Euler Angles

Any rotation can be represented by three consecutive rotations about three basis vectors. Here we use the extrinsic xyz convention.

import numpy as np
import matplotlib.pyplot as plt
from pytransform3d import rotations as pr
from pytransform3d.plot_utils import remove_frame


alpha, beta, gamma = 0.5 * np.pi, 0.5 * np.pi, 0.5 * np.pi
p = np.array([1, 1, 1])

plt.figure(figsize=(5, 5))

ax = pr.plot_basis(R=np.eye(3), p=-1.5 * p, ax_s=2)
pr.plot_axis_angle(ax, [1, 0, 0, alpha], -1.5 * p)

pr.plot_basis(
    ax, pr.active_matrix_from_extrinsic_euler_xyz([alpha, 0, 0]), -0.5 * p)
pr.plot_axis_angle(ax, [0, 1, 0, beta], p=-0.5 * p)

pr.plot_basis(
    ax, pr.active_matrix_from_extrinsic_euler_xyz([alpha, beta, 0]), 0.5 * p)
pr.plot_axis_angle(ax, [0, 0, 1, gamma], 0.5 * p)

pr.plot_basis(
    ax,
    pr.active_matrix_from_extrinsic_euler_xyz([alpha, beta, gamma]), 1.5 * p,
    lw=5)

remove_frame(ax)

plt.show()