def test_random(self):
"""Generation from various args"""
s = (3, 4)
np.random.seed(0)
q = random.rand(s[0], s[1])
self.assertTrue(q.shape == s + (4, ))
self.assertTrue(np.allclose(norm(q), 1))
q = random.rand()
self.assertTrue(q.shape == (4, ))
def test_davenport(self):
"""Perform a rotation and ensure that we can recover it"""
np.random.seed(0)
for i in range(1, 12):
num_points = 2**i
points = np.random.rand(num_points, 3)
rotation = random.rand(1)
translation = np.random.rand(1, 3)
transformed_points = rotate(rotation, points) + translation
q, t = mapping.davenport(points, transformed_points)
# In the case of just two points, the mapping is not unique,
# so we don't check the mapping itself, just the result.
if i > 1:
self.assertTrue(
np.logical_or(
np.allclose(rotation, q),
np.allclose(rotation, -q),
))
self.assertTrue(np.allclose(translation, t))
self.assertTrue(
np.allclose(transformed_points,
rotate(q, points) + t))
def test_equivalent(self):
"""Perform a rotation and ensure that we can recover it"""
# Test on an octahedron
points = [[1, 0, 0], [-1, 0, 0], [0, 1, 0], [0, -1, 0], [0, 0, 1],
[0, 0, -1]]
# This is just a selected subset
eq = [
from_axis_angle([0, 0, 1], a)
for a in [0, np.pi / 2, np.pi, 3 * np.pi / 2]
]
np.random.seed(0)
rotation = random.rand(1)
translation = np.random.rand(1, 3)
transformed_points = rotate(rotation, points) + translation
q, t = mapping.procrustes(points,
transformed_points,
equivalent_quaternions=eq)
# Sort the points in a deterministic manner for comparison
recovered_points = rotate(q, points) + t
ordered_recovered_points = recovered_points[np.argsort(
recovered_points[:, 0])]
ordered_transformed_points = transformed_points[np.argsort(
transformed_points[:, 0])]
self.assertTrue(
np.allclose(ordered_recovered_points, ordered_transformed_points))