Three-dimensional Plotting in Python using Matplotlib

3D plots are very important tools for visualizing data that have three dimensions such as data that have two dependent and one independent variable. By plotting data in 3d plots we can get a deeper understanding of data that have three variables. We can use various matplotlib library functions to plot 3D plots.

Example Of Three-dimensional Plotting using Matplotlib

We will first start with plotting the 3D axis using the Matplotlib library. For plotting the 3D axis we just have to change the projection parameter of plt.axes() from None to 3D.

Python3

import numpy as np
import matplotlib.pyplot as plt


fig = plt.figure()
ax = plt.axes(projection='3d')

Output:

Plotting 3D axes using matplotlib

With the above syntax three -dimensional axes are enabled and data can be plotted in 3 dimensions. 3 dimension graph gives a dynamic approach and makes data more interactive. Like 2-D graphs, we can use different ways to represent to plot 3-D graphs. We can make a scatter plot, contour plot, surface plot, etc. Let’s have a look at different 3-D plots.
Graphs with lines and points are the simplest 3-dimensional graph.  We will use ax.plot3d and ax.scatter functions to plot line and point graph respectively.

3-Dimensional Line Graph Using Matplotlib

For plotting the 3-Dimensional line graph we will use the mplot3d function from the mpl_toolkits library. For plotting lines in 3D we will have to initialize three variable points for the line equation. In our case, we will define three variables as x, y, and z.  

Python3

# importing mplot3d toolkits, numpy and matplotlib
from mpl_toolkits import mplot3d
import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure()

# syntax for 3-D projection
ax = plt.axes(projection ='3d')

# defining all 3 axis
z = np.linspace(0, 1, 100)
x = z * np.sin(25 * z)
y = z * np.cos(25 * z)

# plotting
ax.plot3D(x, y, z, 'green')
ax.set_title('3D line plot geeks for geeks')
plt.show()

Output:

3D line plot graph using the matplotlib library

3-Dimensional Scattered Graph Using Matplotlib

To plot the same graph using scatter points we will use the scatter() function from matplotlib. It will plot the same line equation using distinct points. 

Python3

# importing mplot3d toolkits
from mpl_toolkits import mplot3d
import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure()

# syntax for 3-D projection
ax = plt.axes(projection ='3d')

# defining axes
z = np.linspace(0, 1, 100)
x = z * np.sin(25 * z)
y = z * np.cos(25 * z)
c = x + y
ax.scatter(x, y, z, c = c)

# syntax for plotting
ax.set_title('3d Scatter plot geeks for geeks')
plt.show()

Output:

3D point plot using Matplotlib library

Surface Graphs using Matplotlib library  

Surface graphs and Wireframes graph work on gridded data. They take the grid value and plot it on a three-dimensional surface. We will use the plot_surface() function to plot the surface plot.

Python3

# importing libraries
from mpl_toolkits import mplot3d
import numpy as np
import matplotlib.pyplot as plt

# defining surface and axes
x = np.outer(np.linspace(-2, 2, 10), np.ones(10))
y = x.copy().T
z = np.cos(x ** 2 + y ** 3)

fig = plt.figure()

# syntax for 3-D plotting
ax = plt.axes(projection='3d')

# syntax for plotting
ax.plot_surface(x, y, z, cmap='viridis',\
                edgecolor='green')
ax.set_title('Surface plot geeks for geeks')
plt.show()

Output:

Surface plot using matplotlib library

Wireframes graph using Matplotlib library  

For plotting the wireframes graph we will use the plot_wireframe() function from the matplotlib library.

Python3

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


# function for z axis
def f(x, y):
    return np.sin(np.sqrt(x ** 2 + y ** 2))

# x and y axis
x = np.linspace(-1, 5, 10)
y = np.linspace(-1, 5, 10)

X, Y = np.meshgrid(x, y)
Z = f(X, Y)

fig = plt.figure()
ax = plt.axes(projection ='3d')
ax.plot_wireframe(X, Y, Z, color ='green')
ax.set_title('wireframe geeks for geeks');

Output:

3D wireframe graph using the matplotlib library

Contour Graphs using Matplotlib library

The contour graph takes all the input data in two-dimensional regular grids, and the Z data is evaluated at every point. We use the ax.contour3D function to plot a contour graph. Contour plots are an excellent way to visualize optimization plots. 

Python3

def function(x, y):
    return np.sin(np.sqrt(x ** 2 + y ** 2))


x = np.linspace(-10, 10, 40)
y = np.linspace(-10, 10, 40)

X, Y = np.meshgrid(x, y)
Z = function(X, Y)

fig = plt.figure(figsize=(10, 8))
ax = plt.axes(projection='3d')

ax.plot_surface(X, Y, Z, cmap='cool', alpha=0.8)

ax.set_title('3D Contour Plot of function(x, y) =\
                sin(sqrt(x^2 + y^2))', fontsize=14)
ax.set_xlabel('x', fontsize=12)
ax.set_ylabel('y', fontsize=12)
ax.set_zlabel('z', fontsize=12)

plt.show()

Output:

3D contour plot of a function using matplotlib 

Plotting Surface Triangulations In Python 

The above graph is sometimes overly restricted and inconvenient. So by this method, we use a set of random draws. The function ax.plot_trisurf is used to draw this graph. It is not that clear but more flexible.

Python3

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

def f(x, y):
    return np.sin(np.sqrt(x ** 2 + y ** 2))

x = np.linspace(-6, 6, 30)
y = np.linspace(-6, 6, 30)
X, Y = np.meshgrid(x, y)
Z = f(X, Y)

tri = Triangulation(X.ravel(), Y.ravel())

fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')

ax.plot_trisurf(tri, Z.ravel(), cmap='cool', edgecolor='none', alpha=0.8)

ax.set_title('Surface Triangulation Plot of f(x, y) =\
                sin(sqrt(x^2 + y^2))', fontsize=14)
ax.set_xlabel('x', fontsize=12)
ax.set_ylabel('y', fontsize=12)
ax.set_zlabel('z', fontsize=12)

plt.show()

Output:

Surface triangulation graph of  a contour plot using matplotlib 

Plotting Möbius strip In Python 

Möbius strip also called the twisted cylinder, is a one-sided surface without boundaries. To create the Möbius strip think about its parameterization, it’s a two-dimensional strip, and we need two intrinsic dimensions. Its angle range from 0 to 2 pie around the loop and its width ranges from -1 to 1.

Python3

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

# Define the parameters of the Möbius strip
R = 2

# Define the Möbius strip surface
u = np.linspace(0, 2*np.pi, 100)
v = np.linspace(-1, 1, 100)
u, v = np.meshgrid(u, v)
x = (R + v*np.cos(u/2)) * np.cos(u)
y = (R + v*np.cos(u/2)) * np.sin(u)
z = v * np.sin(u/2)

# Create the plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# Plot the Möbius strip surface
ax.plot_surface(x, y, z, alpha=0.5)

# Set plot properties
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('Möbius Strip')

# Set the limits of the plot
ax.set_xlim([-3, 3])
ax.set_ylim([-3, 3])
ax.set_zlim([-3, 3])

# Show the plot
plt.show()

Output:

Mobius strip plot using matplotlib library