Matplotlib - Wireframe Plots

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A wireframe plot is a visual representation of a design or structure. It is like the skeleton or outline of something, showing only the essential elements without details. In the context of graphics, a wireframe plot is used to sketch the basic layout and structure of a webpage, app, or other visual project.

Imagine that you are planning to build a new house. A wireframe is used to sketch out where rooms and doors will be placed. In 3D modeling, this is like defining the basic shape of a character before adding details−

Wireframe Plots in Matplotlib

We can create a wireframe plot in Matplotlib using the plot_wireframe() function. This function helps to visualize a three-dimensional wireframe plot that represents a surface using lines connecting data points. This type of plot is commonly used in scientific, engineering, and design applications.

The plot_wireframe() Function

The plot_wireframe() function in Matplotlib takes three sets of data points (X, Y, Z) representing a grid in 3D space and connects them with lines to form the wireframe structure. These data points can represent either a surface or a mathematical function in three dimensions.

Following is the syntax of plot_wireframe() function in Matplotlib −

Axes3D.plot_wireframe(X, Y, Z, rstride=1, cstride=1, antialiased=True, *args, **kwargs)

Where,

• X is the x-coordinates of the data points (2D array or meshgrid).
• Y is the y-coordinates of the data points (2D array or meshgrid).
• Z is the z-coordinaes of the data points (2D array or meshgrid).
• rstride is the row stride used for downsampling the wireframe.
• cstride is the column stride used for downsampling the wireframe.
• antialiased is a boolean indicating whether to use antialiased rendering.
• *args and **kwargs are the additional keyword arguments for customization (e.g., colors, linestyles).

Basic Wireframe Plot

Imagine a 3D landscape where the elevation is represented by a mathematical function. A basic wireframe plot shows the contours or outlines of this landscape using a mesh of lines, allowing you to observe how the landscape changes in different directions.

Example

In the following example, we are creating a simple 3D wireframe plot for the sine function over a specified 2D grid −

import matplotlib.pyplot as plt
import numpy as np

# Generating data
x = np.linspace(-5, 5, 50)
y = np.linspace(-5, 5, 50)
X, Y = np.meshgrid(x, y)
Z = np.sin(np.sqrt(X**2 + Y**2))

# Creating a basic wireframe plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(X, Y, Z, color='blue', linewidth=1)

ax.set_title('Basic Wireframe Plot')
ax.set_xlabel('X-axis')
ax.set_ylabel('Y-axis')
ax.set_zlabel('Z-axis')

plt.show()

Output

After executing the above code, we get the following output −

Wireframe Plot with Increased Density

A wireframe plot with increased density in Matplotlib refers to a three-dimensional visualization where the density of lines connecting the data points in the wireframe is increased, resulting in a more detailed representation of the underlying surface.

Example

In here, we are creating a 3D wireframe plot for the sine function, but with increased density specified by the 'rstride' and 'cstride' parameters in the plot_wireframe() function −

import matplotlib.pyplot as plt
import numpy as np

# Generating data
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))

# Creating a wireframe plot with increased density
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(X, Y, Z, rstride=10, cstride=10, color='orange', linewidth=1)

ax.set_title('Dense Wireframe Plot')
ax.set_xlabel('X-axis')
ax.set_ylabel('Y-axis')
ax.set_zlabel('Z-axis')

plt.show()

Output

Following is the output of the above code −

Multiple Wireframe Plots

Multiple wireframe plots in Matplotlib refer to creating a single figure containing subplots, each displaying a distinct three-dimensional (3D) wireframe representation. This approach allows you to compare and visualize different aspects of your data in a structured manner.

Example

Now, we are creating three wireframe plots, each representing a different mathematical function (sine, Gaussian, and hyperbolic). The add_subplot() function is used to create subplots, and the plot_wireframe() function is used to generate wireframe plots for each subplot −

import matplotlib.pyplot as plt
import numpy as np

# Generating data
x = np.linspace(-5, 5, 50)
y = np.linspace(-5, 5, 50)
X, Y = np.meshgrid(x, y)

# Sine function
Z1 = np.sin(np.sqrt(X**2 + Y**2))

# Gaussian function
Z2 = np.exp(-(X**2 + Y**2))

# Hyperbolic function
Z3 = np.sinh(np.sqrt(X**2 + Y**2))

# Creating subplots with multiple wireframe plots
fig = plt.figure(figsize=(12, 4))

# Subplot 1: Sine function
ax1 = fig.add_subplot(131, projection='3d')
ax1.plot_wireframe(X, Y, Z1, color='blue', linewidth=1)
ax1.set_title('Sine Function')

# Subplot 2: Gaussian function
ax2 = fig.add_subplot(132, projection='3d')
ax2.plot_wireframe(X, Y, Z2, color='green', linewidth=1)
ax2.set_title('Gaussian Function')

# Subplot 3: Hyperbolic function
ax3 = fig.add_subplot(133, projection='3d')
ax3.plot_wireframe(X, Y, Z3, color='orange', linewidth=1)
ax3.set_title('Hyperbolic Function')

plt.show()

Output

Output of the above code is as follows −

Parametric Surface Wireframe Plot

A parametric surface wireframe plot in Matplotlib is a three-dimensional visualization that represents a surface using parametric equations. Parametric equations define the coordinates of points on the surface in terms of one or more parameters, allowing for a wide range of complex and dynamic shapes to be visualized.

Example

In the example below, we are defining parametric equations for a torus in the "torus_parametric" function. We then generate parameter values, create a meshgrid from these parameters, and compute 3D coordinates using the parametric equations. Finally, we create a wireframe plot of the torus using the plot_wireframe() function −

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

# Parametric equations for a torus
def torus_parametric(u, v, R=1, r=0.3):
    x = (R + r * np.cos(v)) * np.cos(u)
    y = (R + r * np.cos(v)) * np.sin(u)
    z = r * np.sin(v)
    return x, y, z

# Generating parameter values
u_values = np.linspace(0, 2 * np.pi, 100)
v_values = np.linspace(0, 2 * np.pi, 100)

# Creating a meshgrid from parameter values
U, V = np.meshgrid(u_values, v_values)

# Providing coordinates using parametric equations
X, Y, Z = torus_parametric(U, V)

# Creating a parametric surface wireframe plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(X, Y, Z, color='blue', linewidth=1)

ax.set_title('Parametric Surface Wireframe (Torus)')
ax.set_xlabel('X-axis')
ax.set_ylabel('Y-axis')
ax.set_zlabel('Z-axis')

plt.show()

Output

The output obtained is as shown below −