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fix: preserve small rotations in quaternion logarithms #237

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fix: preserve small rotations in quaternion logarithms #237

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7 changes: 4 additions & 3 deletions spatialmath/quaternion.py
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Original file line number Diff line number Diff line change
Expand Up @@ -406,16 +406,17 @@ def log(self) -> Quaternion:
if smb.iszerovec(self._A[1:4]):
v = np.zeros((3,))
else:
v = math.acos(np.clip(self._A[0] / norm, -1, 1)) * smb.unitvec(
# atan2 retains small angles when s / norm rounds to one.
v = math.atan2(smb.norm(self._A[1:4]), self._A[0]) * smb.unitvec(
self._A[1:4]
)
return Quaternion(s=s, v=v)
else:
v = [
np.zeros((3,))
if smb.iszerovec(A[1:4])
else math.acos(np.clip(A[0] / n, -1, 1)) * smb.unitvec(A[1:4])
for A, n in zip(self._A, norm)
else math.atan2(smb.norm(A[1:4]), A[0]) * smb.unitvec(A[1:4])
for A in self._A
]
return Quaternion(s=s, v=np.array(v))

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50 changes: 50 additions & 0 deletions tests/test_quaternion.py
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Original file line number Diff line number Diff line change
Expand Up @@ -943,6 +943,56 @@ def test_log(self):
self.assertIsInstance(qq, UnitQuaternion)
nt.assert_array_almost_equal(qq.vec, np.r_[1, 0, 0, 0])

def test_log_small_rotation(self):
axis = np.array([1.0, -2.0, 3.0]) / math.sqrt(14)
for angle in (1e-12, -1e-9, 1e-7, 1e-4, 0.3):
for scale in (1.0, 3.0):
with self.subTest(angle=angle, scale=scale):
values = scale * np.r_[cos(angle / 2), sin(angle / 2) * axis]
q = UnitQuaternion(values) if scale == 1 else Quaternion(values)
original = q.vec.copy()
qlog = q.log()
nt.assert_allclose(qlog.v, angle / 2 * axis, rtol=1e-13, atol=0)
self.assertAlmostEqual(qlog.s, math.log(scale))
nt.assert_allclose(qlog.exp().vec, q.vec, rtol=1e-13, atol=0)
nt.assert_array_equal(q.vec, original)

def test_log_small_rotation_sequence(self):
angles = np.array([1e-12, -1e-9, 1e-7, 0.3])
axes = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 0, 0]])
values = np.column_stack(
(np.cos(angles / 2), np.sin(angles[:, None] / 2) * axes)
)
expected = angles[:, None] / 2 * axes
for scales in (np.ones(4), np.array([2.0, 3.0, 4.0, 5.0])):
with self.subTest(scales=scales):
scaled = scales[:, None] * values
q = (
UnitQuaternion(scaled)
if np.all(scales == 1)
else Quaternion(list(scaled))
)
original = q.vec.copy()
qlog = q.log()
self.assertEqual(len(qlog), len(q))
nt.assert_allclose(qlog.v, expected, rtol=1e-13, atol=0)
nt.assert_allclose(qlog.s, np.log(scales), atol=1e-15)
for i in range(len(q)):
nt.assert_allclose(qlog[i].exp().vec, scaled[i], rtol=1e-13, atol=0)
nt.assert_allclose(qlog[i].vec, q[i].log().vec, rtol=1e-13, atol=0)
nt.assert_array_equal(q.vec, original)

def test_log_near_negative_real(self):
# Keep the principal quaternion branch near pi, rather than folding
# a negative scalar part onto the small-angle branch.
angle = 1e-7
q = Quaternion([-cos(angle), sin(angle), 0, 0])
expected = np.r_[0, pi - angle, 0, 0]
nt.assert_allclose(q.log().vec, expected, rtol=0, atol=1e-15)
nt.assert_allclose(
Quaternion([q, q]).log().vec, [expected, expected], rtol=0, atol=1e-15
)

def test_concat(self):
u = Quaternion()
uu = Quaternion([u, u, u, u])
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