-dimensional plotting. To create a 3D Scatter Plot, we use the ax.scatter3D() function from Matplotlib's mplot3d module. This function requires three sets of values—X, Y, and Z coordinates—to define the position of each point in the 3D space. Example:

The following example demonstrates how to create a simple 3D scatter plot using ax.scatter3D().

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

np.random.seed(42)
x = np.random.rand(50)
y = np.random.rand(50)
z = np.random.rand(50)

# Create a figure and 3D axis
fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot(111, projection='3d')

# Create scatter plot
ax.scatter3D(x, y, z, color='red', marker='o')

# Labels
ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
ax.set_title('Basic 3D Scatter Plot')


plt.show()

Output:

Explanation: In this example, we generate three sets of random data and use scatter3D() to visualize them in a 3D space. The points are marked in red with circular markers.

Installation and setup

Before proceeding, ensure you have Matplotlib installed. If not, install it using:

pip install matplotlib

Now, let's explore various examples to understand how 3D scatter plots work.

Example 1: 3D Scatter Plot with Color Mapping

To enhance visualization, we can use color mapping based on the Z-values of the data points.

x = np.random.rand(100)
y = np.random.rand(100)
z = np.random.rand(100)
colors = z  # Color mapped to z-values

# Create figure and 3D axis
fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot(111, projection='3d')

# Scatter plot with color mapping
sc = ax.scatter3D(x, y, z, c=colors, cmap='viridis', marker='^')
plt.colorbar(sc, ax=ax, label='Z Value')

# Labels
ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
ax.set_title('3D Scatter Plot with Color Mapping')

plt.show()

Output:

Explanation: In this example, colors of the points are assigned based on the Z-values using the viridis colormap, making it easier to interpret variations in the dataset.

Example 2: 3D Scatter Plot with Different Markers and Sizes

To improve visualization, we can use different markers and vary the size of the points based on another dataset.

x = np.random.rand(100)
y = np.random.rand(100)
z = np.random.rand(100)
sizes = 100 * np.random.rand(100)  # Size of markers
colors = np.random.rand(100)  # Color variation

# Create figure and 3D axis
fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot(111, projection='3d')

# Scatter plot with varying marker size and colors
sc = ax.scatter3D(x, y, z, s=sizes, c=colors, cmap='coolwarm', alpha=0.7, marker='D')
plt.colorbar(sc, ax=ax, label='Color Mapping')

# Labels
ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
ax.set_title('3D Scatter Plot with Different Markers and Sizes')

plt.show()

Output:

Explanation: Here, we adjust marker sizes randomly to improve visualization and use the coolwarm colormap to enhance the color distribution.

Example 3: Customization and additional features

This example demonstrates how to create a 3D surface plot using matplotlib and numpy while incorporating customization options to enhance visualization. The code plots a 3D function and applies various modifications, such as adjusting the viewing angle, enabling the grid and changing the background color.

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

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

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))

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

# Customization
ax.view_init(elev=30, azim=60)  # Adjust view angle
ax.grid(True)  # Add grid
ax.set_facecolor('lightgray')  # Set background color

plt.show()

Output:

Explanation: This code creates a 3D surface plot using Matplotlib. It generates X, Y coordinates using meshgrid. The surface is plotted with a viridis colormap. Customizations include adjusting the viewing angle, enabling the grid and changing the background color for better visualization.