From 54fb3c895f039041e84f65cb76c044c03f47571e Mon Sep 17 00:00:00 2001
From: Huashuo Lei <139048865+wpyaoxueros@users.noreply.github.com>
Date: Sun, 18 Oct 2026 03:51:59 +0800
Subject: [PATCH 1/2] Normalize the axis in UnitQuaternion.AngVec

---
 spatialmath/quaternion.py         |  3 ++
 tests/test_angvec_nonunit_axis.py | 52 +++++++++++++++++++++++++++++++
 2 files changed, 55 insertions(+)
 create mode 100644 tests/test_angvec_nonunit_axis.py

diff --git a/spatialmath/quaternion.py b/spatialmath/quaternion.py
index 29d68de6..98bffcaa 100644
--- a/spatialmath/quaternion.py
+++ b/spatialmath/quaternion.py
@@ -1551,6 +1551,9 @@ def AngVec(
         """
         v = smb.getvector(v, 3)
         theta = smb.getunit(theta, unit, vector=False)
+        if theta == 0:
+            return cls()
+        v = smb.unitvec(v)
         return cls(
             s=math.cos(theta / 2), v=math.sin(theta / 2) * v, norm=False, check=False
         )
diff --git a/tests/test_angvec_nonunit_axis.py b/tests/test_angvec_nonunit_axis.py
new file mode 100644
index 00000000..8eb3926b
--- /dev/null
+++ b/tests/test_angvec_nonunit_axis.py
@@ -0,0 +1,52 @@
+"""Angle-axis construction preserves unit-quaternion and zero-angle contracts."""
+
+import math
+import unittest
+
+import numpy as np
+from numpy.testing import assert_allclose
+
+from spatialmath import UnitQuaternion
+from spatialmath.base import angvec2r
+
+
+class TestAngVecNonunitAxis(unittest.TestCase):
+    def test_unit_norm(self):
+        assert_allclose(np.linalg.norm(UnitQuaternion.AngVec(0.5, [1, 2, 3]).vec), 1)
+
+    def test_angle_round_trip(self):
+        theta, axis = UnitQuaternion.AngVec(0.5, [1, 2, 3]).angvec()
+        assert_allclose(theta, 0.5)
+        assert_allclose(axis, np.array([1, 2, 3]) / np.sqrt(14))
+
+    def test_rotation_matrix(self):
+        assert_allclose(
+            UnitQuaternion.AngVec(0.5, [1, 2, 3]).R,
+            angvec2r(0.5, [1, 2, 3]),
+            atol=1e-12,
+        )
+
+    def test_degrees(self):
+        assert_allclose(
+            UnitQuaternion.AngVec(90, [0, 0, 4], unit="deg").R,
+            angvec2r(math.pi / 2, [0, 0, 1]),
+            atol=1e-12,
+        )
+
+    def test_unit_axis_control(self):
+        assert_allclose(
+            UnitQuaternion.AngVec(0.5, [1, 0, 0]).vec,
+            [math.cos(0.25), math.sin(0.25), 0, 0],
+        )
+
+    def test_zero_angle_zero_axis(self):
+        assert_allclose(UnitQuaternion.AngVec(0, [0, 0, 0]).vec, [1, 0, 0, 0])
+
+    def test_zero_degrees_zero_axis(self):
+        assert_allclose(
+            UnitQuaternion.AngVec(0, [0, 0, 0], unit="deg").vec, [1, 0, 0, 0]
+        )
+
+    def test_nonzero_angle_requires_nonzero_axis(self):
+        with self.assertRaises(ValueError):
+            UnitQuaternion.AngVec(0.5, [0, 0, 0])

From 6940542e7c68dbe310cfecf80de182db8b220cd4 Mon Sep 17 00:00:00 2001
From: Huashuo Lei <139048865+wpyaoxueros@users.noreply.github.com>
Date: Mon, 19 Oct 2026 12:07:14 +0800
Subject: [PATCH 2/2] Use the scalar zero tolerance for angle-axis quaternions

---
 spatialmath/quaternion.py         |  7 ++++---
 tests/test_angvec_nonunit_axis.py | 30 ++++++++++++++++++++++++++++++
 2 files changed, 34 insertions(+), 3 deletions(-)

diff --git a/spatialmath/quaternion.py b/spatialmath/quaternion.py
index 98bffcaa..f788d738 100644
--- a/spatialmath/quaternion.py
+++ b/spatialmath/quaternion.py
@@ -1544,14 +1544,15 @@ def AngVec(
             >>> print(UQ.AngVec(0, [1,0,0]))
             >>> print(UQ.AngVec(90, [1,0,0], unit='deg'))
 
-        .. note:: :math:`\theta = 0` the result in an identity quaternion, otherwise
-            ``V`` must have a finite length, ie. :math:`|V| > 0`.
+        .. note:: If :math:`\theta` is zero within the default tolerance of
+            :func:`~spatialmath.base.vectors.iszero`, the result is an identity
+            quaternion. Otherwise, ``v`` must have a nonzero norm.
 
         :seealso: :meth:`UnitQuaternion.angvec` :meth:`UnitQuaternion.exp` :func:`~spatialmath.base.transforms3d.angvec2r`
         """
         v = smb.getvector(v, 3)
         theta = smb.getunit(theta, unit, vector=False)
-        if theta == 0:
+        if smb.iszero(theta):
             return cls()
         v = smb.unitvec(v)
         return cls(
diff --git a/tests/test_angvec_nonunit_axis.py b/tests/test_angvec_nonunit_axis.py
index 8eb3926b..22c748df 100644
--- a/tests/test_angvec_nonunit_axis.py
+++ b/tests/test_angvec_nonunit_axis.py
@@ -50,3 +50,33 @@ def test_zero_degrees_zero_axis(self):
     def test_nonzero_angle_requires_nonzero_axis(self):
         with self.assertRaises(ValueError):
             UnitQuaternion.AngVec(0.5, [0, 0, 0])
+
+    def test_near_zero_angle_zero_axis(self):
+        for theta in [1e-20, -1e-20]:
+            with self.subTest(theta=theta):
+                assert_allclose(
+                    UnitQuaternion.AngVec(theta, [0, 0, 0]).vec, [1, 0, 0, 0]
+                )
+
+    def test_near_zero_degrees_zero_axis(self):
+        for theta in [1e-20, -1e-20]:
+            with self.subTest(theta=theta):
+                assert_allclose(
+                    UnitQuaternion.AngVec(theta, [0, 0, 0], unit="deg").vec,
+                    [1, 0, 0, 0],
+                )
+
+    def test_nonzero_small_angle_requires_nonzero_axis(self):
+        for theta in [1e-10, -1e-10]:
+            with self.subTest(theta=theta):
+                with self.assertRaises(ValueError):
+                    UnitQuaternion.AngVec(theta, [0, 0, 0])
+
+    def test_nonzero_small_angle_preserves_rotation(self):
+        for theta in [1e-10, -1e-10]:
+            with self.subTest(theta=theta):
+                assert_allclose(
+                    UnitQuaternion.AngVec(theta, [2, 0, 0]).vec,
+                    [math.cos(theta / 2), math.sin(theta / 2), 0, 0],
+                    atol=0,
+                )