Fix sign error in quaternion-to-Euler conversion at Phi = pi

.zenodo.json

@@ -72,6 +72,9 @@
       "name": "Alexander Clausen",
       "orcid": "0000-0002-9555-7455",
       "affiliation": "Jülich Research Centre, Ernst Ruska Centre"
+    },
+    {
+      "name": "Vincent Gao"
     }
   ]
 }

CHANGELOG.rst

@@ -7,6 +7,17 @@ on `Keep a Changelog <https://keepachangelog.com/en/1.0.0/>`__, and this project
 its best to adhere to `Semantic Versioning <https://semver.org/spec/v2.0.0.html>`__.
 
 
+Unreleased
+==========
+
+Fixed
+-----
+- ``Rotation.to_euler()`` now returns correct Bunge Euler angles for 180 degree
+  rotations about an axis in the xy-plane not aligned with x or y. A sign error in
+  the singular branch of the quaternion-to-Euler conversion previously reflected the
+  reconstructed axis, so the angles did not round-trip back to the input rotation.
+
+
 2026-06-10 - version 0.15.0
 ===========================
 

orix/__init__.py

@@ -39,4 +39,5 @@
     "Dorian Depriester",
     "Eric Prestat",
     "Alexander Clausen",
+    "Vincent Gao",
 ]

orix/quaternion/_conversions.py

@@ -1016,7 +1016,7 @@ def qu2eu_single(qu: np.ndarray) -> np.ndarray:
             a = -2 * qu[0] * qu[3]
             b = qu[0] * qu[0] - qu[3] * qu[3]
         else:
-            a = -2 * qu[1] * qu[2]
+            a = 2 * qu[1] * qu[2]
             b = qu[1] * qu[1] - qu[2] * qu[2]
             eu[1] = np.pi
         eu[0] = np.arctan2(a, b)

orix/tests/test_quaternion/test_conversions.py

@@ -20,7 +20,7 @@
 import numpy as np
 import pytest
 
-from orix.quaternion import Orientation
+from orix.quaternion import Orientation, Rotation
 from orix.quaternion._conversions import (
     ax2qu,
     ax2qu_2d,
@@ -105,6 +105,30 @@ def test_eu2qu2eu(self, euler_angles, quaternions_conversions):
         assert ori.symmetry == Oh
         assert np.allclose(ori.data[0], qu_64[-1], atol=1e-4)
 
+    def test_qu2eu_equatorial_twofold(self):
+        # 180 deg rotations about equatorial (xy-plane) axes hit the Phi = pi
+        # branch of qu2eu (Rowenhorst et al. (2015) Eq. A.14). Off-axis axes,
+        # with x and y both non-zero, must round-trip back to the rotation.
+        psi = np.linspace(0, np.pi, 19)
+        axes = np.column_stack([np.cos(psi), np.sin(psi), np.zeros_like(psi)])
+        qu = ax2qu(axes, np.full(psi.shape, np.pi))
+
+        # jit path: qu -> eu -> qu, compared as matrices to sidestep the
+        # quaternion double cover
+        assert np.allclose(qu2om(qu), qu2om(eu2qu(qu2eu(qu))), atol=1e-6)
+
+        # Pure-Python path
+        for q in qu:
+            q_rt = eu2qu_single.py_func(qu2eu_single.py_func(q))
+            assert np.allclose(
+                qu2om_single.py_func(q), qu2om_single.py_func(q_rt), atol=1e-6
+            )
+
+        # Public API round-trip
+        rot = Rotation.from_axes_angles(axes, np.pi)
+        rot_rt = Rotation.from_euler(rot.to_euler())
+        assert np.allclose(rot.to_matrix(), rot_rt.to_matrix(), atol=1e-6)
+
     def test_get_pyramid(self, cubochoric_coordinates):
         """Cubochoric coordinates situated in expected pyramid."""
         cu_64 = cubochoric_coordinates

orix/tests/test_sampling/test_sampling.py

@@ -206,14 +206,15 @@ def test_get_sample_reduced_fundamental(self):
         v_Oh = R_Oh * vz
         assert np.all(v_Oh <= Oh.fundamental_sector)
 
-        # Some rotations have a phi1 Euler angle of multiples of pi,
-        # presumably due to rounding errors
+        # A few sampled rotations are 180 degree rotations about an axis in
+        # the xy-plane (Phi = pi), where phi1 is degenerate and lands on a
+        # multiple of pi / 2
         phi1_C1 = R_C1.to_euler()[:, 0].round(7)
         assert np.allclose(np.unique(phi1_C1), 0, atol=1e-7)
         phi1_C4 = R_C4.to_euler()[:, 0].round(7)
-        assert np.allclose(np.unique(phi1_C4), [0, np.pi / 2], atol=1e-7)
+        assert np.allclose(np.unique(phi1_C4), [0, np.pi / 2, 3 * np.pi / 2], atol=1e-7)
         phi1_C6 = R_C6.to_euler()[:, 0].round(7)
-        assert np.allclose(np.unique(phi1_C6), [0, np.pi / 2], atol=1e-7)
+        assert np.allclose(np.unique(phi1_C6), [0, np.pi / 2, 3 * np.pi / 2], atol=1e-7)
         phi1_Oh = R_Oh.to_euler()[:, 0].round(7)
         assert np.allclose(np.unique(phi1_Oh), [0, np.pi / 2], atol=1e-7)