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fix: preserve small rotations in quaternion logarithms #237

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Merged
taughz merged 2 commits into from
Oct 13, 2026
Merged

fix: preserve small rotations in quaternion logarithms #237

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0555c01
fix: preserve small rotations in quaternion logarithms
dddd-jh Oct 6, 2026
0f7cf49
Preserve scaled quaternion rotations in logarithms
dddd-jh Oct 11, 2026
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Preserve scaled quaternion rotations in logarithms
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@dddd-jh @taughz
dddd-jh authored and taughz committed Oct 13, 2026
commit 0f7cf491f57101f3d3b69fb8fc7d42698991f6c4
21 changes: 10 additions & 11 deletions spatialmath/quaternion.py
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Original file line number Diff line number Diff line change
Expand Up @@ -381,6 +381,9 @@ def log(self) -> Quaternion:

\ln \| q \|, \langle \frac{\vec{v}}{\| \vec{v} \|} \cos^{-1} \frac{s}{\| q \|} \rangle

The implementation uses the equivalent :math:`\operatorname{atan2}(\|\vec{v}\|, s)`
to avoid the loss of precision in ``acos`` for small rotation angles.

For a ``UnitQuaternion`` the logarithm is a pure quaternion whose vector
part :math:`\vec{v}` and :math:`\vec{v}/2` is a Euler vector: parallel
to the axis of rotation and whose norm is the magnitude of rotation.
Expand All @@ -403,21 +406,17 @@ def log(self) -> Quaternion:
norm = self.norm()
s = np.log(norm)
if len(self) == 1:
if smb.iszerovec(self._A[1:4]):
n = math.hypot(*self._A[1:4])
if n == 0:
v = np.zeros((3,))
else:
# 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]
)
v = math.atan2(n, self._A[0]) * self._A[1:4] / n
return Quaternion(s=s, v=v)
else:
v = [
np.zeros((3,))
if smb.iszerovec(A[1:4])
else math.atan2(smb.norm(A[1:4]), A[0]) * smb.unitvec(A[1:4])
for A in self._A
]
v = []
for A in self._A:
n = math.hypot(*A[1:4])
v.append(np.zeros((3,)) if n == 0 else math.atan2(n, A[0]) * A[1:4] / n)
return Quaternion(s=s, v=np.array(v))

def exp(self, tol: float = 20) -> Quaternion:
Expand Down
8 changes: 6 additions & 2 deletions tests/test_quaternion.py
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Original file line number Diff line number Diff line change
Expand Up @@ -946,7 +946,7 @@ def test_log(self):
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):
for scale in (1.0, 3.0, 1e-6):
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)
Expand All @@ -964,7 +964,11 @@ def test_log_small_rotation_sequence(self):
(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])):
for scales in (
np.ones(4),
np.array([2.0, 3.0, 4.0, 5.0]),
1e-6 * np.ones(4),
):
with self.subTest(scales=scales):
scaled = scales[:, None] * values
q = (
Expand Down
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