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fix: SO3.RotatedVector returned identity for antipodal vectors #201

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fix: SO3.RotatedVector returned identity for antipodal vectors #201

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19 changes: 18 additions & 1 deletion spatialmath/pose3d.py
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Original file line number Diff line number Diff line change
Expand Up @@ -769,7 +769,24 @@ def RotatedVector(cls, v1: ArrayLike3, v2: ArrayLike3, tol=20) -> Self:
v = smb.cross(v1, v2)
s = smb.norm(v)
if abs(s) < tol * np.finfo(float).eps:
return cls(np.eye(3), check=False)
c = np.dot(v1, v2)
if c > 0:
# v1 and v2 already (anti)parallel in the same direction
return cls(np.eye(3), check=False)
# v1 and v2 point in opposite directions -- the formula below
# is singular here too (it divides by s**2), but unlike the
# c > 0 case the answer isn't identity: any 180 degree
# rotation about an axis perpendicular to v1 takes v1 to v2.
# Closed form for a 180 degree rotation about unit axis u:
# R = 2*u*u^T - I (Rodrigues at theta=pi, sin=0, cos=-1).
# Pick u by crossing v1 with whichever world axis it's least
# aligned with, so the cross product is never itself
# degenerate.
axis = np.zeros(3)
axis[np.argmin(np.abs(v1))] = 1.0
u = smb.unitvec(smb.cross(v1, axis))
R = 2 * np.outer(u, u) - np.eye(3)
return cls(R, check=False)
else:
c = np.dot(v1, v2)
V = smb.skew(v)
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13 changes: 13 additions & 0 deletions tests/test_pose3d.py
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Expand Up @@ -726,6 +726,19 @@ def test_rotatedvector(self):
Re = SO3.RotatedVector(v1, v1)
np.testing.assert_almost_equal(Re, np.eye(3))

# Antipodal case: v1 and v2 point in exactly opposite directions.
# The cross product used to find the rotation axis is zero here
# too, same as the parallel case above, but the correct answer is
# a 180 degree flip, not identity -- regression test for a bug
# where this silently returned identity instead.
for v1 in ([1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 2, 3], [-3, 1, 2]):
v1 = unitvec(v1)
v2 = [-x for x in v1]
Re = SO3.RotatedVector(v1, v2)
np.testing.assert_almost_equal(np.asarray(Re * v1).flatten(), v2)
# must actually be a 180 degree rotation, not identity
assert not np.allclose(Re.A, np.eye(3))

R = SO3() # identity matrix case

# Check log and exponential map
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