Compare Rotation Sampling Methods

There are different ways of sampling rotations. We draw random samples of rotations, convert them to rotation matrices, and apply these to the basis vector (1, 0, 0) to obtain points on the unit sphere.

import numpy as np
import matplotlib.pyplot as plt
import pytransform3d.rotations as pr
import pytransform3d.batch_rotations as pbr
import pytransform3d.plot_utils as ppu


rng = np.random.default_rng(1223532)
n_samples = 2000
v = np.array([1.0, 0.0, 0.0])

plt.figure(figsize=(9, 5))

ax1 = plt.subplot(121, projection="3d")
ax1.set_title("Sampled rotation vectors (axis-angle)")
ppu.plot_sphere(ax1, radius=1, n_steps=100)
rotations = np.vstack([pr.random_compact_axis_angle(rng)
                       for _ in range(n_samples)])
R = pbr.matrices_from_compact_axis_angles(rotations)
v_R = np.einsum("nij,j->ni", R, v)
ax1.scatter(v_R[:, 0], v_R[:, 1], v_R[:, 2])

ax2 = plt.subplot(122, projection="3d")
ax2.set_title("Sampled quaternions")
ppu.plot_sphere(ax2, radius=1, n_steps=100)
rotations = np.vstack([pr.random_quaternion(rng) for _ in range(n_samples)])
R = pbr.matrices_from_quaternions(rotations)
v_R = np.einsum("nij,j->ni", R, v)
ax2.scatter(v_R[:, 0], v_R[:, 1], v_R[:, 2])

plt.tight_layout()
plt.show()