Matplotlib - 3D Lines

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A 3D line is used to represent a straight path in three-dimensional space. It has length but no width or thickness. It is defined by three coordinates: one for the x-axis, one for the y-axis, and one for the z-axis.

You can imagine it as a straight trail in the air that goes in any direction: left, right, up, down, or diagonally. That trail represents a 3D line −

3D Lines in Matplotlib

In Matplotlib, a 3D line refers to a visual representation of a sequence of data points in a three-dimensional space. We can use the plot() function within the "mpl_toolkits.mplot3d" module in Matplotlib to create 3D lines.

This function takes arrays of X, Y, and Z coordinates and connects the points with lines, producing a continuous path through the 3D space.

Lets start by drawing a basic 3D line plot.

Basic 3D Line Plot

A basic 3D line plot in Matplotlib is a way to visually represent a sequence of data points in a three-dimensional space. Imagine a series of connected dots forming a continuous line, but now extending not only in the horizontal (X) and vertical (Y) directions but also into a third dimension (Z).

Each dot on the line corresponds to a specific set of coordinates (X, Y, Z), and the line connects these points, creating a path through the 3D space.

Example

In the following example, we are drawing a basic 3D line plot. We generate 3D data by parameterizing the x, y, and z coordinates based on time (t). The resulting plot is a 3D line that traces the motion of a point in space as it moves along a sinusoidal path −

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

# Generating 3D data
t = np.linspace(0, 20, 100)
x = np.sin(t)
y = np.cos(t)
z = t

# Creating a 3D line plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(x, y, z, label='3D Line')

ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
ax.set_title('Basic 3D Line Plot')
plt.legend()
plt.show()

Output

Following is the output of the above code −

Multiple 3D Lines

Multiple 3D lines in Matplotlib allow you to show more than one continuous path through a three-dimensional space on the same plot. Each line has its own unique path through the X, Y, and Z axes, and together, they create a network of interconnected lines.

Example

In here, we are generating 3D data for two lines by parameterizing their x, y, and z coordinates based on time (t). The resulting plot shows two lines in three-dimensional space: one solid line (Line 1) and another dashed line (Line 2) that is a scaled-down version of the first −

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

# Generating 3D data for multiple lines
t = np.linspace(0, 20, 100)
x1, x2 = np.sin(t), 0.8 * np.sin(t)
y1, y2 = np.cos(t), 0.8 * np.cos(t)
z1, z2 = t, 0.8 * t

# Creating multiple 3D lines plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(x1, y1, z1, label='Line 1')
ax.plot(x2, y2, z2, label='Line 2', linestyle='dashed')

ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
ax.set_title('Multiple 3D Lines Plot')
plt.legend()
plt.show()

Output

Output of the above code is as follows −

Helix 3D Line

A helix 3D Line in Matplotlib is like drawing a spring or coil in a three-dimensional space. This visual representation creates a continuous curve that twists and turns in three directions: X, Y, and Z. You can easily generate this helical 3D line plot with Matplotlib's plot() function.

Example

The following example generates 3D data for a helix by parameterizing the x, y, and z coordinates based on time (t). The resulting plot displays a 3D line representing a helix in three-dimensional space.

The x and y coordinates are determined by the cosine and sine functions, creating a circular pattern, while the z coordinate increases linearly with time −

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

# Generating helix 3D data
t = np.linspace(0, 10 * np.pi, 1000)
x = np.cos(t)
y = np.sin(t)
z = t

# Creating a helix 3D line plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(x, y, z, label='Helix 3D Line', color='green')

ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
ax.set_title('Helix 3D Line Plot')
plt.legend()
plt.show()

Output

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

Parametric 3D Line

A parametric 3D line in Matplotlib is a visual representation of a curve where each point is determined by a set of mathematical parameters. Instead of being defined by traditional X, Y, and Z coordinates, this type of line is created by using a set of equations that describe how each coordinate evolves based on a parameter.

Example

Now, we are generating parametric 3D data by parameterizing the x, y, and z coordinates based on the angle "theta". The resulting plot is a 3D line representing a circular path in three-dimensional space.

The x and y coordinates are determined by the cosine and sine functions, creating a circular pattern, while the z coordinate increases linearly with the angle theta −

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

# Generating parametric 3D data
theta = np.linspace(0, 2 * np.pi, 100)
x = np.cos(theta)
y = np.sin(theta)
z = theta

# Creating a parametric 3D line plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(x, y, z, label='Parametric 3D Line')

ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
ax.set_title('Parametric 3D Line Plot')
plt.legend()
plt.show()

Output

The output obtained is as shown below −