How to rotate plotted data?

I advice you to have a look at the rotation matrix. The topic from Wikipedia is a good start! Let's implement it:

We can operate 3 rotations according the 3 axis.

Workflow:

• First, we must be sure to deal with radian angle.
• Second, we need to implement the rotation matrix
• Then we compute the rotation using the numpy.dot

np.array([np.dot(rotation_matrix, vect) for vect in zip(X, Y, Z)]) 

• Finally plot the results

Full code:

# Modules from mpl_toolkits.mplot3d import Axes3D import numpy as np import matplotlib.pyplot as plt from math import cos, sin, pi # Input angles angle_x = 90 angle_y = 90 angle_z = 90 # Conversion radian theta_x = angle_x*pi/180 theta_y = angle_y*pi/180 theta_z = angle_z*pi/180 # rotation matrix R_x = np.array([[1, 0 , 0 ], [0, cos(theta_x), -sin(theta_x)], [0, sin(theta_x), cos(theta_x)]]) R_y = np.array([[ cos(theta_y), 0, sin(theta_y)], [ 0 , 1, 0 ], [-sin(theta_y), 0, cos(theta_y)]]) R_z = np.array([[cos(theta_z), -sin(theta_z), 0], [sin(theta_z), cos(theta_z), 0], [0 , 0 , 1]]) # Compute initial curve theta = np.linspace(-4 * np.pi, 4 * np.pi, 100) Z = np.linspace(-2, 2, 100) r = Z**2 + 1 X = r * np.sin(theta) Y = r * np.cos(theta) # Compute rotation rotated_x = np.array([np.dot(R_x, vect) for vect in zip(X, Y, Z)]) rotated_y = np.array([np.dot(R_y, vect) for vect in zip(X, Y, Z)]) rotated_z = np.array([np.dot(R_z, vect) for vect in zip(X, Y, Z)]) # Extras for plotting def addExtras(ax): ax.plot(X, Y, Z, label='Initial curve') ax.set_xlabel('X Axis') ax.set_ylabel('Y Axis') ax.set_zlabel('Z Axis') plt.legend() # Create figure fig = plt.figure() # Create subplots ax = fig.add_subplot(2, 2, 1, projection='3d') addExtras(ax) ax = fig.add_subplot(2, 2, 2, projection='3d') ax.plot(rotated_x[:, 0], rotated_x[:, 1], rotated_x[:, 2], label='X+90° rotation curve') addExtras(ax) ax = fig.add_subplot(2, 2, 3, projection='3d') ax.plot(rotated_y[:, 0], rotated_y[:, 1], rotated_y[:, 2], label='Y+90° rotation curve') addExtras(ax) ax = fig.add_subplot(2, 2, 4, projection='3d') ax.plot(rotated_z[:, 0], rotated_z[:, 1], rotated_z[:, 2], label='Z+90° rotation curve') addExtras(ax) # Show results plt.show() 

Output