Seaborn: 3D Plot of Surface

3D Plot of Surface

• Matplotlib provides the Axes3D module to create 3D plots. The mpl_toolkits.mplot3d library enables plotting in three dimensions.

• The add_subplot() method is used in 3D plotting.

•  ax = fig.add_subplot(111, projection='3d') does not create a 3D plot by itself. It only creates a 3D plotting area (axes) inside the figure. To actually plot something, we need to add a scatter plot or line plot using additional commands.

 

1. The 3D scatter plot

•  A 3D scatter plot is used to display data points in three dimensions (X, Y, Z). It helps visualize the relationship between three variables. Each dot represents a data point in 3D space.

Demo example

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure()

# Add a 3D subplot

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

# Generate sample data

np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

y = np.array([5, 3, 8, 12, 7, 9, 4, 6, 10, 15])

z = np.array([10, 12, 14, 8, 6, 9, 11, 7, 5, 13])

# Create a 3D scatter plot

ax.scatter(x, y, z, color='brown', marker='0')

# Set custom tick marks

ax.set_xticks([1, 3, 5, 7, 9])

ax.set_yticks([3, 6, 9, 12, 15])

ax.set_zticks([5, 7, 9, 11, 13])

ax.set_xlabel("X‒axis")

ax.set_ylabel("Y‒axis")

ax.set_zlabel("Z‒axis")

ax.set_title("Simple 3D Scatter Plot Demo")

plt.show()

Output

Simple 3D Scatter Plot Demo

Code explanation: In above code,

1) We have imported three library files

•  numpy: Helps us create and manipulate arrays (for x, y, z data).

•  matplotlib.pyplot: Used for creating plots and visualizations.

•  mpl_toolkits.mplot3d: Allows us to create 3D plots in Matplotlib.

2) plt.figure() : Creates an empty figure (window) where we can add plots.

3) fig.add_subplot(111, projection='3d'): Adds a 3D subplot inside the figure. 111 means 1 row, 1 column, and 1st (only) subplot. projection='3d' tells Matplotlib to create a 3D plot instead of the default 2D.

4) We create three arrays (x, y, z), each containing 10 values. These values represent coordinates in a 3D space. Each (x, y, z) point is one dot in the 3D scatter plot.

5) ax.scatter(x, y, z, color='brown', marker='o') : Plots brown dots (o) at (x, y, z) positions.

6) Then we set Tick marks on x,y and z axis. Tick marks are the numbers shown on the axes.

7) Then the x, y and z axis labels and title to the plot is created.

8) plt.show(): Displays the figure with the 3D scatter plot. Until we call plt.show(), nothing appears on the screen.

 

2. The 3D line plot

•  A 3D line plot connects points in 3D space, showing trends over three variables.

Demo example

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

x = [1, 2, 3, 4, 5]

y = [2, 3, 5, 7, 11]

z = [1, 4, 6, 8, 10]

fig = plt.figure()

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

ax.plot(x, y, z, marker='0')

ax.set_xlabel('X axis')

ax.set_ylabel('Y axis')

ax.set_zlabel('Z axis')

ax.set_title('Simple 3D Line Plot Demo')

plt.show()

Output

Simple 3D Line Plot Demo

Code explanation: In above code,

1) We have imported three library files

•  numpy: Helps us create and manipulate arrays (for x, y, z data).

•  matplotlib.pyplot : Used for creating plots and visualizations.

•  mpl_toolkits.mplot3d: Allows us to create 3D plots in Matplotlib.

2) plt.figure() : Creates an empty figure (window) where we can add plots.

3) fig.add_subplot(111, projection='3d'): Adds a 3D subplot inside the figure. 111 means 1 row, 1 column, and 1st (only) subplot. projection='3d' tells Matplotlib to create a 3D plot instead of the default 2D.

4) We create three arrays (x, y, z), then using ax.plot(x, y, z, marker='0') we draw a 3D line with marker for each point.

5) Then the x,y and z axis labels and title to the plot is created.

6) plt.show(): Displays the figure with the 3D line plot.

 

3. The 3D surface plot

• A surface plot is a three‒dimensional (3D) plot that shows the relationship between three continuous variables.

•  It creates a 3D surface that represents the z‒values for each pair of x and y coordinates.

•  Surface plots are commonly used to visualize complex data and identify patterns, trends, and interactions between variables.

Demo example

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

x = np.array([1, 2, 3, 4, 5])

y = np.array([1, 2, 3, 4, 5])

x, y = np.meshgrid(x, y)

z = x**3+ y**3 # Example surface

fig = plt.figure()

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

asurf = ax.plot_surface(x, y, z, cmap='plasma')

ax.set_xlabel('X axis')

ax.set_ylabel('Y axis')

ax.set_zlabel('Z axis')

ax.set_title('Simple 3D Surface Plot Demo')

plt.show()

Output

Simple 3D Surface Plot Demo

 

Example:1

Create an intriguing 3D plot where the x values stretch from 0 to 10.

Let y follow the parabolic path y = x^2.

Let z shoot up in a cubic trajectory z = x^3.

1) Draw a stunning blue line

2) Customize the tick marks on all axes to guide the path.

3) Add a stylish background color to your plot.

Solution :

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

import numpy as np

# Data for plotting

x = np.linspace(0, 10, 100)

y = x**2

z = x**3

# Create a 3D plot

fig = plt.figure()

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

# Plotting the 3D line

ax.plot(x, y, z, color='blue')

# Changing tick marks for all axes

ax.set_xticks([0, 2, 4, 6, 8, 10])

ax.set_yticks([0, 20, 40, 60, 80, 100])

ax.set_zticks([0, 200, 400, 600, 800, 1000])

# Changing the background color of the plot

ax.set_facecolor('lightgreen')

# Adding labels and title

ax.set_xlabel('X‒axis')

ax.set_ylabel('Y‒axis')

ax.set_zlabel('Z‒axis')

ax.set_title('3D Plotting Demo with Custom Ticks and Background Color')

plt.show()

Output

3D Plotting Demo with Custom Ticks and Background Color

 

Example:2

Create a 3D bar chart where:

x = [1, 2, 3, 4, 5]

y=[10, 20, 30, 40, 50]

z=0 (all bars start from height 0)

Heights of bars = [5, 10, 15, 20, 25]

Use ax.bar3d(x, y, z, dx, dy, dz) to create bars

Solution :

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

import numpy as np

x = np.array([1, 2, 3, 4, 5])

y = np.array([10, 20, 30, 40, 50])

z = np.zeros(5)  # All bars start from height 0

dx = np.ones(5)  # Width of bars

dy= np.ones(5)  # Depth of bars

dz = np.array([5, 10, 15, 20, 25])  # Heights of bars

# Create a 3D plot

fig = plt.figure()

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

# Plotting the 3D bars

ax.bar3d(x, y, z, dx, dy, dz, color='red')

# Adding labels and title

ax.set_xlabel('X‒axis')

ax.set_ylabel('Y‒axis')

ax.set_zlabel('Z‒axis')

ax.set_title('*************     3D Bar Chart Demo     ************)

# Show plot

plt.show()

Output

 

Review Question

1. How to visualize a three dimensional function in Python? Illustrate with a code.