From df9ca1de8b27bb880f2158f999c12734b05f0515 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <argerlt@gmail.com>
Date: Mon, 19 May 2025 01:11:45 -0600
Subject: [PATCH 01/23] adding ancillary capabilities from PR442
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-Authored-By: Håkon Wiik Ånes <hwaanes@gmail.com>
---
 CHANGELOG.rst                             |  8 ++-
 orix/quaternion/misorientation.py         | 49 ++++++++++++++++++
 orix/quaternion/quaternion.py             | 62 +++++++++++++++++++++++
 orix/tests/quaternion/test_orientation.py | 30 ++++++-----
 4 files changed, 133 insertions(+), 16 deletions(-)

diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 8b2b47049..305b8b33e 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -31,10 +31,14 @@ Changed
 
 Removed
 -------
-
+- ``verbose`` parameter in ``reduce()``
+  (replacing ``map_into_symmetry_reduced_zone()``).
+  
 Deprecated
 ----------
-
+- ``map_into_symmetry_reduced_zone()`` is deprecated since 0.14 and will be removed in
+  0.15. Use ``reduce()`` instead.
+  
 Fixed
 -----
 - minor speedups to 'pytest'
diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index d5005865f..c7cc140c4 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -31,6 +31,7 @@
 from scipy.spatial.transform import Rotation as SciPyRotation
 from tqdm import tqdm
 
+from orix._util import deprecated
 from orix.quaternion.orientation_region import OrientationRegion
 from orix.quaternion.rotation import Rotation
 from orix.quaternion.symmetry import C1, Symmetry, _get_unique_symmetry_elements
@@ -340,6 +341,7 @@ def equivalent(self, grain_exchange: bool = False) -> Misorientation:
 
         return self.__class__(equivalent).flatten()
 
+    @deprecated(since="0.14", removal="0.15", alternative="reduce")
     def map_into_symmetry_reduced_zone(self, verbose: bool = False) -> Misorientation:
         """Return equivalent transformations which have the smallest
         angle of rotation as a new misorientation.
@@ -382,6 +384,53 @@ def map_into_symmetry_reduced_zone(self, verbose: bool = False) -> Misorientatio
         o_inside._symmetry = (Gl, Gr)
         return o_inside
 
+    def reduce(self) -> Misorientation:
+        """Return equivalent transformations which have the smallest
+        angle of rotation as a new misorientation.
+
+        Parameters
+        ----------
+        verbose
+            Whether to print a progressbar. Default is ``False``.
+
+        Returns
+        -------
+        M
+            A new misorientation object with the assigned symmetry.
+
+        Examples
+        --------
+        >>> from orix.quaternion.symmetry import C4, C2
+        >>> data = np.array([[0.5, 0.5, 0.5, 0.5], [0, 1, 0, 0]])
+        >>> M = Misorientation(data)
+        >>> M.symmetry = (C4, C2)
+        >>> M.reduce()
+        Misorientation (2,) 4, 2
+        [[-0.7071  0.7071  0.      0.    ]
+        [ 0.      1.      0.      0.    ]]
+        """
+        # create an itertool object for iterating over every
+        # combination of left and right symmetry operations
+        Gl, Gr = self._symmetry
+        symmetry_pairs = iproduct(Gl, Gr)
+
+        # Define a Fundamental Zone (fz). for every misorientation, there
+        # is one and only one combination in `symmetry_pairs` that rotates
+        # it into the fz.
+        fz = OrientationRegion.from_symmetry(Gl, Gr)
+        reduced = self.__class__.identity(self.shape)
+        outside = np.ones(self.shape, dtype=bool)
+        # apply transformations to unreduced misorientations and save the
+        # reduced ones to `reduced` until all are inside the fz
+        for gl, gr in symmetry_pairs:
+            o_transformed = gl * self[outside] * gr
+            reduced[outside] = o_transformed
+            outside = ~(reduced < fz)
+            if not np.any(outside):
+                break
+        reduced._symmetry = (Gl, Gr)
+        return reduced
+
     def scatter(
         self,
         projection: str = "axangle",
diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index 099abf872..cc2243481 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -246,6 +246,16 @@ def __eq__(self, other: Any | Quaternion) -> bool:
 
     # ------------------------ Class methods ------------------------- #
 
+    @classmethod
+    def random(cls, shape: Union[int, tuple] = 1) -> Quaternion:
+        quat = super().random(shape)
+        quat.data[:, 0] = np.abs(quat.data[:, 0])
+        return quat
+
+        O = super().__invert__()
+        O.symmetry = self.symmetry
+        return O
+
     @classmethod
     def from_axes_angles(
         cls,
@@ -685,6 +695,58 @@ def from_align_vectors(
 
         return out[0] if len(out) == 1 else tuple(out)
 
+    @classmethod
+    def from_path_ends(
+        cls, waypoints: Quaternion, close_loop: bool = False, steps: int = 100
+    ) -> Quaternion:
+        """Return Quaternions tracing the shortest path between two or more
+        consecutive waypoints.
+
+        Parameters
+        ----------
+        waypoints : Quaternion
+            Two or more quaternions that define waypoints along a path through
+            rotation space (SO3).
+        close_loop : bool, optional
+            Option to add a final trip from the last waypoint back to the
+            first, thus closing the loop. Default is False.
+        steps : int, optional
+        Number of points to return along the path between each pair of
+        waypoints. The default is 100.
+
+        Returns
+        -------
+        path :Quaternion
+            quaternions that map out a path between the given waypoints.
+
+        Notes
+        -----
+        This method can use Orientations and Misorientations as inputs, and
+        will return an object of the same class. However, symmetry is ignored
+        when determining the shortest routes.
+        """
+        waypoints = waypoints.flatten()
+        n = waypoints.size
+        if not close_loop:
+            n = n - 1
+
+        path_list = []
+        for i in range(n):
+            # get start and end for this leg of the trip
+            q1 = waypoints[i]
+            q2 = waypoints[(i + 1) % (waypoints.size)]
+            # find the ax/ang describing the trip between points
+            ax, ang = _conversions.qu2ax((~q1 * q2).data)
+            # get 100 steps along the trip and add them to the journey
+            trip = Quaternion.from_axes_angles(ax, np.linspace(0, ang, steps))
+            path_list.append((q1 * (trip.flatten())).data)
+        path_data = np.concatenate(path_list, axis=0)
+        path = waypoints.__class__(path_data)
+        # copy the symmetry if it exists
+        if hasattr(waypoints, "_symmetry"):
+            path._symmetry = waypoints._symmetry
+        return path
+
     @classmethod
     def triple_cross(cls, q1: Quaternion, q2: Quaternion, q3: Quaternion) -> Quaternion:
         """Pointwise cross product of three quaternions.
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index 4ea13b1d9..003c22ceb 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -101,7 +101,7 @@ def test_quaternion_subclasses_copy_constructor_casting():
 )
 def test_set_symmetry(orientation, symmetry, expected):
     o = Orientation(orientation.data, symmetry=symmetry)
-    o = o.map_into_symmetry_reduced_zone()
+    o = o.reduce()
     assert np.allclose(o.data, expected, atol=1e-3)
 
 
@@ -114,7 +114,7 @@ def test_orientation_persistence(symmetry, vector):
     v = symmetry.outer(vector).flatten()
     o = Orientation.random()
     oc = Orientation(o.data, symmetry=symmetry)
-    oc = oc.map_into_symmetry_reduced_zone()
+    oc = oc.reduce()
     v1 = o * v
     v1 = Vector3d(v1.data.round(4))
     v2 = oc * v
@@ -207,7 +207,7 @@ def test_equivalent(Gl):
     """
     m = Misorientation([1, 1, 1, 1])  # any will do
     m_new = Misorientation(m.data, symmetry=(Gl, C4))
-    m_new = m_new.map_into_symmetry_reduced_zone()
+    m_new = m_new.reduce()
     _ = m_new.equivalent(grain_exchange=True)
 
 
@@ -220,13 +220,13 @@ def test_repr_ori():
     shape = (2, 3)
     o = Orientation.identity(shape)
     o.symmetry = O
-    o = o.map_into_symmetry_reduced_zone()
+    o = o.reduce()
     assert repr(o).split("\n")[0] == f"Orientation {shape} {O.name}"
 
 
 def test_sub():
     o = Orientation([1, 1, 1, 1], symmetry=C4)  # any will do
-    o = o.map_into_symmetry_reduced_zone()
+    o = o.reduce()
     m = o - o
     assert np.allclose(m.data, [1, 0, 0, 0])
 
@@ -247,8 +247,10 @@ def test_map_into_reduced_symmetry_zone_verbose():
     o = Orientation.random()
     o.symmetry = Oh
     o1 = o.map_into_symmetry_reduced_zone()
-    o2 = o.map_into_symmetry_reduced_zone(verbose=True)
+    o2 = o.reduce()
+    o3 = o.map_into_symmetry_reduced_zone(verbose=True)
     assert np.allclose(o1.data, o2.data)
+    assert np.allclose(o1.data, o3.data)
 
 
 @pytest.mark.parametrize(
@@ -264,7 +266,7 @@ def test_transpose_3d(shape, expected_shape, axes):
 def test_transpose_symmetry():
     o1 = Orientation.random_vonmises((11, 3))
     o1.symmetry = Oh
-    o1 = o1.map_into_symmetry_reduced_zone()
+    o1 = o1.reduce()
     o2 = o1.transpose()
     assert o1.symmetry == o2.symmetry
 
@@ -488,11 +490,11 @@ def test_from_euler_symmetry(self):
         assert np.allclose(o1.data, [0, -0.3827, 0, -0.9239], atol=1e-4)
         assert o1.symmetry.name == "1"
         o2 = Orientation.from_euler(euler, symmetry=Oh)
-        o2 = o2.map_into_symmetry_reduced_zone()
+        o2 = o2.reduce()
         assert np.allclose(o2.data, [0.9239, 0, 0.3827, 0], atol=1e-4)
         assert o2.symmetry.name == "m-3m"
         o3 = Orientation(o1.data, symmetry=Oh)
-        o3 = o3.map_into_symmetry_reduced_zone()
+        o3 = o3.reduce()
         assert np.allclose(o3.data, o2.data)
 
         o4 = Orientation.from_euler(np.rad2deg(euler), degrees=True)
@@ -508,13 +510,13 @@ def test_from_matrix_symmetry(self):
         )
         assert o1.symmetry.name == "1"
         o2 = Orientation.from_matrix(om, symmetry=Oh)
-        o2 = o2.map_into_symmetry_reduced_zone()
+        o2 = o2.reduce()
         assert np.allclose(
             o2.data, np.array([1, 0, 0, 0] * 2 + [-1, 0, 0, 0] * 2).reshape(4, 4)
         )
         assert o2.symmetry.name == "m-3m"
         o3 = Orientation(o1.data, symmetry=Oh)
-        o3 = o3.map_into_symmetry_reduced_zone()
+        o3 = o3.reduce()
         assert np.allclose(o3.data, o2.data)
 
     def test_from_align_vectors(self):
@@ -601,7 +603,7 @@ class TestOrientation:
     def test_get_distance_matrix(self, symmetry):
         q = [(0.5, 0.5, 0.5, 0.5), (0.5**0.5, 0, 0, 0.5**0.5)]
         o = Orientation(q, symmetry=symmetry)
-        o = o.map_into_symmetry_reduced_zone()
+        o = o.reduce()
         angles_numpy = o.get_distance_matrix()
         assert isinstance(angles_numpy, np.ndarray)
         assert angles_numpy.shape == (2, 2)
@@ -694,7 +696,7 @@ def test_angle_with(self, symmetry):
     def test_negate_orientation(self):
         o = Orientation.identity()
         o.symmetry = Oh
-        o = o.map_into_symmetry_reduced_zone()
+        o = o.reduce()
         on = -o
         assert on.symmetry.name == o.symmetry.name
 
@@ -703,7 +705,7 @@ def test_scatter(self, orientation, pure_misorientation):
         if pure_misorientation:
             orientation = Misorientation(orientation)
             orientation.symmetry = (C2, D6)
-            orientation = orientation.map_into_symmetry_reduced_zone()
+            orientation = orientation.reduce()
         fig_size = (5, 5)
         fig_axangle = orientation.scatter(
             return_figure=True, figure_kwargs=dict(figsize=fig_size)

From e67ff70a8972ebbe37068dd79392edc57b28d9f8 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Tue, 27 May 2025 15:35:29 -0600
Subject: [PATCH 02/23] add tests for 'from_path_ends`

---
 orix/quaternion/quaternion.py             |  50 ++++++---
 orix/tests/quaternion/test_orientation.py |  45 ++++++--
 orix/tests/quaternion/test_quaternion.py  | 122 ++++++++++++++++++----
 3 files changed, 170 insertions(+), 47 deletions(-)

diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index cc2243481..c18f1d5af 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -505,7 +505,9 @@ def from_euler(
 
         eu = np.atleast_2d(euler)
         if np.any(np.abs(eu) > 4 * np.pi):
-            warnings.warn("Angles are quite high, did you forget to set degrees=True?")
+            warnings.warn(
+                "Angles are quite high, did you forget to set degrees=True?"
+            )
 
         Q = _conversions.eu2qu(eu)
         Q = cls(Q)
@@ -544,7 +546,9 @@ def from_matrix(cls, matrix: np.ndarray | tuple | list) -> Quaternion:
         # Verify the input can be interpreted as an array of (3, 3) arrays
         om = np.atleast_2d(matrix)
         if om.shape[-2:] != (3, 3):
-            raise ValueError("the last two dimensions of 'matrix' must be (3, 3)")
+            raise ValueError(
+                "the last two dimensions of 'matrix' must be (3, 3)"
+            )
 
         Q = _conversions.om2qu(om)
         Q = cls(Q)
@@ -737,7 +741,7 @@ def from_path_ends(
             q2 = waypoints[(i + 1) % (waypoints.size)]
             # find the ax/ang describing the trip between points
             ax, ang = _conversions.qu2ax((~q1 * q2).data)
-            # get 100 steps along the trip and add them to the journey
+            # get 'steps=n' steps along the trip and add them to the journey
             trip = Quaternion.from_axes_angles(ax, np.linspace(0, ang, steps))
             path_list.append((q1 * (trip.flatten())).data)
         path_data = np.concatenate(path_list, axis=0)
@@ -748,7 +752,9 @@ def from_path_ends(
         return path
 
     @classmethod
-    def triple_cross(cls, q1: Quaternion, q2: Quaternion, q3: Quaternion) -> Quaternion:
+    def triple_cross(
+        cls, q1: Quaternion, q2: Quaternion, q3: Quaternion
+    ) -> Quaternion:
         """Pointwise cross product of three quaternions.
 
         Parameters
@@ -1195,7 +1201,9 @@ def outer(
                     qu12 = np.outer(qu1, qu2).reshape(*qu1.shape, *qu2.shape)
                     qu = quaternion.as_float_array(qu12)
                 else:  # pragma: no cover
-                    Q12 = Quaternion(self).reshape(-1, 1) * other.reshape(1, -1)
+                    Q12 = Quaternion(self).reshape(-1, 1) * other.reshape(
+                        1, -1
+                    )
                     qu = Q12.data.reshape(*self.shape, *other.shape, 4)
             return other.__class__(qu)
         elif isinstance(other, Vector3d):
@@ -1368,7 +1376,9 @@ def _outer_dask(
 
 
 @nb.guvectorize("(n)->(n)", cache=True)
-def qu_conj_gufunc(qu: np.ndarray, qu2: np.ndarray) -> None:  # pragma: no cover
+def qu_conj_gufunc(
+    qu: np.ndarray, qu2: np.ndarray
+) -> None:  # pragma: no cover
     qu2[0] = qu[0]
     qu2[1] = -qu[1]
     qu2[2] = -qu[2]
@@ -1379,13 +1389,23 @@ def qu_conj_gufunc(qu: np.ndarray, qu2: np.ndarray) -> None:  # pragma: no cover
 def qu_multiply_gufunc(
     qu1: np.ndarray, qu2: np.ndarray, qu12: np.ndarray
 ) -> None:  # pragma: no cover
-    qu12[0] = qu1[0] * qu2[0] - qu1[1] * qu2[1] - qu1[2] * qu2[2] - qu1[3] * qu2[3]
-    qu12[1] = qu1[1] * qu2[0] + qu1[0] * qu2[1] - qu1[3] * qu2[2] + qu1[2] * qu2[3]
-    qu12[2] = qu1[2] * qu2[0] + qu1[3] * qu2[1] + qu1[0] * qu2[2] - qu1[1] * qu2[3]
-    qu12[3] = qu1[3] * qu2[0] - qu1[2] * qu2[1] + qu1[1] * qu2[2] + qu1[0] * qu2[3]
-
-
-def qu_multiply(qu1: np.ndarray, qu2: np.ndarray) -> np.ndarray:  # pragma: no cover
+    qu12[0] = (
+        qu1[0] * qu2[0] - qu1[1] * qu2[1] - qu1[2] * qu2[2] - qu1[3] * qu2[3]
+    )
+    qu12[1] = (
+        qu1[1] * qu2[0] + qu1[0] * qu2[1] - qu1[3] * qu2[2] + qu1[2] * qu2[3]
+    )
+    qu12[2] = (
+        qu1[2] * qu2[0] + qu1[3] * qu2[1] + qu1[0] * qu2[2] - qu1[1] * qu2[3]
+    )
+    qu12[3] = (
+        qu1[3] * qu2[0] - qu1[2] * qu2[1] + qu1[1] * qu2[2] + qu1[0] * qu2[3]
+    )
+
+
+def qu_multiply(
+    qu1: np.ndarray, qu2: np.ndarray
+) -> np.ndarray:  # pragma: no cover
     shape = np.broadcast_shapes(qu1.shape, qu2.shape)
     if not np.issubdtype(qu1.dtype, np.float64):
         qu1 = qu1.astype(np.float64)
@@ -1410,7 +1430,9 @@ def qu_rotate_vec_gufunc(
     v2[2] = z - c * tx + b * ty + a * tz
 
 
-def qu_rotate_vec(qu: np.ndarray, v: np.ndarray) -> np.ndarray:  # pragma: no cover
+def qu_rotate_vec(
+    qu: np.ndarray, v: np.ndarray
+) -> np.ndarray:  # pragma: no cover
     qu = np.atleast_2d(qu)
     v = np.atleast_2d(v)
     shape = np.broadcast_shapes(qu.shape[:-1], v.shape[:-1]) + (3,)
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index 003c22ceb..57a31139a 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -301,7 +301,8 @@ def test_symmetry_property_wrong_type_orientation():
 
 
 @pytest.mark.parametrize(
-    "error_type, value", [(ValueError, (1, 2)), (ValueError, (C1, 2)), (TypeError, 1)]
+    "error_type, value",
+    [(ValueError, (1, 2)), (ValueError, (C1, 2)), (TypeError, 1)],
 )
 def test_symmetry_property_wrong_type_misorientation(error_type, value):
     mori = Misorientation.random((3, 2))
@@ -313,7 +314,9 @@ def test_symmetry_property_wrong_type_misorientation(error_type, value):
     "error_type, value",
     [(ValueError, (C1,)), (ValueError, (C1, C2, C1))],
 )
-def test_symmetry_property_wrong_number_of_values_misorientation(error_type, value):
+def test_symmetry_property_wrong_number_of_values_misorientation(
+    error_type, value
+):
     o = Misorientation.random((3, 2))
     with pytest.raises(error_type, match="Value must be a 2-tuple"):
         # less than 2 Symmetry
@@ -506,13 +509,15 @@ def test_from_matrix_symmetry(self):
         )
         o1 = Orientation.from_matrix(om)
         assert np.allclose(
-            o1.data, np.array([1, 0, 0, 0] * 2 + [0, 1, 0, 0] * 2).reshape(4, 4)
+            o1.data,
+            np.array([1, 0, 0, 0] * 2 + [0, 1, 0, 0] * 2).reshape(4, 4),
         )
         assert o1.symmetry.name == "1"
         o2 = Orientation.from_matrix(om, symmetry=Oh)
         o2 = o2.reduce()
         assert np.allclose(
-            o2.data, np.array([1, 0, 0, 0] * 2 + [-1, 0, 0, 0] * 2).reshape(4, 4)
+            o2.data,
+            np.array([1, 0, 0, 0] * 2 + [-1, 0, 0, 0] * 2).reshape(4, 4),
         )
         assert o2.symmetry.name == "m-3m"
         o3 = Orientation(o1.data, symmetry=Oh)
@@ -597,9 +602,19 @@ def test_from_scipy_rotation(self):
         with pytest.raises(TypeError, match="Value must be an instance of"):
             _ = Orientation.from_scipy_rotation(r_scipy, (Oh, Oh))
 
+    def test_from_path_ends(self):
+        # generate paths with misorientations and orientations to check
+        # symmetry copying
+        wp_o = Orientation(data=np.eye(4)[:2], symmetry=Oh)
+        wp_m = Misorientation(data=np.eye(4)[2:], symmetry=[Oh, C3])
+        assert Orientation.from_path_ends(wp_o)._symmetry == (C1, Oh)
+        assert Misorientation.from_path_ends(wp_m)._symmetry == (Oh, C3)
+
 
 class TestOrientation:
-    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
+    @pytest.mark.parametrize(
+        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
+    )
     def test_get_distance_matrix(self, symmetry):
         q = [(0.5, 0.5, 0.5, 0.5), (0.5**0.5, 0, 0, 0.5**0.5)]
         o = Orientation(q, symmetry=symmetry)
@@ -626,11 +641,15 @@ def test_get_distance_matrix_lazy_parameters(self):
         o = Orientation(abcd)
 
         angle1 = o.get_distance_matrix(lazy=True, chunk_size=5)
-        angle2 = o.get_distance_matrix(lazy=True, chunk_size=10, progressbar=False)
+        angle2 = o.get_distance_matrix(
+            lazy=True, chunk_size=10, progressbar=False
+        )
 
         assert np.allclose(angle1.data, angle2.data)
 
-    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
+    @pytest.mark.parametrize(
+        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
+    )
     def test_angle_with_outer(self, symmetry):
         shape = (5,)
         o = Orientation.random(shape)
@@ -677,7 +696,9 @@ def test_angle_with_outer_shape(self):
         assert awo_o12s.shape == awo_r12.shape
         assert not np.allclose(awo_o12s, awo_r12)
 
-    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
+    @pytest.mark.parametrize(
+        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
+    )
     def test_angle_with(self, symmetry):
         q = [(0.5, 0.5, 0.5, 0.5), (0.5**0.5, 0, 0, 0.5**0.5)]
         r = Rotation(q)
@@ -712,7 +733,9 @@ def test_scatter(self, orientation, pure_misorientation):
         )
         assert (fig_axangle.get_size_inches() == fig_size).all()
         assert isinstance(fig_axangle.axes[0], AxAnglePlot)
-        fig_rodrigues = orientation.scatter(projection="rodrigues", return_figure=True)
+        fig_rodrigues = orientation.scatter(
+            projection="rodrigues", return_figure=True
+        )
         assert isinstance(fig_rodrigues.axes[0], RodriguesPlot)
 
         # Add multiple axes to figure, one at a time
@@ -805,7 +828,9 @@ def test_in_fundamental_region(self):
         for pg in _proper_groups:
             ori.symmetry = pg
             region = np.radians(pg.euler_fundamental_region)
-            assert np.all(np.max(ori.in_euler_fundamental_region(), axis=0) <= region)
+            assert np.all(
+                np.max(ori.in_euler_fundamental_region(), axis=0) <= region
+            )
 
     def test_inverse(self):
         O1 = Orientation([np.sqrt(2) / 2, np.sqrt(2) / 2, 0, 0], D6)
diff --git a/orix/tests/quaternion/test_quaternion.py b/orix/tests/quaternion/test_quaternion.py
index 7f6be1d11..c82483bca 100644
--- a/orix/tests/quaternion/test_quaternion.py
+++ b/orix/tests/quaternion/test_quaternion.py
@@ -78,7 +78,9 @@ def test_neg(self, quaternion):
         assert np.allclose((-quaternion).data, (-quaternion.data))
 
     def test_norm(self, quaternion):
-        assert np.allclose(quaternion.norm, (quaternion.data**2).sum(axis=-1) ** 0.5)
+        assert np.allclose(
+            quaternion.norm, (quaternion.data**2).sum(axis=-1) ** 0.5
+        )
 
     def test_unit(self, quaternion):
         assert np.allclose(quaternion.unit.norm, 1)
@@ -102,7 +104,9 @@ def test_mul(self, quaternion, something):
         assert np.allclose(q1.d, qa * sd + qb * sc - qc * sb + qd * sa)
 
     def test_mul_identity(self, quaternion):
-        assert np.allclose((quaternion * Quaternion.identity()).data, quaternion.data)
+        assert np.allclose(
+            (quaternion * Quaternion.identity()).data, quaternion.data
+        )
 
     def test_no_multiplicative_inverse(self, quaternion, something):
         q1 = quaternion * something
@@ -193,7 +197,9 @@ def test_antipodal(self, quaternion):
         assert qa.size == 2 * q.size
 
     def test_edgecase_outer(self, quaternion):
-        with pytest.raises(NotImplementedError, match="This operation is currently "):
+        with pytest.raises(
+            NotImplementedError, match="This operation is currently "
+        ):
             _ = quaternion.outer([3, 2])
 
     def test_failing_mul(self, quaternion):
@@ -298,7 +304,9 @@ def test_outer_dask_wrong_type_raises(self):
         q = Quaternion(abcd)
         # not Quaternion or Vector3d
         other = np.random.rand(7, 3)
-        with pytest.raises(TypeError, match="Other must be Quaternion or Vector3d"):
+        with pytest.raises(
+            TypeError, match="Other must be Quaternion or Vector3d"
+        ):
             q._outer_dask(other)
 
     def test_from_align_vectors(self):
@@ -308,7 +316,8 @@ def test_from_align_vectors(self):
         q1 = Quaternion.from_align_vectors(v1, v2)
         assert isinstance(q1, Quaternion)
         assert np.allclose(
-            q1.data, np.array([[0.65328148, 0.70532785, -0.05012611, -0.27059805]])
+            q1.data,
+            np.array([[0.65328148, 0.70532785, -0.05012611, -0.27059805]]),
         )
         assert np.allclose(v1.unit.data, (q1 * v2.unit).data)
 
@@ -317,8 +326,12 @@ def test_from_align_vectors(self):
         error = out[1]
         assert error == 0
 
-        _, sens_mat = Quaternion.from_align_vectors(v1, v2, return_sensitivity=True)
-        assert np.allclose(sens_mat, np.array([[1, 0, 0], [0, 1, 0], [0, 0, 0.5]]))
+        _, sens_mat = Quaternion.from_align_vectors(
+            v1, v2, return_sensitivity=True
+        )
+        assert np.allclose(
+            sens_mat, np.array([[1, 0, 0], [0, 1, 0], [0, 0, 0.5]])
+        )
 
         out = Quaternion.from_align_vectors(
             v1, v2, return_rmsd=True, return_sensitivity=True
@@ -330,6 +343,37 @@ def test_from_align_vectors(self):
         )
         assert np.allclose(q2.data, q1.data)
 
+    def test_from_path_ends(self):
+        # choose a path with repeats and 180 tilts to test edge cases
+        waypoints = Quaternion(
+            data=np.array(
+                [
+                    [1, 0, 0, 0],
+                    [1, 0, 0, 0],
+                    [1, 1, 0, 0],
+                    [1, 0, 1, 0],
+                    [1, 0, 0, 1],
+                    [1, 0, 0, 1],
+                    [1, 0, -1, 0],
+                    [1, 0, 1, 0],
+                    [-1, 0, 1, 0],
+                    [1, 0, 0, -1],
+                    [-1, 0, 0, -1],
+                    [-1, 0, 0, 1],
+                ]
+            )
+        )
+        path = Quaternion.from_path_ends(waypoints)
+        loop = Quaternion.from_path_ends(waypoints, close_loop=True, steps=11)
+        # check the sizes are as expected
+        assert path.shape == (1100,)
+        assert loop.shape == (132,)
+        # check the spacing between points is homogenous
+        path_spacing = [(x[1:]).dot(x[:-1]) for x in path.reshape(11, 100)]
+        loop_spacing = [(x[1:]).dot(x[:-1]) for x in loop.reshape(12, 11)]
+        assert np.all(np.std(path_spacing, axis=1) < 1e-12)
+        assert np.all(np.std(loop_spacing, axis=1) < 1e-12)
+
     def test_equality(self):
         Q1 = Quaternion.from_axes_angles([1, 1, 1], -np.pi / 3)
         Q2 = Quaternion.from_axes_angles([1, 1, 1], np.pi / 3)
@@ -361,7 +405,9 @@ def test_direction_values(self, eu):
         assert np.allclose((q_l2c * q_c2l).data, [1, 0, 0, 0])
 
     def test_direction_kwarg_dumb(self, eu):
-        with pytest.raises(ValueError, match="The chosen direction is not one of "):
+        with pytest.raises(
+            ValueError, match="The chosen direction is not one of "
+        ):
             _ = Quaternion.from_euler(eu, direction="dumb_direction")
 
     def test_edge_cases_to_euler(self):
@@ -372,19 +418,25 @@ def test_edge_cases_to_euler(self):
         _ = q.to_euler()
 
     def test_passing_degrees_warns(self):
-        with pytest.warns(UserWarning, match="Angles are quite high, did you forget "):
+        with pytest.warns(
+            UserWarning, match="Angles are quite high, did you forget "
+        ):
             q = Quaternion.from_euler([90, 0, 0])
             assert np.allclose(q.data, [0.5253, 0, 0, -0.8509], atol=1e-4)
 
 
 class TestFromToMatrix:
     def test_to_matrix(self):
-        q = Quaternion([[1, 0, 0, 0], [3, 0, 0, 0], [0, 1, 0, 0], [0, 2, 0, 0]])
+        q = Quaternion(
+            [[1, 0, 0, 0], [3, 0, 0, 0], [0, 1, 0, 0], [0, 2, 0, 0]]
+        )
         om = np.array(
             [np.eye(3), np.eye(3), np.diag([1, -1, -1]), np.diag([1, -1, -1])]
         )
         # Shapes are handled correctly
-        assert np.allclose(q.reshape(2, 2).unit.to_matrix(), om.reshape(2, 2, 3, 3))
+        assert np.allclose(
+            q.reshape(2, 2).unit.to_matrix(), om.reshape(2, 2, 3, 3)
+        )
 
         q2 = Quaternion(
             [
@@ -398,19 +450,25 @@ def test_to_matrix(self):
         # Inverse equal to transpose
         assert all(np.allclose(np.linalg.inv(i), i.T) for i in om_from_q2)
         # Cross product of any two rows gives the third
-        assert all(np.allclose(np.cross(i[:, 0], i[:, 1]), i[:, 2]) for i in om_from_q2)
+        assert all(
+            np.allclose(np.cross(i[:, 0], i[:, 1]), i[:, 2])
+            for i in om_from_q2
+        )
         # Sum of squares of any column or row equals unity
         assert np.allclose(np.sum(np.square(om_from_q2), axis=1), 1)  # Rows
         assert np.allclose(np.sum(np.square(om_from_q2), axis=2), 1)  # Columns
 
     def test_from_matrix(self):
-        q = Quaternion([[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0]])
+        q = Quaternion(
+            [[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0]]
+        )
         ident = np.identity(3)
         rot_180x = np.diag([1, -1, -1])
         om = np.array([ident, 2 * ident, rot_180x, 2 * rot_180x])
         assert np.allclose(Quaternion.from_matrix(om).data, q.data)
         assert np.allclose(
-            Quaternion.from_matrix(om.reshape(2, 2, 3, 3)).data, q.reshape(2, 2).data
+            Quaternion.from_matrix(om.reshape(2, 2, 3, 3)).data,
+            q.reshape(2, 2).data,
         )
 
     def test_from_to_matrix(self):
@@ -447,7 +505,9 @@ def test_get_rotation_matrix_from_diffpy(self):
         q = Quaternion.from_matrix([i.R for i in sg225.symop_list])
         assert not np.isnan(q.data).any()
 
-    def test_from_matrix_raises(self, quaternions_conversions, orientation_matrices):
+    def test_from_matrix_raises(
+        self, quaternions_conversions, orientation_matrices
+    ):
         qu = Quaternion.from_matrix(orientation_matrices).data
         assert np.allclose(qu, quaternions_conversions, atol=1e-4)
         with pytest.raises(ValueError, match="(3, 3)"):
@@ -467,12 +527,16 @@ def test_from_axes_angles(self, rotations, extra_dim):
             rotations = rotations.__class__(rotations.data[..., np.newaxis, :])
         ax = AxAngle.from_rotation(rotations)
         Q1 = Quaternion.from_axes_angles(ax.axis.data, ax.angle)
-        Q2 = Quaternion.from_axes_angles(ax.axis, np.rad2deg(ax.angle), degrees=True)
+        Q2 = Quaternion.from_axes_angles(
+            ax.axis, np.rad2deg(ax.angle), degrees=True
+        )
         assert np.allclose(Q1.data, Q2.data)
 
     def test_to_axes_angles(self, quaternions_conversions, axis_angle_pairs):
         ax = Quaternion(quaternions_conversions).to_axes_angles()
-        assert np.allclose(np.deg2rad(ax.angle), axis_angle_pairs[:, 3], atol=4)
+        assert np.allclose(
+            np.deg2rad(ax.angle), axis_angle_pairs[:, 3], atol=4
+        )
 
     def test_from_axes_angles_empty(self):
         q = Quaternion.from_axes_angles([], [])
@@ -484,12 +548,16 @@ class TestFromToRodrigues:
     Rodrigues and Rodrigues-Frank vectors.
     """
 
-    def test_from_to_rodrigues(self, quaternions_conversions, rodrigues_vectors):
+    def test_from_to_rodrigues(
+        self, quaternions_conversions, rodrigues_vectors
+    ):
         axes = rodrigues_vectors[..., :3]
         angles = rodrigues_vectors[..., 3]
 
         q1 = Quaternion(quaternions_conversions)
-        with pytest.warns(UserWarning, match="Highest angle is greater than 179.999 "):
+        with pytest.warns(
+            UserWarning, match="Highest angle is greater than 179.999 "
+        ):
             q2 = Quaternion.from_rodrigues(axes, angles)
         assert np.allclose(q1.data, q2.data, atol=1e-4)
         ro = q1.to_rodrigues(frank=True)
@@ -499,7 +567,9 @@ def test_from_to_rodrigues(self, quaternions_conversions, rodrigues_vectors):
             _ = Quaternion.from_rodrigues([1e15, 1e15, 1e10])
         with pytest.warns(UserWarning, match="Max."):
             _ = Quaternion.from_rodrigues([0, 0, 1e-16])
-        with pytest.raises(ValueError, match="Final dimension of vector array must be"):
+        with pytest.raises(
+            ValueError, match="Final dimension of vector array must be"
+        ):
             Quaternion.from_rodrigues([1, 2, 3, 4])
 
     def test_from_rodrigues_empty(self):
@@ -512,7 +582,9 @@ class TestFromToHomochoric:
     homochoric vectors.
     """
 
-    def test_from_to_homochoric(self, homochoric_vectors, quaternions_conversions):
+    def test_from_to_homochoric(
+        self, homochoric_vectors, quaternions_conversions
+    ):
         ho1 = homochoric_vectors
         ho2 = Vector3d(ho1)
         ho3 = Homochoric(ho1)
@@ -526,7 +598,9 @@ def test_from_to_homochoric(self, homochoric_vectors, quaternions_conversions):
         assert np.allclose(q1.data, quaternions_conversions, atol=1e-4)
         assert np.allclose(q2.data, quaternions_conversions, atol=1e-4)
         assert np.allclose(q3.data, quaternions_conversions, atol=1e-4)
-        assert np.allclose(q4.data, quaternions_conversions.reshape(2, 5, 4), atol=1e-4)
+        assert np.allclose(
+            q4.data, quaternions_conversions.reshape(2, 5, 4), atol=1e-4
+        )
 
         assert np.allclose(ho1, q1.to_homochoric().data, atol=1e-4)
         assert np.allclose(ho1, q2.to_homochoric().data, atol=1e-4)
@@ -534,7 +608,9 @@ def test_from_to_homochoric(self, homochoric_vectors, quaternions_conversions):
         assert np.allclose(ho4, q4.to_homochoric().data, atol=1e-4)
 
     def test_from_homochoric_raises(self):
-        with pytest.raises(ValueError, match="Final dimension of vector array must be"):
+        with pytest.raises(
+            ValueError, match="Final dimension of vector array must be"
+        ):
             Quaternion.from_homochoric([1, 2])
 
     def test_from_homochoric_empty(self):

From 5ffecb3b5353065e71de2746d18c4348a5231e02 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Tue, 27 May 2025 15:37:31 -0600
Subject: [PATCH 03/23] black formatting

---
 orix/quaternion/quaternion.py             | 48 ++++---------
 orix/tests/quaternion/test_orientation.py | 28 ++------
 orix/tests/quaternion/test_quaternion.py  | 85 ++++++-----------------
 3 files changed, 41 insertions(+), 120 deletions(-)

diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index c18f1d5af..f72d6b704 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -505,9 +505,7 @@ def from_euler(
 
         eu = np.atleast_2d(euler)
         if np.any(np.abs(eu) > 4 * np.pi):
-            warnings.warn(
-                "Angles are quite high, did you forget to set degrees=True?"
-            )
+            warnings.warn("Angles are quite high, did you forget to set degrees=True?")
 
         Q = _conversions.eu2qu(eu)
         Q = cls(Q)
@@ -546,9 +544,7 @@ def from_matrix(cls, matrix: np.ndarray | tuple | list) -> Quaternion:
         # Verify the input can be interpreted as an array of (3, 3) arrays
         om = np.atleast_2d(matrix)
         if om.shape[-2:] != (3, 3):
-            raise ValueError(
-                "the last two dimensions of 'matrix' must be (3, 3)"
-            )
+            raise ValueError("the last two dimensions of 'matrix' must be (3, 3)")
 
         Q = _conversions.om2qu(om)
         Q = cls(Q)
@@ -752,9 +748,7 @@ def from_path_ends(
         return path
 
     @classmethod
-    def triple_cross(
-        cls, q1: Quaternion, q2: Quaternion, q3: Quaternion
-    ) -> Quaternion:
+    def triple_cross(cls, q1: Quaternion, q2: Quaternion, q3: Quaternion) -> Quaternion:
         """Pointwise cross product of three quaternions.
 
         Parameters
@@ -1201,9 +1195,7 @@ def outer(
                     qu12 = np.outer(qu1, qu2).reshape(*qu1.shape, *qu2.shape)
                     qu = quaternion.as_float_array(qu12)
                 else:  # pragma: no cover
-                    Q12 = Quaternion(self).reshape(-1, 1) * other.reshape(
-                        1, -1
-                    )
+                    Q12 = Quaternion(self).reshape(-1, 1) * other.reshape(1, -1)
                     qu = Q12.data.reshape(*self.shape, *other.shape, 4)
             return other.__class__(qu)
         elif isinstance(other, Vector3d):
@@ -1376,9 +1368,7 @@ def _outer_dask(
 
 
 @nb.guvectorize("(n)->(n)", cache=True)
-def qu_conj_gufunc(
-    qu: np.ndarray, qu2: np.ndarray
-) -> None:  # pragma: no cover
+def qu_conj_gufunc(qu: np.ndarray, qu2: np.ndarray) -> None:  # pragma: no cover
     qu2[0] = qu[0]
     qu2[1] = -qu[1]
     qu2[2] = -qu[2]
@@ -1389,23 +1379,13 @@ def qu_conj_gufunc(
 def qu_multiply_gufunc(
     qu1: np.ndarray, qu2: np.ndarray, qu12: np.ndarray
 ) -> None:  # pragma: no cover
-    qu12[0] = (
-        qu1[0] * qu2[0] - qu1[1] * qu2[1] - qu1[2] * qu2[2] - qu1[3] * qu2[3]
-    )
-    qu12[1] = (
-        qu1[1] * qu2[0] + qu1[0] * qu2[1] - qu1[3] * qu2[2] + qu1[2] * qu2[3]
-    )
-    qu12[2] = (
-        qu1[2] * qu2[0] + qu1[3] * qu2[1] + qu1[0] * qu2[2] - qu1[1] * qu2[3]
-    )
-    qu12[3] = (
-        qu1[3] * qu2[0] - qu1[2] * qu2[1] + qu1[1] * qu2[2] + qu1[0] * qu2[3]
-    )
-
-
-def qu_multiply(
-    qu1: np.ndarray, qu2: np.ndarray
-) -> np.ndarray:  # pragma: no cover
+    qu12[0] = qu1[0] * qu2[0] - qu1[1] * qu2[1] - qu1[2] * qu2[2] - qu1[3] * qu2[3]
+    qu12[1] = qu1[1] * qu2[0] + qu1[0] * qu2[1] - qu1[3] * qu2[2] + qu1[2] * qu2[3]
+    qu12[2] = qu1[2] * qu2[0] + qu1[3] * qu2[1] + qu1[0] * qu2[2] - qu1[1] * qu2[3]
+    qu12[3] = qu1[3] * qu2[0] - qu1[2] * qu2[1] + qu1[1] * qu2[2] + qu1[0] * qu2[3]
+
+
+def qu_multiply(qu1: np.ndarray, qu2: np.ndarray) -> np.ndarray:  # pragma: no cover
     shape = np.broadcast_shapes(qu1.shape, qu2.shape)
     if not np.issubdtype(qu1.dtype, np.float64):
         qu1 = qu1.astype(np.float64)
@@ -1430,9 +1410,7 @@ def qu_rotate_vec_gufunc(
     v2[2] = z - c * tx + b * ty + a * tz
 
 
-def qu_rotate_vec(
-    qu: np.ndarray, v: np.ndarray
-) -> np.ndarray:  # pragma: no cover
+def qu_rotate_vec(qu: np.ndarray, v: np.ndarray) -> np.ndarray:  # pragma: no cover
     qu = np.atleast_2d(qu)
     v = np.atleast_2d(v)
     shape = np.broadcast_shapes(qu.shape[:-1], v.shape[:-1]) + (3,)
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index 57a31139a..0645a135e 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -314,9 +314,7 @@ def test_symmetry_property_wrong_type_misorientation(error_type, value):
     "error_type, value",
     [(ValueError, (C1,)), (ValueError, (C1, C2, C1))],
 )
-def test_symmetry_property_wrong_number_of_values_misorientation(
-    error_type, value
-):
+def test_symmetry_property_wrong_number_of_values_misorientation(error_type, value):
     o = Misorientation.random((3, 2))
     with pytest.raises(error_type, match="Value must be a 2-tuple"):
         # less than 2 Symmetry
@@ -612,9 +610,7 @@ def test_from_path_ends(self):
 
 
 class TestOrientation:
-    @pytest.mark.parametrize(
-        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
-    )
+    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
     def test_get_distance_matrix(self, symmetry):
         q = [(0.5, 0.5, 0.5, 0.5), (0.5**0.5, 0, 0, 0.5**0.5)]
         o = Orientation(q, symmetry=symmetry)
@@ -641,15 +637,11 @@ def test_get_distance_matrix_lazy_parameters(self):
         o = Orientation(abcd)
 
         angle1 = o.get_distance_matrix(lazy=True, chunk_size=5)
-        angle2 = o.get_distance_matrix(
-            lazy=True, chunk_size=10, progressbar=False
-        )
+        angle2 = o.get_distance_matrix(lazy=True, chunk_size=10, progressbar=False)
 
         assert np.allclose(angle1.data, angle2.data)
 
-    @pytest.mark.parametrize(
-        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
-    )
+    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
     def test_angle_with_outer(self, symmetry):
         shape = (5,)
         o = Orientation.random(shape)
@@ -696,9 +688,7 @@ def test_angle_with_outer_shape(self):
         assert awo_o12s.shape == awo_r12.shape
         assert not np.allclose(awo_o12s, awo_r12)
 
-    @pytest.mark.parametrize(
-        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
-    )
+    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
     def test_angle_with(self, symmetry):
         q = [(0.5, 0.5, 0.5, 0.5), (0.5**0.5, 0, 0, 0.5**0.5)]
         r = Rotation(q)
@@ -733,9 +723,7 @@ def test_scatter(self, orientation, pure_misorientation):
         )
         assert (fig_axangle.get_size_inches() == fig_size).all()
         assert isinstance(fig_axangle.axes[0], AxAnglePlot)
-        fig_rodrigues = orientation.scatter(
-            projection="rodrigues", return_figure=True
-        )
+        fig_rodrigues = orientation.scatter(projection="rodrigues", return_figure=True)
         assert isinstance(fig_rodrigues.axes[0], RodriguesPlot)
 
         # Add multiple axes to figure, one at a time
@@ -828,9 +816,7 @@ def test_in_fundamental_region(self):
         for pg in _proper_groups:
             ori.symmetry = pg
             region = np.radians(pg.euler_fundamental_region)
-            assert np.all(
-                np.max(ori.in_euler_fundamental_region(), axis=0) <= region
-            )
+            assert np.all(np.max(ori.in_euler_fundamental_region(), axis=0) <= region)
 
     def test_inverse(self):
         O1 = Orientation([np.sqrt(2) / 2, np.sqrt(2) / 2, 0, 0], D6)
diff --git a/orix/tests/quaternion/test_quaternion.py b/orix/tests/quaternion/test_quaternion.py
index c82483bca..332193a0a 100644
--- a/orix/tests/quaternion/test_quaternion.py
+++ b/orix/tests/quaternion/test_quaternion.py
@@ -78,9 +78,7 @@ def test_neg(self, quaternion):
         assert np.allclose((-quaternion).data, (-quaternion.data))
 
     def test_norm(self, quaternion):
-        assert np.allclose(
-            quaternion.norm, (quaternion.data**2).sum(axis=-1) ** 0.5
-        )
+        assert np.allclose(quaternion.norm, (quaternion.data**2).sum(axis=-1) ** 0.5)
 
     def test_unit(self, quaternion):
         assert np.allclose(quaternion.unit.norm, 1)
@@ -104,9 +102,7 @@ def test_mul(self, quaternion, something):
         assert np.allclose(q1.d, qa * sd + qb * sc - qc * sb + qd * sa)
 
     def test_mul_identity(self, quaternion):
-        assert np.allclose(
-            (quaternion * Quaternion.identity()).data, quaternion.data
-        )
+        assert np.allclose((quaternion * Quaternion.identity()).data, quaternion.data)
 
     def test_no_multiplicative_inverse(self, quaternion, something):
         q1 = quaternion * something
@@ -197,9 +193,7 @@ def test_antipodal(self, quaternion):
         assert qa.size == 2 * q.size
 
     def test_edgecase_outer(self, quaternion):
-        with pytest.raises(
-            NotImplementedError, match="This operation is currently "
-        ):
+        with pytest.raises(NotImplementedError, match="This operation is currently "):
             _ = quaternion.outer([3, 2])
 
     def test_failing_mul(self, quaternion):
@@ -304,9 +298,7 @@ def test_outer_dask_wrong_type_raises(self):
         q = Quaternion(abcd)
         # not Quaternion or Vector3d
         other = np.random.rand(7, 3)
-        with pytest.raises(
-            TypeError, match="Other must be Quaternion or Vector3d"
-        ):
+        with pytest.raises(TypeError, match="Other must be Quaternion or Vector3d"):
             q._outer_dask(other)
 
     def test_from_align_vectors(self):
@@ -326,12 +318,8 @@ def test_from_align_vectors(self):
         error = out[1]
         assert error == 0
 
-        _, sens_mat = Quaternion.from_align_vectors(
-            v1, v2, return_sensitivity=True
-        )
-        assert np.allclose(
-            sens_mat, np.array([[1, 0, 0], [0, 1, 0], [0, 0, 0.5]])
-        )
+        _, sens_mat = Quaternion.from_align_vectors(v1, v2, return_sensitivity=True)
+        assert np.allclose(sens_mat, np.array([[1, 0, 0], [0, 1, 0], [0, 0, 0.5]]))
 
         out = Quaternion.from_align_vectors(
             v1, v2, return_rmsd=True, return_sensitivity=True
@@ -405,9 +393,7 @@ def test_direction_values(self, eu):
         assert np.allclose((q_l2c * q_c2l).data, [1, 0, 0, 0])
 
     def test_direction_kwarg_dumb(self, eu):
-        with pytest.raises(
-            ValueError, match="The chosen direction is not one of "
-        ):
+        with pytest.raises(ValueError, match="The chosen direction is not one of "):
             _ = Quaternion.from_euler(eu, direction="dumb_direction")
 
     def test_edge_cases_to_euler(self):
@@ -418,25 +404,19 @@ def test_edge_cases_to_euler(self):
         _ = q.to_euler()
 
     def test_passing_degrees_warns(self):
-        with pytest.warns(
-            UserWarning, match="Angles are quite high, did you forget "
-        ):
+        with pytest.warns(UserWarning, match="Angles are quite high, did you forget "):
             q = Quaternion.from_euler([90, 0, 0])
             assert np.allclose(q.data, [0.5253, 0, 0, -0.8509], atol=1e-4)
 
 
 class TestFromToMatrix:
     def test_to_matrix(self):
-        q = Quaternion(
-            [[1, 0, 0, 0], [3, 0, 0, 0], [0, 1, 0, 0], [0, 2, 0, 0]]
-        )
+        q = Quaternion([[1, 0, 0, 0], [3, 0, 0, 0], [0, 1, 0, 0], [0, 2, 0, 0]])
         om = np.array(
             [np.eye(3), np.eye(3), np.diag([1, -1, -1]), np.diag([1, -1, -1])]
         )
         # Shapes are handled correctly
-        assert np.allclose(
-            q.reshape(2, 2).unit.to_matrix(), om.reshape(2, 2, 3, 3)
-        )
+        assert np.allclose(q.reshape(2, 2).unit.to_matrix(), om.reshape(2, 2, 3, 3))
 
         q2 = Quaternion(
             [
@@ -450,18 +430,13 @@ def test_to_matrix(self):
         # Inverse equal to transpose
         assert all(np.allclose(np.linalg.inv(i), i.T) for i in om_from_q2)
         # Cross product of any two rows gives the third
-        assert all(
-            np.allclose(np.cross(i[:, 0], i[:, 1]), i[:, 2])
-            for i in om_from_q2
-        )
+        assert all(np.allclose(np.cross(i[:, 0], i[:, 1]), i[:, 2]) for i in om_from_q2)
         # Sum of squares of any column or row equals unity
         assert np.allclose(np.sum(np.square(om_from_q2), axis=1), 1)  # Rows
         assert np.allclose(np.sum(np.square(om_from_q2), axis=2), 1)  # Columns
 
     def test_from_matrix(self):
-        q = Quaternion(
-            [[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0]]
-        )
+        q = Quaternion([[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0]])
         ident = np.identity(3)
         rot_180x = np.diag([1, -1, -1])
         om = np.array([ident, 2 * ident, rot_180x, 2 * rot_180x])
@@ -505,9 +480,7 @@ def test_get_rotation_matrix_from_diffpy(self):
         q = Quaternion.from_matrix([i.R for i in sg225.symop_list])
         assert not np.isnan(q.data).any()
 
-    def test_from_matrix_raises(
-        self, quaternions_conversions, orientation_matrices
-    ):
+    def test_from_matrix_raises(self, quaternions_conversions, orientation_matrices):
         qu = Quaternion.from_matrix(orientation_matrices).data
         assert np.allclose(qu, quaternions_conversions, atol=1e-4)
         with pytest.raises(ValueError, match="(3, 3)"):
@@ -527,16 +500,12 @@ def test_from_axes_angles(self, rotations, extra_dim):
             rotations = rotations.__class__(rotations.data[..., np.newaxis, :])
         ax = AxAngle.from_rotation(rotations)
         Q1 = Quaternion.from_axes_angles(ax.axis.data, ax.angle)
-        Q2 = Quaternion.from_axes_angles(
-            ax.axis, np.rad2deg(ax.angle), degrees=True
-        )
+        Q2 = Quaternion.from_axes_angles(ax.axis, np.rad2deg(ax.angle), degrees=True)
         assert np.allclose(Q1.data, Q2.data)
 
     def test_to_axes_angles(self, quaternions_conversions, axis_angle_pairs):
         ax = Quaternion(quaternions_conversions).to_axes_angles()
-        assert np.allclose(
-            np.deg2rad(ax.angle), axis_angle_pairs[:, 3], atol=4
-        )
+        assert np.allclose(np.deg2rad(ax.angle), axis_angle_pairs[:, 3], atol=4)
 
     def test_from_axes_angles_empty(self):
         q = Quaternion.from_axes_angles([], [])
@@ -548,16 +517,12 @@ class TestFromToRodrigues:
     Rodrigues and Rodrigues-Frank vectors.
     """
 
-    def test_from_to_rodrigues(
-        self, quaternions_conversions, rodrigues_vectors
-    ):
+    def test_from_to_rodrigues(self, quaternions_conversions, rodrigues_vectors):
         axes = rodrigues_vectors[..., :3]
         angles = rodrigues_vectors[..., 3]
 
         q1 = Quaternion(quaternions_conversions)
-        with pytest.warns(
-            UserWarning, match="Highest angle is greater than 179.999 "
-        ):
+        with pytest.warns(UserWarning, match="Highest angle is greater than 179.999 "):
             q2 = Quaternion.from_rodrigues(axes, angles)
         assert np.allclose(q1.data, q2.data, atol=1e-4)
         ro = q1.to_rodrigues(frank=True)
@@ -567,9 +532,7 @@ def test_from_to_rodrigues(
             _ = Quaternion.from_rodrigues([1e15, 1e15, 1e10])
         with pytest.warns(UserWarning, match="Max."):
             _ = Quaternion.from_rodrigues([0, 0, 1e-16])
-        with pytest.raises(
-            ValueError, match="Final dimension of vector array must be"
-        ):
+        with pytest.raises(ValueError, match="Final dimension of vector array must be"):
             Quaternion.from_rodrigues([1, 2, 3, 4])
 
     def test_from_rodrigues_empty(self):
@@ -582,9 +545,7 @@ class TestFromToHomochoric:
     homochoric vectors.
     """
 
-    def test_from_to_homochoric(
-        self, homochoric_vectors, quaternions_conversions
-    ):
+    def test_from_to_homochoric(self, homochoric_vectors, quaternions_conversions):
         ho1 = homochoric_vectors
         ho2 = Vector3d(ho1)
         ho3 = Homochoric(ho1)
@@ -598,9 +559,7 @@ def test_from_to_homochoric(
         assert np.allclose(q1.data, quaternions_conversions, atol=1e-4)
         assert np.allclose(q2.data, quaternions_conversions, atol=1e-4)
         assert np.allclose(q3.data, quaternions_conversions, atol=1e-4)
-        assert np.allclose(
-            q4.data, quaternions_conversions.reshape(2, 5, 4), atol=1e-4
-        )
+        assert np.allclose(q4.data, quaternions_conversions.reshape(2, 5, 4), atol=1e-4)
 
         assert np.allclose(ho1, q1.to_homochoric().data, atol=1e-4)
         assert np.allclose(ho1, q2.to_homochoric().data, atol=1e-4)
@@ -608,9 +567,7 @@ def test_from_to_homochoric(
         assert np.allclose(ho4, q4.to_homochoric().data, atol=1e-4)
 
     def test_from_homochoric_raises(self):
-        with pytest.raises(
-            ValueError, match="Final dimension of vector array must be"
-        ):
+        with pytest.raises(ValueError, match="Final dimension of vector array must be"):
             Quaternion.from_homochoric([1, 2])
 
     def test_from_homochoric_empty(self):

From b15fff83011cbd333d8dd42fa88c68634afb33e0 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <argerlt@gmail.com>
Date: Sun, 13 Jul 2025 04:29:15 -0600
Subject: [PATCH 04/23] adding requested changes fomr #558

---
 orix/quaternion/misorientation.py |  5 ----
 orix/quaternion/quaternion.py     | 46 ++++++++++++++-----------------
 2 files changed, 21 insertions(+), 30 deletions(-)

diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index c7cc140c4..c4710cf5c 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -388,11 +388,6 @@ def reduce(self) -> Misorientation:
         """Return equivalent transformations which have the smallest
         angle of rotation as a new misorientation.
 
-        Parameters
-        ----------
-        verbose
-            Whether to print a progressbar. Default is ``False``.
-
         Returns
         -------
         M
diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index f72d6b704..e321be0fd 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -247,15 +247,11 @@ def __eq__(self, other: Any | Quaternion) -> bool:
     # ------------------------ Class methods ------------------------- #
 
     @classmethod
-    def random(cls, shape: Union[int, tuple] = 1) -> Quaternion:
+    def random(cls, shape: int | tuple = 1) -> Quaternion:
         quat = super().random(shape)
         quat.data[:, 0] = np.abs(quat.data[:, 0])
         return quat
 
-        O = super().__invert__()
-        O.symmetry = self.symmetry
-        return O
-
     @classmethod
     def from_axes_angles(
         cls,
@@ -697,22 +693,22 @@ def from_align_vectors(
 
     @classmethod
     def from_path_ends(
-        cls, waypoints: Quaternion, close_loop: bool = False, steps: int = 100
+        cls, points: Quaternion, closed: bool = False, steps: int = 100
     ) -> Quaternion:
-        """Return Quaternions tracing the shortest path between two or more
-        consecutive waypoints.
+        """Return quaternions tracing the shortest path between two or more
+        consecutive points.
 
         Parameters
         ----------
-        waypoints : Quaternion
+        points
             Two or more quaternions that define waypoints along a path through
             rotation space (SO3).
-        close_loop : bool, optional
+        closed
             Option to add a final trip from the last waypoint back to the
-            first, thus closing the loop. Default is False.
-        steps : int, optional
-        Number of points to return along the path between each pair of
-        waypoints. The default is 100.
+            first, thus closing the loop. The default is False.
+        steps
+            Number of quaternions to return along the path between each
+            pair of waypoints. The default is 100.
 
         Returns
         -------
@@ -721,30 +717,30 @@ def from_path_ends(
 
         Notes
         -----
-        This method can use Orientations and Misorientations as inputs, and
-        will return an object of the same class. However, symmetry is ignored
-        when determining the shortest routes.
+        This method can use :class:Orientation and :class:Misorientation as
+        inputs and will return an object of the same class. However,
+        symmetry is ignored when determining the shortest routes.
         """
-        waypoints = waypoints.flatten()
-        n = waypoints.size
-        if not close_loop:
+        points = points.flatten()
+        n = points.size
+        if not closed:
             n = n - 1
 
         path_list = []
         for i in range(n):
             # get start and end for this leg of the trip
-            q1 = waypoints[i]
-            q2 = waypoints[(i + 1) % (waypoints.size)]
+            q1 = points[i]
+            q2 = points[(i + 1) % (points.size)]
             # find the ax/ang describing the trip between points
             ax, ang = _conversions.qu2ax((~q1 * q2).data)
             # get 'steps=n' steps along the trip and add them to the journey
             trip = Quaternion.from_axes_angles(ax, np.linspace(0, ang, steps))
             path_list.append((q1 * (trip.flatten())).data)
         path_data = np.concatenate(path_list, axis=0)
-        path = waypoints.__class__(path_data)
+        path = points.__class__(path_data)
         # copy the symmetry if it exists
-        if hasattr(waypoints, "_symmetry"):
-            path._symmetry = waypoints._symmetry
+        if hasattr(points, "_symmetry"):
+            path._symmetry = points._symmetry
         return path
 
     @classmethod

From 4b3d35b9a9d79bb5703e7f52ab1282692e32759d Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Thu, 17 Jul 2025 15:46:34 -0600
Subject: [PATCH 05/23] made Quaternion.from_path_ends blind to symmetry, and
 added symmetry-aware counterpart to Misorientation

---
 orix/quaternion/misorientation.py         | 32 +++++++++++++++++++++++
 orix/quaternion/quaternion.py             | 24 ++++++-----------
 orix/tests/quaternion/test_orientation.py | 28 ++++++++++++++++++++
 orix/tests/quaternion/test_quaternion.py  |  2 +-
 4 files changed, 69 insertions(+), 17 deletions(-)

diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index c4710cf5c..9175bd5e5 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -266,6 +266,38 @@ def from_scipy_rotation(
             M.symmetry = symmetry
         return M
 
+    @classmethod
+    def from_path_ends(
+        cls, points: Misorientation, closed: bool = False, steps: int = 100
+    ) -> Misorientation:
+        """Return (mis)orientations tracing the shortest path between
+        two or more consecutive points.
+
+        Parameters
+        ----------
+        points
+            Two or more (mis)orientations that define waypoints along
+            a path through rotation space (SO3).
+        closed
+            Option to add a final trip from the last waypoint back to
+            the first, thus closing the loop. The default is False.
+        steps
+            Number of (mis)orientations to return along the path
+            between each pair of waypoints. The default is 100.
+
+        Returns
+        -------
+        path :Quaternion
+            quaternions that map a path between the given waypoints.
+
+        """
+        out = super().from_path_ends(points=points, closed=closed, steps=steps)
+        path = cls(out.data)
+        # copy the symmetry if it exists.
+        if hasattr(points, "_symmetry"):
+            path._symmetry = points._symmetry
+        return path
+
     @classmethod
     def random(
         cls,
diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index e321be0fd..5e9db9f3b 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -695,17 +695,17 @@ def from_align_vectors(
     def from_path_ends(
         cls, points: Quaternion, closed: bool = False, steps: int = 100
     ) -> Quaternion:
-        """Return quaternions tracing the shortest path between two or more
-        consecutive points.
+        """Return quaternions tracing the shortest path between two or
+        more consecutive points.
 
         Parameters
         ----------
         points
-            Two or more quaternions that define waypoints along a path through
-            rotation space (SO3).
+            Two or more quaternions that define waypoints along a path
+            through rotation space (SO3).
         closed
-            Option to add a final trip from the last waypoint back to the
-            first, thus closing the loop. The default is False.
+            Option to add a final trip from the last waypoint back to
+            the first, thus closing the loop. The default is False.
         steps
             Number of quaternions to return along the path between each
             pair of waypoints. The default is 100.
@@ -713,13 +713,8 @@ def from_path_ends(
         Returns
         -------
         path :Quaternion
-            quaternions that map out a path between the given waypoints.
+            quaternions that map a path between the given waypoints.
 
-        Notes
-        -----
-        This method can use :class:Orientation and :class:Misorientation as
-        inputs and will return an object of the same class. However,
-        symmetry is ignored when determining the shortest routes.
         """
         points = points.flatten()
         n = points.size
@@ -737,10 +732,7 @@ def from_path_ends(
             trip = Quaternion.from_axes_angles(ax, np.linspace(0, ang, steps))
             path_list.append((q1 * (trip.flatten())).data)
         path_data = np.concatenate(path_list, axis=0)
-        path = points.__class__(path_data)
-        # copy the symmetry if it exists
-        if hasattr(points, "_symmetry"):
-            path._symmetry = points._symmetry
+        path = cls(path_data)
         return path
 
     @classmethod
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index 0645a135e..96677a507 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -441,6 +441,34 @@ def test_from_scipy_rotation(self):
         with pytest.raises(TypeError, match="Value must be a 2-tuple of"):
             _ = Misorientation.from_scipy_rotation(r_scipy, Oh)
 
+    def test_from_path_ends(self):
+        """check from_path_ends returns what you would expect and
+        preserves symmetry information."""
+        q = Quaternion.random(10)
+        r = Rotation.random(10)
+        o = Orientation.random(10, Oh)
+        m = Misorientation.random(10, [D3, Oh])
+
+        # make sure the result is the correct class.
+        a = Quaternion.from_path_ends(q)
+        b = Rotation.from_path_ends(q)
+        c = Orientation.from_path_ends(r)
+        d = Quaternion.from_path_ends(o)
+        e = Orientation.from_path_ends(q)
+        f = Misorientation.from_path_ends(m)
+        g = Orientation.from_path_ends(o)
+        assert isinstance(a, Quaternion)
+        assert isinstance(b, Rotation)
+        assert isinstance(c, Orientation)
+        assert isinstance(d, Quaternion)
+        assert isinstance(e, Orientation)
+        assert isinstance(f, Misorientation)
+        assert isinstance(g, Orientation)
+
+        # make sure symmetry information is preserved.
+        assert f.symmetry == m.symmetry
+        assert g.symmetry == o.symmetry
+
     def test_inverse(self):
         M1 = Misorientation([np.sqrt(2) / 2, np.sqrt(2) / 2, 0, 0], (Oh, D6))
         M2 = ~M1
diff --git a/orix/tests/quaternion/test_quaternion.py b/orix/tests/quaternion/test_quaternion.py
index 332193a0a..41a9e2605 100644
--- a/orix/tests/quaternion/test_quaternion.py
+++ b/orix/tests/quaternion/test_quaternion.py
@@ -352,7 +352,7 @@ def test_from_path_ends(self):
             )
         )
         path = Quaternion.from_path_ends(waypoints)
-        loop = Quaternion.from_path_ends(waypoints, close_loop=True, steps=11)
+        loop = Quaternion.from_path_ends(waypoints, closed=True, steps=11)
         # check the sizes are as expected
         assert path.shape == (1100,)
         assert loop.shape == (132,)

From 6fe959f9ccb4729db9031ca9c09a43f97f87933f Mon Sep 17 00:00:00 2001
From: Austin Gerlt <argerlt@gmail.com>
Date: Fri, 18 Jul 2025 03:07:45 -0600
Subject: [PATCH 06/23] fixing docstring styling

---
 orix/quaternion/quaternion.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index 5e9db9f3b..249ead06e 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -701,7 +701,7 @@ def from_path_ends(
         Parameters
         ----------
         points
-            Two or more quaternions that define waypoints along a path
+            Two or more quaternions that define points along a path
             through rotation space (SO3).
         closed
             Option to add a final trip from the last waypoint back to
@@ -712,7 +712,7 @@ def from_path_ends(
 
         Returns
         -------
-        path :Quaternion
+        path
             quaternions that map a path between the given waypoints.
 
         """

From 18088ef307a4e4e5e89924c9d3fdd668ac74f481 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Fri, 18 Jul 2025 11:48:07 -0600
Subject: [PATCH 07/23] formatting and clarifying tests

---
 orix/quaternion/misorientation.py         |  3 +-
 orix/quaternion/quaternion.py             |  1 -
 orix/tests/quaternion/test_orientation.py | 75 +++++++++++++----------
 3 files changed, 42 insertions(+), 37 deletions(-)

diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index 9175bd5e5..eafd7b6db 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -287,9 +287,8 @@ def from_path_ends(
 
         Returns
         -------
-        path :Quaternion
+        path
             quaternions that map a path between the given waypoints.
-
         """
         out = super().from_path_ends(points=points, closed=closed, steps=steps)
         path = cls(out.data)
diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index 249ead06e..d11fa2b60 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -714,7 +714,6 @@ def from_path_ends(
         -------
         path
             quaternions that map a path between the given waypoints.
-
         """
         points = points.flatten()
         n = points.size
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index 96677a507..c4e93c661 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -321,6 +321,39 @@ def test_symmetry_property_wrong_number_of_values_misorientation(error_type, val
         o.symmetry = value
 
 
+def test_from_path_ends():
+    """check from_path_ends returns what you would expect and
+    preserves symmetry information.
+
+    In particular, ensure the class of the returned object matches the class
+    used for creating it, NOT the class of the object passed in.
+    """
+    q = Quaternion.random(10)
+    r = Rotation.random(10)
+    o = Orientation.random(10, Oh)
+    m = Misorientation.random(10, [D3, Oh])
+
+    # make sure the result is the correct class.
+    a = Quaternion.from_path_ends(q)
+    b = Rotation.from_path_ends(q)
+    c = Orientation.from_path_ends(r)
+    d = Quaternion.from_path_ends(o)
+    e = Orientation.from_path_ends(q)
+    f = Misorientation.from_path_ends(m)
+    g = Orientation.from_path_ends(o)
+    assert isinstance(a, Quaternion)
+    assert isinstance(b, Rotation)
+    assert isinstance(c, Orientation)
+    assert isinstance(d, Quaternion)
+    assert isinstance(e, Orientation)
+    assert isinstance(f, Misorientation)
+    assert isinstance(g, Orientation)
+
+    # make sure symmetry information is preserved.
+    assert f.symmetry == m.symmetry
+    assert g.symmetry == o.symmetry
+
+
 class TestMisorientation:
     def test_get_distance_matrix(self):
         """Compute distance between every misorientation in an instance
@@ -442,32 +475,9 @@ def test_from_scipy_rotation(self):
             _ = Misorientation.from_scipy_rotation(r_scipy, Oh)
 
     def test_from_path_ends(self):
-        """check from_path_ends returns what you would expect and
-        preserves symmetry information."""
-        q = Quaternion.random(10)
-        r = Rotation.random(10)
-        o = Orientation.random(10, Oh)
-        m = Misorientation.random(10, [D3, Oh])
-
-        # make sure the result is the correct class.
-        a = Quaternion.from_path_ends(q)
-        b = Rotation.from_path_ends(q)
-        c = Orientation.from_path_ends(r)
-        d = Quaternion.from_path_ends(o)
-        e = Orientation.from_path_ends(q)
-        f = Misorientation.from_path_ends(m)
-        g = Orientation.from_path_ends(o)
-        assert isinstance(a, Quaternion)
-        assert isinstance(b, Rotation)
-        assert isinstance(c, Orientation)
-        assert isinstance(d, Quaternion)
-        assert isinstance(e, Orientation)
-        assert isinstance(f, Misorientation)
-        assert isinstance(g, Orientation)
-
-        # make sure symmetry information is preserved.
-        assert f.symmetry == m.symmetry
-        assert g.symmetry == o.symmetry
+        # generate paths with misorientations to check symmetry copying
+        wp_m = Misorientation(data=np.eye(4)[2:], symmetry=[Oh, C3])
+        assert Misorientation.from_path_ends(wp_m)._symmetry == (Oh, C3)
 
     def test_inverse(self):
         M1 = Misorientation([np.sqrt(2) / 2, np.sqrt(2) / 2, 0, 0], (Oh, D6))
@@ -628,14 +638,6 @@ def test_from_scipy_rotation(self):
         with pytest.raises(TypeError, match="Value must be an instance of"):
             _ = Orientation.from_scipy_rotation(r_scipy, (Oh, Oh))
 
-    def test_from_path_ends(self):
-        # generate paths with misorientations and orientations to check
-        # symmetry copying
-        wp_o = Orientation(data=np.eye(4)[:2], symmetry=Oh)
-        wp_m = Misorientation(data=np.eye(4)[2:], symmetry=[Oh, C3])
-        assert Orientation.from_path_ends(wp_o)._symmetry == (C1, Oh)
-        assert Misorientation.from_path_ends(wp_m)._symmetry == (Oh, C3)
-
 
 class TestOrientation:
     @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
@@ -846,6 +848,11 @@ def test_in_fundamental_region(self):
             region = np.radians(pg.euler_fundamental_region)
             assert np.all(np.max(ori.in_euler_fundamental_region(), axis=0) <= region)
 
+    def test_from_path_ends(self):
+        # generate paths with orientations to check symmetry copying
+        wp_o = Orientation(data=np.eye(4)[:2], symmetry=Oh)
+        assert Orientation.from_path_ends(wp_o)._symmetry == (C1, Oh)
+
     def test_inverse(self):
         O1 = Orientation([np.sqrt(2) / 2, np.sqrt(2) / 2, 0, 0], D6)
         O2 = ~O1

From 892054acee019b65bc85796197535cd50e6dd387 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Fri, 18 Jul 2025 12:38:21 -0600
Subject: [PATCH 08/23] clarifying tests and adding from_path_ends example

---
 examples/plotting/plot_non_euclidean_paths.py | 81 +++++++++++++++++++
 orix/tests/quaternion/test_quaternion.py      | 12 +++
 2 files changed, 93 insertions(+)
 create mode 100644 examples/plotting/plot_non_euclidean_paths.py

diff --git a/examples/plotting/plot_non_euclidean_paths.py b/examples/plotting/plot_non_euclidean_paths.py
new file mode 100644
index 000000000..3a3b6ca16
--- /dev/null
+++ b/examples/plotting/plot_non_euclidean_paths.py
@@ -0,0 +1,81 @@
+r"""
+========================
+Plot symmetry operations
+========================
+
+This example shows how to use the `from_path_ends` functions from
+:class:`~orix.vector.Vector3d`, :class:`~orix.quaternions.Rotation`, and
+:class:`~orix.quaternions.Orientation` to draw paths through thier
+respective non-Euclidean spaces.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from orix.quaternion import Orientation, Rotation
+from orix.quaternion.symmetry import Oh, D3
+from orix.vector import Vector3d
+
+
+fig = plt.figure()
+
+# plot a path in homochoric space with no symmetry
+rot_path = Rotation(
+    data=np.array(
+        [
+            [1, 0, 0, 0],
+            [1, 1, 0, 0],
+            [1, 0, 1, 0],
+            [1, 0, 0, 1],
+            [1, 0, -1, 0],
+            [1, 0, 0, -1],
+            [1, 0, 0, -1],
+        ]
+    )
+)
+rotation_path = Rotation.from_path_ends(rot_path, closed=True)
+# cast the rotation to a symmetry-less orientation for plotting purposes
+Orientation(rotation_path).scatter(
+    figure=fig, position=[2, 2, 1], marker=">", c=np.arange(700)
+)
+
+# plot a path in rodrigues space with m-3m (cubic) symmetry.
+m3m_path = Orientation(
+    data=np.array(
+        [
+            [1, 0, 0, 0],
+            [2, 1, 0, 0],
+            [3, 0, 1, 0],
+            [4, 0, 0, 1],
+            [5, 0, -1, 0],
+            [6, 0, 0, -1],
+            [7, 0, 0, -1],
+            [8, 1, 0, 0],
+            [9, 0, 1, 0],
+            [10, 0, 0, 1],
+            [11, 0, -1, 0],
+            [12, 0, 0, -1],
+            [13, 0, 0, -1],
+        ]
+    ),
+    symmetry=Oh,
+)
+orientation_path = Orientation.from_path_ends(m3m_path.reduce(), closed=True).reduce()
+orientation_path.scatter(figure=fig, position=[2, 2, 2], marker=">", c=np.arange(1300))
+
+# plot a second path in rodrigues space with symmetry, but while also crossing a
+# symmetry boundary
+fiber_start = Rotation.identity(1)
+fiber_middle = Rotation.from_axes_angles([1, 2, 3], np.pi)
+fiber_end = Rotation.from_axes_angles([1, 2, 3], 2 * np.pi)
+fiber_points = Orientation.stack([fiber_start, fiber_middle, fiber_end])
+fiber_points.symmetry = Oh
+fiber_path = Orientation.from_path_ends(fiber_points, closed=False).reduce()
+fiber_path.scatter(figure=fig, position=[2, 2, 3], marker=">", c=np.arange(200))
+
+
+# plot vectors
+ax4 = plt.subplot(2, 2, 4, projection="stereographic")
+vector_points = Vector3d(np.array([[-1,0,0],[0,1,0.1],[1,0,0.2],[0,-1,0.3],[-1,0,0.4]]))
+
+vector_path = Vector3d.from_path_ends(vector_points,steps = 200)
+ax4.scatter(vector_path, figure=fig, marker=">", c=np.arange(vector_path.size))
diff --git a/orix/tests/quaternion/test_quaternion.py b/orix/tests/quaternion/test_quaternion.py
index 41a9e2605..fea55e915 100644
--- a/orix/tests/quaternion/test_quaternion.py
+++ b/orix/tests/quaternion/test_quaternion.py
@@ -362,6 +362,18 @@ def test_from_path_ends(self):
         assert np.all(np.std(path_spacing, axis=1) < 1e-12)
         assert np.all(np.std(loop_spacing, axis=1) < 1e-12)
 
+    def test_from_path_ends_fiber(self):
+        # check that a linear path in quaternion space follows an explicitly defined
+        # fiber along the same path.
+        # this ensures the path is the shortest distance in SO3 space, (as opposed
+        # to rodrigues or quaternion space) and also evenly spaced along the path.
+        Q1 = Quaternion.identity()
+        Q2 = Quaternion.from_axes_angles([1, 1, 1], 60, degrees=True)
+        Q12 = Quaternion.stack((Q1, Q2))
+        Q_path1 = Quaternion.from_axes_angles([1, 1, 1], np.arange(59), degrees=True)
+        Q_path2 = Quaternion.from_path_ends(Q12, steps=Q_path1.size)
+        assert np.allclose(Q_path1.dot(Q_path2), 1, atol=1e-3)
+
     def test_equality(self):
         Q1 = Quaternion.from_axes_angles([1, 1, 1], -np.pi / 3)
         Q2 = Quaternion.from_axes_angles([1, 1, 1], np.pi / 3)

From 269996cff3a7df5033171b3ace20b8be47adb1ce Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Fri, 18 Jul 2025 12:48:54 -0600
Subject: [PATCH 09/23] formatting

---
 examples/plotting/plot_non_euclidean_paths.py | 12 +++++++-----
 1 file changed, 7 insertions(+), 5 deletions(-)

diff --git a/examples/plotting/plot_non_euclidean_paths.py b/examples/plotting/plot_non_euclidean_paths.py
index 3a3b6ca16..50dbe2060 100644
--- a/examples/plotting/plot_non_euclidean_paths.py
+++ b/examples/plotting/plot_non_euclidean_paths.py
@@ -9,13 +9,13 @@
 respective non-Euclidean spaces.
 """
 
-import numpy as np
 import matplotlib.pyplot as plt
+import numpy as np
+
 from orix.quaternion import Orientation, Rotation
-from orix.quaternion.symmetry import Oh, D3
+from orix.quaternion.symmetry import D3, Oh
 from orix.vector import Vector3d
 
-
 fig = plt.figure()
 
 # plot a path in homochoric space with no symmetry
@@ -75,7 +75,9 @@
 
 # plot vectors
 ax4 = plt.subplot(2, 2, 4, projection="stereographic")
-vector_points = Vector3d(np.array([[-1,0,0],[0,1,0.1],[1,0,0.2],[0,-1,0.3],[-1,0,0.4]]))
+vector_points = Vector3d(
+    np.array([[-1, 0, 0], [0, 1, 0.1], [1, 0, 0.2], [0, -1, 0.3], [-1, 0, 0.4]])
+)
 
-vector_path = Vector3d.from_path_ends(vector_points,steps = 200)
+vector_path = Vector3d.from_path_ends(vector_points, steps=200)
 ax4.scatter(vector_path, figure=fig, marker=">", c=np.arange(vector_path.size))

From e5c307f7c57bc07a860bcfa1d2204a942af37573 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Wed, 3 Sep 2025 19:56:12 -0600
Subject: [PATCH 10/23] including suggestions and updating example

---
 examples/plotting/plot_non_euclidean_paths.py | 138 +++++++++++-------
 orix/quaternion/misorientation.py             |  18 ++-
 orix/quaternion/orientation.py                |  35 +++++
 orix/tests/quaternion/test_orientation.py     |  53 +++++--
 4 files changed, 169 insertions(+), 75 deletions(-)

diff --git a/examples/plotting/plot_non_euclidean_paths.py b/examples/plotting/plot_non_euclidean_paths.py
index 50dbe2060..2768c0a2a 100644
--- a/examples/plotting/plot_non_euclidean_paths.py
+++ b/examples/plotting/plot_non_euclidean_paths.py
@@ -1,83 +1,115 @@
 r"""
-========================
-Plot symmetry operations
-========================
+========================================
+Plot Paths Through Non-Euclidean Spaces
+========================================
 
-This example shows how to use the `from_path_ends` functions from
-:class:`~orix.vector.Vector3d`, :class:`~orix.quaternions.Rotation`, and
-:class:`~orix.quaternions.Orientation` to draw paths through thier
-respective non-Euclidean spaces.
+This example shows three variations on how 'from_path_ends' can be
+used to plot paths between points in rotational and vector spaces.
+
+This functionality is available in :class:`~orix.vector.Vector3d`,
+:class:`~orix.quaternions.Rotation`,
+:class:`~orix.quaternions.Orientation`,
+and :class:`~orix.quaternions.Misorientation`.
 """
 
 import matplotlib.pyplot as plt
+from matplotlib import cm
 import numpy as np
 
-from orix.quaternion import Orientation, Rotation
+from orix.quaternion import Misorientation, Orientation, Rotation
 from orix.quaternion.symmetry import D3, Oh
 from orix.vector import Vector3d
 
-fig = plt.figure()
+fig = plt.figure(figsize=(4, 8))
 
-# plot a path in homochoric space with no symmetry
-rot_path = Rotation(
+# ========= #
+# Example 1: Plotting a path of rotations with no symmetry in homochoric space
+# ========= #
+rots_along_path = Rotation(
     data=np.array(
         [
             [1, 0, 0, 0],
-            [1, 1, 0, 0],
-            [1, 0, 1, 0],
             [1, 0, 0, 1],
-            [1, 0, -1, 0],
-            [1, 0, 0, -1],
-            [1, 0, 0, -1],
+            [1, 1, 1, 1],
         ]
     )
 )
-rotation_path = Rotation.from_path_ends(rot_path, closed=True)
-# cast the rotation to a symmetry-less orientation for plotting purposes
-Orientation(rotation_path).scatter(
-    figure=fig, position=[2, 2, 1], marker=">", c=np.arange(700)
-)
+n_steps = 20
+rotation_path = Rotation.from_path_ends(rots_along_path, steps=n_steps)
+# create an Orientation loop using this path with no symmetry elements
+ori_path = Orientation(rotation_path)
+# plot the path in homochoric space
+segment_colors = cm.inferno(np.linspace(0, 1, n_steps))
 
-# plot a path in rodrigues space with m-3m (cubic) symmetry.
-m3m_path = Orientation(
+path_colors = np.vstack([segment_colors for x in range(rots_along_path.size - 1)])
+ori_path.scatter(figure=fig, position=[3, 1, 1], marker=">", c=path_colors)
+fig.axes[0].set_title(r"$90^\circ$ rotation around X, then Y")
+
+# ========= #
+# Example 2: Plotting the rotation of several orientations in m3m Rodrigues
+# space around the z axis.
+# ========= #
+oris = Orientation(
     data=np.array(
         [
-            [1, 0, 0, 0],
-            [2, 1, 0, 0],
-            [3, 0, 1, 0],
-            [4, 0, 0, 1],
-            [5, 0, -1, 0],
-            [6, 0, 0, -1],
-            [7, 0, 0, -1],
-            [8, 1, 0, 0],
-            [9, 0, 1, 0],
-            [10, 0, 0, 1],
-            [11, 0, -1, 0],
-            [12, 0, 0, -1],
-            [13, 0, 0, -1],
+            [0.69, 0.24, 0.68, 0.01],
+            [0.26, 0.59, 0.32, 0.7],
+            [0.07, 0.17, 0.93, 0.31],
+            [0.6, 0.03, 0.61, 0.52],
+            [0.51, 0.38, 0.34, 0.69],
+            [0.31, 0.86, 0.22, 0.35],
+            [0.68, 0.67, 0.06, 0.31],
+            [0.01, 0.12, 0.05, 0.99],
+            [0.39, 0.45, 0.34, 0.72],
+            [0.65, 0.59, 0.46, 0.15],
         ]
     ),
     symmetry=Oh,
+).reduce()
+# define a 20 degree rotation around the z axis
+shift = Orientation.from_axes_angles([0, 0, 1], np.pi / 9)
+segment_colors = cm.inferno(np.linspace(0, 1, 10))
+
+ori_paths = []
+for ori in oris:
+    shifted = (shift * ori).reduce()
+    to_from = Orientation.stack([ori, shifted]).flatten()
+    ori_paths.append(Orientation.from_path_ends(to_from, steps=10))
+# plot a path in roddrigues space with m-3m (cubic) symmetry.
+ori_path = Orientation.stack(ori_paths).flatten()
+ori_path.symmetry = Oh
+ori_path.scatter(
+    figure=fig,
+    position=[3, 1, 2],
+    marker=">",
+    c=np.tile(segment_colors, [10, 1]),
+    projection="rodrigues",
 )
-orientation_path = Orientation.from_path_ends(m3m_path.reduce(), closed=True).reduce()
-orientation_path.scatter(figure=fig, position=[2, 2, 2], marker=">", c=np.arange(1300))
+fig.axes[1].set_title(r"$20^{\circ}$ rotations around X-axis in m3m")
 
-# plot a second path in rodrigues space with symmetry, but while also crossing a
-# symmetry boundary
-fiber_start = Rotation.identity(1)
-fiber_middle = Rotation.from_axes_angles([1, 2, 3], np.pi)
-fiber_end = Rotation.from_axes_angles([1, 2, 3], 2 * np.pi)
-fiber_points = Orientation.stack([fiber_start, fiber_middle, fiber_end])
-fiber_points.symmetry = Oh
-fiber_path = Orientation.from_path_ends(fiber_points, closed=False).reduce()
-fiber_path.scatter(figure=fig, position=[2, 2, 3], marker=">", c=np.arange(200))
+# ========= #
+# Example 3: creating a customized Wulf Plotting the rotation of several orientations in m3m Rodrigues
+# space around the z axis.
+# ========= #
 
 
 # plot vectors
-ax4 = plt.subplot(2, 2, 4, projection="stereographic")
-vector_points = Vector3d(
-    np.array([[-1, 0, 0], [0, 1, 0.1], [1, 0, 0.2], [0, -1, 0.3], [-1, 0, 0.4]])
-)
+ax_upper = plt.subplot(3, 1, 3, projection="stereographic", hemisphere="upper")
+r90x = Rotation.from_axes_angles([1, -1, -1], [0, 60], degrees=True)
+x_axis_points = r90x * Vector3d.xvector()
+y_axis_points = r90x * Vector3d.yvector()
+z_axis_points = r90x * Vector3d.zvector()
+
+x_axis_path = Vector3d.from_path_ends(x_axis_points.unique())
+y_axis_path = Vector3d.from_path_ends(y_axis_points.unique())
+z_axis_path = Vector3d.from_path_ends(z_axis_points.unique())
+cx = cm.Reds(np.linspace(0.1, 1, x_axis_path.size))
+cy = cm.Greens(np.linspace(0.1, 1, y_axis_path.size))
+cz = cm.Blues(np.linspace(0.1, 1, z_axis_path.size))
+
+spx = ax_upper.scatter(x_axis_path, figure=fig, marker=">", c=cx, label="X")
+spy = ax_upper.scatter(y_axis_path, figure=fig, marker=">", c=cy, label="Y")
+spz = ax_upper.scatter(z_axis_path, figure=fig, marker=">", c=cz, label="Z")
+ax_upper.legend(loc="lower center", ncols=3)
 
-vector_path = Vector3d.from_path_ends(vector_points, steps=200)
-ax4.scatter(vector_path, figure=fig, marker=">", c=np.arange(vector_path.size))
+plt.tight_layout()
diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index eafd7b6db..018d0d06c 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -270,31 +270,35 @@ def from_scipy_rotation(
     def from_path_ends(
         cls, points: Misorientation, closed: bool = False, steps: int = 100
     ) -> Misorientation:
-        """Return (mis)orientations tracing the shortest path between
+        """Return misorientations tracing the shortest path between
         two or more consecutive points.
 
         Parameters
         ----------
         points
-            Two or more (mis)orientations that define waypoints along
+            Two or more misorientations that define waypoints along
             a path through rotation space (SO3).
         closed
             Option to add a final trip from the last waypoint back to
             the first, thus closing the loop. The default is False.
         steps
-            Number of (mis)orientations to return along the path
+            Number of misorientations to return along the path
             between each pair of waypoints. The default is 100.
 
         Returns
         -------
         path
-            quaternions that map a path between the given waypoints.
+            misorientations that map a path between the given waypoints.
         """
+        # Confirm `points` are (mis)orientations.
+        if not isinstance(points, Misorientation):
+            raise TypeError(
+                f"Points must be a Misorientation, not of type {type(points)}"
+            )
+        # Create a path through Quaternion space, then reapply the symmetry.
         out = super().from_path_ends(points=points, closed=closed, steps=steps)
         path = cls(out.data)
-        # copy the symmetry if it exists.
-        if hasattr(points, "_symmetry"):
-            path._symmetry = points._symmetry
+        path._symmetry = points._symmetry
         return path
 
     @classmethod
diff --git a/orix/quaternion/orientation.py b/orix/quaternion/orientation.py
index 598208c75..d93b524d5 100644
--- a/orix/quaternion/orientation.py
+++ b/orix/quaternion/orientation.py
@@ -346,6 +346,41 @@ def from_scipy_rotation(
             O.symmetry = symmetry
         return O
 
+    @classmethod
+    def from_path_ends(
+        cls, points: Orientation, closed: bool = False, steps: int = 100
+    ) -> Misorientation:
+        """Return orientations tracing the shortest path between
+        two or more consecutive points.
+
+        Parameters
+        ----------
+        points
+            Two or more orientations that define waypoints along
+            a path through rotation space (SO3).
+        closed
+            Option to add a final trip from the last waypoint back to
+            the first, thus closing the loop. The default is False.
+        steps
+            Number of orientations to return along the path
+            between each pair of waypoints. The default is 100.
+
+        Returns
+        -------
+        path
+            orientations that map a path between the given waypoints.
+        """
+        # Confirm `points` are orientations.
+        if not isinstance(points, Orientation):
+            raise TypeError(
+                f"Points must be an Orientation instance, not of type {type(points)}"
+            )
+        # Create a path through Quaternion space, then reapply the symmetry.
+        out = super().from_path_ends(points=points, closed=closed, steps=steps)
+        path = cls(out.data)
+        path._symmetry = points._symmetry
+        return path
+
     @classmethod
     def random(
         cls, shape: Union[int, tuple] = 1, symmetry: Optional[Symmetry] = None
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index c4e93c661..a259fc998 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -333,25 +333,48 @@ def test_from_path_ends():
     o = Orientation.random(10, Oh)
     m = Misorientation.random(10, [D3, Oh])
 
-    # make sure the result is the correct class.
+    # Quaternion sanity checks
     a = Quaternion.from_path_ends(q)
-    b = Rotation.from_path_ends(q)
-    c = Orientation.from_path_ends(r)
-    d = Quaternion.from_path_ends(o)
-    e = Orientation.from_path_ends(q)
-    f = Misorientation.from_path_ends(m)
-    g = Orientation.from_path_ends(o)
     assert isinstance(a, Quaternion)
-    assert isinstance(b, Rotation)
-    assert isinstance(c, Orientation)
+    b = Quaternion.from_path_ends(r)
+    assert isinstance(b, Quaternion)
+    c = Quaternion.from_path_ends(o)
+    assert isinstance(c, Quaternion)
+    d = Quaternion.from_path_ends(m)
     assert isinstance(d, Quaternion)
-    assert isinstance(e, Orientation)
-    assert isinstance(f, Misorientation)
-    assert isinstance(g, Orientation)
 
-    # make sure symmetry information is preserved.
-    assert f.symmetry == m.symmetry
-    assert g.symmetry == o.symmetry
+    # Rotation sanity checks
+    a = Rotation.from_path_ends(q)
+    assert isinstance(a, Rotation)
+    b = Rotation.from_path_ends(r)
+    assert isinstance(b, Rotation)
+    c = Rotation.from_path_ends(o)
+    assert isinstance(c, Rotation)
+    d = Rotation.from_path_ends(m)
+    assert isinstance(d, Rotation)
+
+    # Misorientation sanity checks
+    with pytest.raises(TypeError, match="Points must be a Misorientation"):
+        a = Misorientation.from_path_ends(q)
+    with pytest.raises(TypeError, match="Points must be a Misorientation"):
+        b = Misorientation.from_path_ends(r)
+    c = Misorientation.from_path_ends(o)
+    assert isinstance(c, Misorientation)
+    d = Misorientation.from_path_ends(m)
+    assert isinstance(d, Misorientation)
+    assert c.symmetry[1] == o.symmetry
+    assert d.symmetry == m.symmetry
+
+    # Orientation sanity checks
+    with pytest.raises(TypeError, match="Points must be an Orientation"):
+        a = Orientation.from_path_ends(q)
+    with pytest.raises(TypeError, match="Points must be an Orientation"):
+        b = Orientation.from_path_ends(r)
+    c = Orientation.from_path_ends(o)
+    assert c.symmetry == o.symmetry
+    assert isinstance(c, Orientation)
+    with pytest.raises(TypeError, match="Points must be an Orientation"):
+        d = Orientation.from_path_ends(m)
 
 
 class TestMisorientation:

From 70a877cbc69a2da090c095e1cea72f29a93eee96 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Thu, 4 Sep 2025 16:47:33 -0600
Subject: [PATCH 11/23] hotfix for projections

---
 orix/plot/__init__.py  | 12 +++++++++++-
 orix/plot/__init__.pyi |  6 ------
 2 files changed, 11 insertions(+), 7 deletions(-)

diff --git a/orix/plot/__init__.py b/orix/plot/__init__.py
index b5010328a..de90d82d4 100644
--- a/orix/plot/__init__.py
+++ b/orix/plot/__init__.py
@@ -22,10 +22,20 @@
 :class:`~orix.quaternion.Orientation`,
 :class:`~orix.quaternion.Misorientation`, and
 :class:`~orix.crystal_map.CrystalMap`.
-"""
 
+NOTE: While lazy loading is preferred, the following six classes
+are explicitly imported in order to populate matplotlib.projections
+"""
 import lazy_loader
 
+from orix.plot.crystal_map_plot import CrystalMapPlot
+from orix.plot.rotation_plot import AxAnglePlot, RodriguesPlot, RotationPlot
+from orix.plot.stereographic_plot import StereographicPlot
+
+# Must be imported below StereographicPlot since it imports it
+from orix.plot.inverse_pole_figure_plot import InversePoleFigurePlot  # isort: skip
+
+
 # Imports from stub file (see contributor guide for details)
 __getattr__, __dir__, __all__ = lazy_loader.attach_stub(__name__, __file__)
 
diff --git a/orix/plot/__init__.pyi b/orix/plot/__init__.pyi
index c34d2e7dd..b4c339971 100644
--- a/orix/plot/__init__.pyi
+++ b/orix/plot/__init__.pyi
@@ -30,15 +30,9 @@ from .inverse_pole_figure_plot import InversePoleFigurePlot  # isort: skip
 # Lazily imported in module init
 __all__ = [
     # Classes
-    "AxAnglePlot",
-    "CrystalMapPlot",
     "DirectionColorKeyTSL",
     "EulerColorKey",
-    "InversePoleFigurePlot",
     "IPFColorKeyTSL",
-    "RodriguesPlot",
-    "RotationPlot",
-    "StereographicPlot",
     # Functions
     "format_labels",
 ]

From 81c6b1d55b2b26ea2803550bcb134cb48deaea1f Mon Sep 17 00:00:00 2001
From: Austin Gerlt <argerlt@gmail.com>
Date: Mon, 19 May 2025 01:11:45 -0600
Subject: [PATCH 12/23] adding ancillary capabilities from PR442
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-Authored-By: Håkon Wiik Ånes <hwaanes@gmail.com>
---
 CHANGELOG.rst                             |  8 ++-
 orix/quaternion/misorientation.py         | 49 ++++++++++++++++++
 orix/quaternion/quaternion.py             | 62 +++++++++++++++++++++++
 orix/tests/quaternion/test_orientation.py | 30 ++++++-----
 4 files changed, 133 insertions(+), 16 deletions(-)

diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 8b2b47049..305b8b33e 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -31,10 +31,14 @@ Changed
 
 Removed
 -------
-
+- ``verbose`` parameter in ``reduce()``
+  (replacing ``map_into_symmetry_reduced_zone()``).
+  
 Deprecated
 ----------
-
+- ``map_into_symmetry_reduced_zone()`` is deprecated since 0.14 and will be removed in
+  0.15. Use ``reduce()`` instead.
+  
 Fixed
 -----
 - minor speedups to 'pytest'
diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index d5005865f..c7cc140c4 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -31,6 +31,7 @@
 from scipy.spatial.transform import Rotation as SciPyRotation
 from tqdm import tqdm
 
+from orix._util import deprecated
 from orix.quaternion.orientation_region import OrientationRegion
 from orix.quaternion.rotation import Rotation
 from orix.quaternion.symmetry import C1, Symmetry, _get_unique_symmetry_elements
@@ -340,6 +341,7 @@ def equivalent(self, grain_exchange: bool = False) -> Misorientation:
 
         return self.__class__(equivalent).flatten()
 
+    @deprecated(since="0.14", removal="0.15", alternative="reduce")
     def map_into_symmetry_reduced_zone(self, verbose: bool = False) -> Misorientation:
         """Return equivalent transformations which have the smallest
         angle of rotation as a new misorientation.
@@ -382,6 +384,53 @@ def map_into_symmetry_reduced_zone(self, verbose: bool = False) -> Misorientatio
         o_inside._symmetry = (Gl, Gr)
         return o_inside
 
+    def reduce(self) -> Misorientation:
+        """Return equivalent transformations which have the smallest
+        angle of rotation as a new misorientation.
+
+        Parameters
+        ----------
+        verbose
+            Whether to print a progressbar. Default is ``False``.
+
+        Returns
+        -------
+        M
+            A new misorientation object with the assigned symmetry.
+
+        Examples
+        --------
+        >>> from orix.quaternion.symmetry import C4, C2
+        >>> data = np.array([[0.5, 0.5, 0.5, 0.5], [0, 1, 0, 0]])
+        >>> M = Misorientation(data)
+        >>> M.symmetry = (C4, C2)
+        >>> M.reduce()
+        Misorientation (2,) 4, 2
+        [[-0.7071  0.7071  0.      0.    ]
+        [ 0.      1.      0.      0.    ]]
+        """
+        # create an itertool object for iterating over every
+        # combination of left and right symmetry operations
+        Gl, Gr = self._symmetry
+        symmetry_pairs = iproduct(Gl, Gr)
+
+        # Define a Fundamental Zone (fz). for every misorientation, there
+        # is one and only one combination in `symmetry_pairs` that rotates
+        # it into the fz.
+        fz = OrientationRegion.from_symmetry(Gl, Gr)
+        reduced = self.__class__.identity(self.shape)
+        outside = np.ones(self.shape, dtype=bool)
+        # apply transformations to unreduced misorientations and save the
+        # reduced ones to `reduced` until all are inside the fz
+        for gl, gr in symmetry_pairs:
+            o_transformed = gl * self[outside] * gr
+            reduced[outside] = o_transformed
+            outside = ~(reduced < fz)
+            if not np.any(outside):
+                break
+        reduced._symmetry = (Gl, Gr)
+        return reduced
+
     def scatter(
         self,
         projection: str = "axangle",
diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index 099abf872..cc2243481 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -246,6 +246,16 @@ def __eq__(self, other: Any | Quaternion) -> bool:
 
     # ------------------------ Class methods ------------------------- #
 
+    @classmethod
+    def random(cls, shape: Union[int, tuple] = 1) -> Quaternion:
+        quat = super().random(shape)
+        quat.data[:, 0] = np.abs(quat.data[:, 0])
+        return quat
+
+        O = super().__invert__()
+        O.symmetry = self.symmetry
+        return O
+
     @classmethod
     def from_axes_angles(
         cls,
@@ -685,6 +695,58 @@ def from_align_vectors(
 
         return out[0] if len(out) == 1 else tuple(out)
 
+    @classmethod
+    def from_path_ends(
+        cls, waypoints: Quaternion, close_loop: bool = False, steps: int = 100
+    ) -> Quaternion:
+        """Return Quaternions tracing the shortest path between two or more
+        consecutive waypoints.
+
+        Parameters
+        ----------
+        waypoints : Quaternion
+            Two or more quaternions that define waypoints along a path through
+            rotation space (SO3).
+        close_loop : bool, optional
+            Option to add a final trip from the last waypoint back to the
+            first, thus closing the loop. Default is False.
+        steps : int, optional
+        Number of points to return along the path between each pair of
+        waypoints. The default is 100.
+
+        Returns
+        -------
+        path :Quaternion
+            quaternions that map out a path between the given waypoints.
+
+        Notes
+        -----
+        This method can use Orientations and Misorientations as inputs, and
+        will return an object of the same class. However, symmetry is ignored
+        when determining the shortest routes.
+        """
+        waypoints = waypoints.flatten()
+        n = waypoints.size
+        if not close_loop:
+            n = n - 1
+
+        path_list = []
+        for i in range(n):
+            # get start and end for this leg of the trip
+            q1 = waypoints[i]
+            q2 = waypoints[(i + 1) % (waypoints.size)]
+            # find the ax/ang describing the trip between points
+            ax, ang = _conversions.qu2ax((~q1 * q2).data)
+            # get 100 steps along the trip and add them to the journey
+            trip = Quaternion.from_axes_angles(ax, np.linspace(0, ang, steps))
+            path_list.append((q1 * (trip.flatten())).data)
+        path_data = np.concatenate(path_list, axis=0)
+        path = waypoints.__class__(path_data)
+        # copy the symmetry if it exists
+        if hasattr(waypoints, "_symmetry"):
+            path._symmetry = waypoints._symmetry
+        return path
+
     @classmethod
     def triple_cross(cls, q1: Quaternion, q2: Quaternion, q3: Quaternion) -> Quaternion:
         """Pointwise cross product of three quaternions.
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index 4ea13b1d9..003c22ceb 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -101,7 +101,7 @@ def test_quaternion_subclasses_copy_constructor_casting():
 )
 def test_set_symmetry(orientation, symmetry, expected):
     o = Orientation(orientation.data, symmetry=symmetry)
-    o = o.map_into_symmetry_reduced_zone()
+    o = o.reduce()
     assert np.allclose(o.data, expected, atol=1e-3)
 
 
@@ -114,7 +114,7 @@ def test_orientation_persistence(symmetry, vector):
     v = symmetry.outer(vector).flatten()
     o = Orientation.random()
     oc = Orientation(o.data, symmetry=symmetry)
-    oc = oc.map_into_symmetry_reduced_zone()
+    oc = oc.reduce()
     v1 = o * v
     v1 = Vector3d(v1.data.round(4))
     v2 = oc * v
@@ -207,7 +207,7 @@ def test_equivalent(Gl):
     """
     m = Misorientation([1, 1, 1, 1])  # any will do
     m_new = Misorientation(m.data, symmetry=(Gl, C4))
-    m_new = m_new.map_into_symmetry_reduced_zone()
+    m_new = m_new.reduce()
     _ = m_new.equivalent(grain_exchange=True)
 
 
@@ -220,13 +220,13 @@ def test_repr_ori():
     shape = (2, 3)
     o = Orientation.identity(shape)
     o.symmetry = O
-    o = o.map_into_symmetry_reduced_zone()
+    o = o.reduce()
     assert repr(o).split("\n")[0] == f"Orientation {shape} {O.name}"
 
 
 def test_sub():
     o = Orientation([1, 1, 1, 1], symmetry=C4)  # any will do
-    o = o.map_into_symmetry_reduced_zone()
+    o = o.reduce()
     m = o - o
     assert np.allclose(m.data, [1, 0, 0, 0])
 
@@ -247,8 +247,10 @@ def test_map_into_reduced_symmetry_zone_verbose():
     o = Orientation.random()
     o.symmetry = Oh
     o1 = o.map_into_symmetry_reduced_zone()
-    o2 = o.map_into_symmetry_reduced_zone(verbose=True)
+    o2 = o.reduce()
+    o3 = o.map_into_symmetry_reduced_zone(verbose=True)
     assert np.allclose(o1.data, o2.data)
+    assert np.allclose(o1.data, o3.data)
 
 
 @pytest.mark.parametrize(
@@ -264,7 +266,7 @@ def test_transpose_3d(shape, expected_shape, axes):
 def test_transpose_symmetry():
     o1 = Orientation.random_vonmises((11, 3))
     o1.symmetry = Oh
-    o1 = o1.map_into_symmetry_reduced_zone()
+    o1 = o1.reduce()
     o2 = o1.transpose()
     assert o1.symmetry == o2.symmetry
 
@@ -488,11 +490,11 @@ def test_from_euler_symmetry(self):
         assert np.allclose(o1.data, [0, -0.3827, 0, -0.9239], atol=1e-4)
         assert o1.symmetry.name == "1"
         o2 = Orientation.from_euler(euler, symmetry=Oh)
-        o2 = o2.map_into_symmetry_reduced_zone()
+        o2 = o2.reduce()
         assert np.allclose(o2.data, [0.9239, 0, 0.3827, 0], atol=1e-4)
         assert o2.symmetry.name == "m-3m"
         o3 = Orientation(o1.data, symmetry=Oh)
-        o3 = o3.map_into_symmetry_reduced_zone()
+        o3 = o3.reduce()
         assert np.allclose(o3.data, o2.data)
 
         o4 = Orientation.from_euler(np.rad2deg(euler), degrees=True)
@@ -508,13 +510,13 @@ def test_from_matrix_symmetry(self):
         )
         assert o1.symmetry.name == "1"
         o2 = Orientation.from_matrix(om, symmetry=Oh)
-        o2 = o2.map_into_symmetry_reduced_zone()
+        o2 = o2.reduce()
         assert np.allclose(
             o2.data, np.array([1, 0, 0, 0] * 2 + [-1, 0, 0, 0] * 2).reshape(4, 4)
         )
         assert o2.symmetry.name == "m-3m"
         o3 = Orientation(o1.data, symmetry=Oh)
-        o3 = o3.map_into_symmetry_reduced_zone()
+        o3 = o3.reduce()
         assert np.allclose(o3.data, o2.data)
 
     def test_from_align_vectors(self):
@@ -601,7 +603,7 @@ class TestOrientation:
     def test_get_distance_matrix(self, symmetry):
         q = [(0.5, 0.5, 0.5, 0.5), (0.5**0.5, 0, 0, 0.5**0.5)]
         o = Orientation(q, symmetry=symmetry)
-        o = o.map_into_symmetry_reduced_zone()
+        o = o.reduce()
         angles_numpy = o.get_distance_matrix()
         assert isinstance(angles_numpy, np.ndarray)
         assert angles_numpy.shape == (2, 2)
@@ -694,7 +696,7 @@ def test_angle_with(self, symmetry):
     def test_negate_orientation(self):
         o = Orientation.identity()
         o.symmetry = Oh
-        o = o.map_into_symmetry_reduced_zone()
+        o = o.reduce()
         on = -o
         assert on.symmetry.name == o.symmetry.name
 
@@ -703,7 +705,7 @@ def test_scatter(self, orientation, pure_misorientation):
         if pure_misorientation:
             orientation = Misorientation(orientation)
             orientation.symmetry = (C2, D6)
-            orientation = orientation.map_into_symmetry_reduced_zone()
+            orientation = orientation.reduce()
         fig_size = (5, 5)
         fig_axangle = orientation.scatter(
             return_figure=True, figure_kwargs=dict(figsize=fig_size)

From d01b78be3473eb66b63bf8b72e5fc58b1c139cb4 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Tue, 27 May 2025 15:35:29 -0600
Subject: [PATCH 13/23] add tests for 'from_path_ends`

---
 orix/quaternion/quaternion.py             |  50 ++++++---
 orix/tests/quaternion/test_orientation.py |  45 ++++++--
 orix/tests/quaternion/test_quaternion.py  | 122 ++++++++++++++++++----
 3 files changed, 170 insertions(+), 47 deletions(-)

diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index cc2243481..c18f1d5af 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -505,7 +505,9 @@ def from_euler(
 
         eu = np.atleast_2d(euler)
         if np.any(np.abs(eu) > 4 * np.pi):
-            warnings.warn("Angles are quite high, did you forget to set degrees=True?")
+            warnings.warn(
+                "Angles are quite high, did you forget to set degrees=True?"
+            )
 
         Q = _conversions.eu2qu(eu)
         Q = cls(Q)
@@ -544,7 +546,9 @@ def from_matrix(cls, matrix: np.ndarray | tuple | list) -> Quaternion:
         # Verify the input can be interpreted as an array of (3, 3) arrays
         om = np.atleast_2d(matrix)
         if om.shape[-2:] != (3, 3):
-            raise ValueError("the last two dimensions of 'matrix' must be (3, 3)")
+            raise ValueError(
+                "the last two dimensions of 'matrix' must be (3, 3)"
+            )
 
         Q = _conversions.om2qu(om)
         Q = cls(Q)
@@ -737,7 +741,7 @@ def from_path_ends(
             q2 = waypoints[(i + 1) % (waypoints.size)]
             # find the ax/ang describing the trip between points
             ax, ang = _conversions.qu2ax((~q1 * q2).data)
-            # get 100 steps along the trip and add them to the journey
+            # get 'steps=n' steps along the trip and add them to the journey
             trip = Quaternion.from_axes_angles(ax, np.linspace(0, ang, steps))
             path_list.append((q1 * (trip.flatten())).data)
         path_data = np.concatenate(path_list, axis=0)
@@ -748,7 +752,9 @@ def from_path_ends(
         return path
 
     @classmethod
-    def triple_cross(cls, q1: Quaternion, q2: Quaternion, q3: Quaternion) -> Quaternion:
+    def triple_cross(
+        cls, q1: Quaternion, q2: Quaternion, q3: Quaternion
+    ) -> Quaternion:
         """Pointwise cross product of three quaternions.
 
         Parameters
@@ -1195,7 +1201,9 @@ def outer(
                     qu12 = np.outer(qu1, qu2).reshape(*qu1.shape, *qu2.shape)
                     qu = quaternion.as_float_array(qu12)
                 else:  # pragma: no cover
-                    Q12 = Quaternion(self).reshape(-1, 1) * other.reshape(1, -1)
+                    Q12 = Quaternion(self).reshape(-1, 1) * other.reshape(
+                        1, -1
+                    )
                     qu = Q12.data.reshape(*self.shape, *other.shape, 4)
             return other.__class__(qu)
         elif isinstance(other, Vector3d):
@@ -1368,7 +1376,9 @@ def _outer_dask(
 
 
 @nb.guvectorize("(n)->(n)", cache=True)
-def qu_conj_gufunc(qu: np.ndarray, qu2: np.ndarray) -> None:  # pragma: no cover
+def qu_conj_gufunc(
+    qu: np.ndarray, qu2: np.ndarray
+) -> None:  # pragma: no cover
     qu2[0] = qu[0]
     qu2[1] = -qu[1]
     qu2[2] = -qu[2]
@@ -1379,13 +1389,23 @@ def qu_conj_gufunc(qu: np.ndarray, qu2: np.ndarray) -> None:  # pragma: no cover
 def qu_multiply_gufunc(
     qu1: np.ndarray, qu2: np.ndarray, qu12: np.ndarray
 ) -> None:  # pragma: no cover
-    qu12[0] = qu1[0] * qu2[0] - qu1[1] * qu2[1] - qu1[2] * qu2[2] - qu1[3] * qu2[3]
-    qu12[1] = qu1[1] * qu2[0] + qu1[0] * qu2[1] - qu1[3] * qu2[2] + qu1[2] * qu2[3]
-    qu12[2] = qu1[2] * qu2[0] + qu1[3] * qu2[1] + qu1[0] * qu2[2] - qu1[1] * qu2[3]
-    qu12[3] = qu1[3] * qu2[0] - qu1[2] * qu2[1] + qu1[1] * qu2[2] + qu1[0] * qu2[3]
-
-
-def qu_multiply(qu1: np.ndarray, qu2: np.ndarray) -> np.ndarray:  # pragma: no cover
+    qu12[0] = (
+        qu1[0] * qu2[0] - qu1[1] * qu2[1] - qu1[2] * qu2[2] - qu1[3] * qu2[3]
+    )
+    qu12[1] = (
+        qu1[1] * qu2[0] + qu1[0] * qu2[1] - qu1[3] * qu2[2] + qu1[2] * qu2[3]
+    )
+    qu12[2] = (
+        qu1[2] * qu2[0] + qu1[3] * qu2[1] + qu1[0] * qu2[2] - qu1[1] * qu2[3]
+    )
+    qu12[3] = (
+        qu1[3] * qu2[0] - qu1[2] * qu2[1] + qu1[1] * qu2[2] + qu1[0] * qu2[3]
+    )
+
+
+def qu_multiply(
+    qu1: np.ndarray, qu2: np.ndarray
+) -> np.ndarray:  # pragma: no cover
     shape = np.broadcast_shapes(qu1.shape, qu2.shape)
     if not np.issubdtype(qu1.dtype, np.float64):
         qu1 = qu1.astype(np.float64)
@@ -1410,7 +1430,9 @@ def qu_rotate_vec_gufunc(
     v2[2] = z - c * tx + b * ty + a * tz
 
 
-def qu_rotate_vec(qu: np.ndarray, v: np.ndarray) -> np.ndarray:  # pragma: no cover
+def qu_rotate_vec(
+    qu: np.ndarray, v: np.ndarray
+) -> np.ndarray:  # pragma: no cover
     qu = np.atleast_2d(qu)
     v = np.atleast_2d(v)
     shape = np.broadcast_shapes(qu.shape[:-1], v.shape[:-1]) + (3,)
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index 003c22ceb..57a31139a 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -301,7 +301,8 @@ def test_symmetry_property_wrong_type_orientation():
 
 
 @pytest.mark.parametrize(
-    "error_type, value", [(ValueError, (1, 2)), (ValueError, (C1, 2)), (TypeError, 1)]
+    "error_type, value",
+    [(ValueError, (1, 2)), (ValueError, (C1, 2)), (TypeError, 1)],
 )
 def test_symmetry_property_wrong_type_misorientation(error_type, value):
     mori = Misorientation.random((3, 2))
@@ -313,7 +314,9 @@ def test_symmetry_property_wrong_type_misorientation(error_type, value):
     "error_type, value",
     [(ValueError, (C1,)), (ValueError, (C1, C2, C1))],
 )
-def test_symmetry_property_wrong_number_of_values_misorientation(error_type, value):
+def test_symmetry_property_wrong_number_of_values_misorientation(
+    error_type, value
+):
     o = Misorientation.random((3, 2))
     with pytest.raises(error_type, match="Value must be a 2-tuple"):
         # less than 2 Symmetry
@@ -506,13 +509,15 @@ def test_from_matrix_symmetry(self):
         )
         o1 = Orientation.from_matrix(om)
         assert np.allclose(
-            o1.data, np.array([1, 0, 0, 0] * 2 + [0, 1, 0, 0] * 2).reshape(4, 4)
+            o1.data,
+            np.array([1, 0, 0, 0] * 2 + [0, 1, 0, 0] * 2).reshape(4, 4),
         )
         assert o1.symmetry.name == "1"
         o2 = Orientation.from_matrix(om, symmetry=Oh)
         o2 = o2.reduce()
         assert np.allclose(
-            o2.data, np.array([1, 0, 0, 0] * 2 + [-1, 0, 0, 0] * 2).reshape(4, 4)
+            o2.data,
+            np.array([1, 0, 0, 0] * 2 + [-1, 0, 0, 0] * 2).reshape(4, 4),
         )
         assert o2.symmetry.name == "m-3m"
         o3 = Orientation(o1.data, symmetry=Oh)
@@ -597,9 +602,19 @@ def test_from_scipy_rotation(self):
         with pytest.raises(TypeError, match="Value must be an instance of"):
             _ = Orientation.from_scipy_rotation(r_scipy, (Oh, Oh))
 
+    def test_from_path_ends(self):
+        # generate paths with misorientations and orientations to check
+        # symmetry copying
+        wp_o = Orientation(data=np.eye(4)[:2], symmetry=Oh)
+        wp_m = Misorientation(data=np.eye(4)[2:], symmetry=[Oh, C3])
+        assert Orientation.from_path_ends(wp_o)._symmetry == (C1, Oh)
+        assert Misorientation.from_path_ends(wp_m)._symmetry == (Oh, C3)
+
 
 class TestOrientation:
-    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
+    @pytest.mark.parametrize(
+        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
+    )
     def test_get_distance_matrix(self, symmetry):
         q = [(0.5, 0.5, 0.5, 0.5), (0.5**0.5, 0, 0, 0.5**0.5)]
         o = Orientation(q, symmetry=symmetry)
@@ -626,11 +641,15 @@ def test_get_distance_matrix_lazy_parameters(self):
         o = Orientation(abcd)
 
         angle1 = o.get_distance_matrix(lazy=True, chunk_size=5)
-        angle2 = o.get_distance_matrix(lazy=True, chunk_size=10, progressbar=False)
+        angle2 = o.get_distance_matrix(
+            lazy=True, chunk_size=10, progressbar=False
+        )
 
         assert np.allclose(angle1.data, angle2.data)
 
-    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
+    @pytest.mark.parametrize(
+        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
+    )
     def test_angle_with_outer(self, symmetry):
         shape = (5,)
         o = Orientation.random(shape)
@@ -677,7 +696,9 @@ def test_angle_with_outer_shape(self):
         assert awo_o12s.shape == awo_r12.shape
         assert not np.allclose(awo_o12s, awo_r12)
 
-    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
+    @pytest.mark.parametrize(
+        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
+    )
     def test_angle_with(self, symmetry):
         q = [(0.5, 0.5, 0.5, 0.5), (0.5**0.5, 0, 0, 0.5**0.5)]
         r = Rotation(q)
@@ -712,7 +733,9 @@ def test_scatter(self, orientation, pure_misorientation):
         )
         assert (fig_axangle.get_size_inches() == fig_size).all()
         assert isinstance(fig_axangle.axes[0], AxAnglePlot)
-        fig_rodrigues = orientation.scatter(projection="rodrigues", return_figure=True)
+        fig_rodrigues = orientation.scatter(
+            projection="rodrigues", return_figure=True
+        )
         assert isinstance(fig_rodrigues.axes[0], RodriguesPlot)
 
         # Add multiple axes to figure, one at a time
@@ -805,7 +828,9 @@ def test_in_fundamental_region(self):
         for pg in _proper_groups:
             ori.symmetry = pg
             region = np.radians(pg.euler_fundamental_region)
-            assert np.all(np.max(ori.in_euler_fundamental_region(), axis=0) <= region)
+            assert np.all(
+                np.max(ori.in_euler_fundamental_region(), axis=0) <= region
+            )
 
     def test_inverse(self):
         O1 = Orientation([np.sqrt(2) / 2, np.sqrt(2) / 2, 0, 0], D6)
diff --git a/orix/tests/quaternion/test_quaternion.py b/orix/tests/quaternion/test_quaternion.py
index 7f6be1d11..c82483bca 100644
--- a/orix/tests/quaternion/test_quaternion.py
+++ b/orix/tests/quaternion/test_quaternion.py
@@ -78,7 +78,9 @@ def test_neg(self, quaternion):
         assert np.allclose((-quaternion).data, (-quaternion.data))
 
     def test_norm(self, quaternion):
-        assert np.allclose(quaternion.norm, (quaternion.data**2).sum(axis=-1) ** 0.5)
+        assert np.allclose(
+            quaternion.norm, (quaternion.data**2).sum(axis=-1) ** 0.5
+        )
 
     def test_unit(self, quaternion):
         assert np.allclose(quaternion.unit.norm, 1)
@@ -102,7 +104,9 @@ def test_mul(self, quaternion, something):
         assert np.allclose(q1.d, qa * sd + qb * sc - qc * sb + qd * sa)
 
     def test_mul_identity(self, quaternion):
-        assert np.allclose((quaternion * Quaternion.identity()).data, quaternion.data)
+        assert np.allclose(
+            (quaternion * Quaternion.identity()).data, quaternion.data
+        )
 
     def test_no_multiplicative_inverse(self, quaternion, something):
         q1 = quaternion * something
@@ -193,7 +197,9 @@ def test_antipodal(self, quaternion):
         assert qa.size == 2 * q.size
 
     def test_edgecase_outer(self, quaternion):
-        with pytest.raises(NotImplementedError, match="This operation is currently "):
+        with pytest.raises(
+            NotImplementedError, match="This operation is currently "
+        ):
             _ = quaternion.outer([3, 2])
 
     def test_failing_mul(self, quaternion):
@@ -298,7 +304,9 @@ def test_outer_dask_wrong_type_raises(self):
         q = Quaternion(abcd)
         # not Quaternion or Vector3d
         other = np.random.rand(7, 3)
-        with pytest.raises(TypeError, match="Other must be Quaternion or Vector3d"):
+        with pytest.raises(
+            TypeError, match="Other must be Quaternion or Vector3d"
+        ):
             q._outer_dask(other)
 
     def test_from_align_vectors(self):
@@ -308,7 +316,8 @@ def test_from_align_vectors(self):
         q1 = Quaternion.from_align_vectors(v1, v2)
         assert isinstance(q1, Quaternion)
         assert np.allclose(
-            q1.data, np.array([[0.65328148, 0.70532785, -0.05012611, -0.27059805]])
+            q1.data,
+            np.array([[0.65328148, 0.70532785, -0.05012611, -0.27059805]]),
         )
         assert np.allclose(v1.unit.data, (q1 * v2.unit).data)
 
@@ -317,8 +326,12 @@ def test_from_align_vectors(self):
         error = out[1]
         assert error == 0
 
-        _, sens_mat = Quaternion.from_align_vectors(v1, v2, return_sensitivity=True)
-        assert np.allclose(sens_mat, np.array([[1, 0, 0], [0, 1, 0], [0, 0, 0.5]]))
+        _, sens_mat = Quaternion.from_align_vectors(
+            v1, v2, return_sensitivity=True
+        )
+        assert np.allclose(
+            sens_mat, np.array([[1, 0, 0], [0, 1, 0], [0, 0, 0.5]])
+        )
 
         out = Quaternion.from_align_vectors(
             v1, v2, return_rmsd=True, return_sensitivity=True
@@ -330,6 +343,37 @@ def test_from_align_vectors(self):
         )
         assert np.allclose(q2.data, q1.data)
 
+    def test_from_path_ends(self):
+        # choose a path with repeats and 180 tilts to test edge cases
+        waypoints = Quaternion(
+            data=np.array(
+                [
+                    [1, 0, 0, 0],
+                    [1, 0, 0, 0],
+                    [1, 1, 0, 0],
+                    [1, 0, 1, 0],
+                    [1, 0, 0, 1],
+                    [1, 0, 0, 1],
+                    [1, 0, -1, 0],
+                    [1, 0, 1, 0],
+                    [-1, 0, 1, 0],
+                    [1, 0, 0, -1],
+                    [-1, 0, 0, -1],
+                    [-1, 0, 0, 1],
+                ]
+            )
+        )
+        path = Quaternion.from_path_ends(waypoints)
+        loop = Quaternion.from_path_ends(waypoints, close_loop=True, steps=11)
+        # check the sizes are as expected
+        assert path.shape == (1100,)
+        assert loop.shape == (132,)
+        # check the spacing between points is homogenous
+        path_spacing = [(x[1:]).dot(x[:-1]) for x in path.reshape(11, 100)]
+        loop_spacing = [(x[1:]).dot(x[:-1]) for x in loop.reshape(12, 11)]
+        assert np.all(np.std(path_spacing, axis=1) < 1e-12)
+        assert np.all(np.std(loop_spacing, axis=1) < 1e-12)
+
     def test_equality(self):
         Q1 = Quaternion.from_axes_angles([1, 1, 1], -np.pi / 3)
         Q2 = Quaternion.from_axes_angles([1, 1, 1], np.pi / 3)
@@ -361,7 +405,9 @@ def test_direction_values(self, eu):
         assert np.allclose((q_l2c * q_c2l).data, [1, 0, 0, 0])
 
     def test_direction_kwarg_dumb(self, eu):
-        with pytest.raises(ValueError, match="The chosen direction is not one of "):
+        with pytest.raises(
+            ValueError, match="The chosen direction is not one of "
+        ):
             _ = Quaternion.from_euler(eu, direction="dumb_direction")
 
     def test_edge_cases_to_euler(self):
@@ -372,19 +418,25 @@ def test_edge_cases_to_euler(self):
         _ = q.to_euler()
 
     def test_passing_degrees_warns(self):
-        with pytest.warns(UserWarning, match="Angles are quite high, did you forget "):
+        with pytest.warns(
+            UserWarning, match="Angles are quite high, did you forget "
+        ):
             q = Quaternion.from_euler([90, 0, 0])
             assert np.allclose(q.data, [0.5253, 0, 0, -0.8509], atol=1e-4)
 
 
 class TestFromToMatrix:
     def test_to_matrix(self):
-        q = Quaternion([[1, 0, 0, 0], [3, 0, 0, 0], [0, 1, 0, 0], [0, 2, 0, 0]])
+        q = Quaternion(
+            [[1, 0, 0, 0], [3, 0, 0, 0], [0, 1, 0, 0], [0, 2, 0, 0]]
+        )
         om = np.array(
             [np.eye(3), np.eye(3), np.diag([1, -1, -1]), np.diag([1, -1, -1])]
         )
         # Shapes are handled correctly
-        assert np.allclose(q.reshape(2, 2).unit.to_matrix(), om.reshape(2, 2, 3, 3))
+        assert np.allclose(
+            q.reshape(2, 2).unit.to_matrix(), om.reshape(2, 2, 3, 3)
+        )
 
         q2 = Quaternion(
             [
@@ -398,19 +450,25 @@ def test_to_matrix(self):
         # Inverse equal to transpose
         assert all(np.allclose(np.linalg.inv(i), i.T) for i in om_from_q2)
         # Cross product of any two rows gives the third
-        assert all(np.allclose(np.cross(i[:, 0], i[:, 1]), i[:, 2]) for i in om_from_q2)
+        assert all(
+            np.allclose(np.cross(i[:, 0], i[:, 1]), i[:, 2])
+            for i in om_from_q2
+        )
         # Sum of squares of any column or row equals unity
         assert np.allclose(np.sum(np.square(om_from_q2), axis=1), 1)  # Rows
         assert np.allclose(np.sum(np.square(om_from_q2), axis=2), 1)  # Columns
 
     def test_from_matrix(self):
-        q = Quaternion([[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0]])
+        q = Quaternion(
+            [[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0]]
+        )
         ident = np.identity(3)
         rot_180x = np.diag([1, -1, -1])
         om = np.array([ident, 2 * ident, rot_180x, 2 * rot_180x])
         assert np.allclose(Quaternion.from_matrix(om).data, q.data)
         assert np.allclose(
-            Quaternion.from_matrix(om.reshape(2, 2, 3, 3)).data, q.reshape(2, 2).data
+            Quaternion.from_matrix(om.reshape(2, 2, 3, 3)).data,
+            q.reshape(2, 2).data,
         )
 
     def test_from_to_matrix(self):
@@ -447,7 +505,9 @@ def test_get_rotation_matrix_from_diffpy(self):
         q = Quaternion.from_matrix([i.R for i in sg225.symop_list])
         assert not np.isnan(q.data).any()
 
-    def test_from_matrix_raises(self, quaternions_conversions, orientation_matrices):
+    def test_from_matrix_raises(
+        self, quaternions_conversions, orientation_matrices
+    ):
         qu = Quaternion.from_matrix(orientation_matrices).data
         assert np.allclose(qu, quaternions_conversions, atol=1e-4)
         with pytest.raises(ValueError, match="(3, 3)"):
@@ -467,12 +527,16 @@ def test_from_axes_angles(self, rotations, extra_dim):
             rotations = rotations.__class__(rotations.data[..., np.newaxis, :])
         ax = AxAngle.from_rotation(rotations)
         Q1 = Quaternion.from_axes_angles(ax.axis.data, ax.angle)
-        Q2 = Quaternion.from_axes_angles(ax.axis, np.rad2deg(ax.angle), degrees=True)
+        Q2 = Quaternion.from_axes_angles(
+            ax.axis, np.rad2deg(ax.angle), degrees=True
+        )
         assert np.allclose(Q1.data, Q2.data)
 
     def test_to_axes_angles(self, quaternions_conversions, axis_angle_pairs):
         ax = Quaternion(quaternions_conversions).to_axes_angles()
-        assert np.allclose(np.deg2rad(ax.angle), axis_angle_pairs[:, 3], atol=4)
+        assert np.allclose(
+            np.deg2rad(ax.angle), axis_angle_pairs[:, 3], atol=4
+        )
 
     def test_from_axes_angles_empty(self):
         q = Quaternion.from_axes_angles([], [])
@@ -484,12 +548,16 @@ class TestFromToRodrigues:
     Rodrigues and Rodrigues-Frank vectors.
     """
 
-    def test_from_to_rodrigues(self, quaternions_conversions, rodrigues_vectors):
+    def test_from_to_rodrigues(
+        self, quaternions_conversions, rodrigues_vectors
+    ):
         axes = rodrigues_vectors[..., :3]
         angles = rodrigues_vectors[..., 3]
 
         q1 = Quaternion(quaternions_conversions)
-        with pytest.warns(UserWarning, match="Highest angle is greater than 179.999 "):
+        with pytest.warns(
+            UserWarning, match="Highest angle is greater than 179.999 "
+        ):
             q2 = Quaternion.from_rodrigues(axes, angles)
         assert np.allclose(q1.data, q2.data, atol=1e-4)
         ro = q1.to_rodrigues(frank=True)
@@ -499,7 +567,9 @@ def test_from_to_rodrigues(self, quaternions_conversions, rodrigues_vectors):
             _ = Quaternion.from_rodrigues([1e15, 1e15, 1e10])
         with pytest.warns(UserWarning, match="Max."):
             _ = Quaternion.from_rodrigues([0, 0, 1e-16])
-        with pytest.raises(ValueError, match="Final dimension of vector array must be"):
+        with pytest.raises(
+            ValueError, match="Final dimension of vector array must be"
+        ):
             Quaternion.from_rodrigues([1, 2, 3, 4])
 
     def test_from_rodrigues_empty(self):
@@ -512,7 +582,9 @@ class TestFromToHomochoric:
     homochoric vectors.
     """
 
-    def test_from_to_homochoric(self, homochoric_vectors, quaternions_conversions):
+    def test_from_to_homochoric(
+        self, homochoric_vectors, quaternions_conversions
+    ):
         ho1 = homochoric_vectors
         ho2 = Vector3d(ho1)
         ho3 = Homochoric(ho1)
@@ -526,7 +598,9 @@ def test_from_to_homochoric(self, homochoric_vectors, quaternions_conversions):
         assert np.allclose(q1.data, quaternions_conversions, atol=1e-4)
         assert np.allclose(q2.data, quaternions_conversions, atol=1e-4)
         assert np.allclose(q3.data, quaternions_conversions, atol=1e-4)
-        assert np.allclose(q4.data, quaternions_conversions.reshape(2, 5, 4), atol=1e-4)
+        assert np.allclose(
+            q4.data, quaternions_conversions.reshape(2, 5, 4), atol=1e-4
+        )
 
         assert np.allclose(ho1, q1.to_homochoric().data, atol=1e-4)
         assert np.allclose(ho1, q2.to_homochoric().data, atol=1e-4)
@@ -534,7 +608,9 @@ def test_from_to_homochoric(self, homochoric_vectors, quaternions_conversions):
         assert np.allclose(ho4, q4.to_homochoric().data, atol=1e-4)
 
     def test_from_homochoric_raises(self):
-        with pytest.raises(ValueError, match="Final dimension of vector array must be"):
+        with pytest.raises(
+            ValueError, match="Final dimension of vector array must be"
+        ):
             Quaternion.from_homochoric([1, 2])
 
     def test_from_homochoric_empty(self):

From e8afae0ef6713293d7a7873f48815944685a031a Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Tue, 27 May 2025 15:37:31 -0600
Subject: [PATCH 14/23] black formatting

---
 orix/quaternion/quaternion.py             | 48 ++++---------
 orix/tests/quaternion/test_orientation.py | 28 ++------
 orix/tests/quaternion/test_quaternion.py  | 85 ++++++-----------------
 3 files changed, 41 insertions(+), 120 deletions(-)

diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index c18f1d5af..f72d6b704 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -505,9 +505,7 @@ def from_euler(
 
         eu = np.atleast_2d(euler)
         if np.any(np.abs(eu) > 4 * np.pi):
-            warnings.warn(
-                "Angles are quite high, did you forget to set degrees=True?"
-            )
+            warnings.warn("Angles are quite high, did you forget to set degrees=True?")
 
         Q = _conversions.eu2qu(eu)
         Q = cls(Q)
@@ -546,9 +544,7 @@ def from_matrix(cls, matrix: np.ndarray | tuple | list) -> Quaternion:
         # Verify the input can be interpreted as an array of (3, 3) arrays
         om = np.atleast_2d(matrix)
         if om.shape[-2:] != (3, 3):
-            raise ValueError(
-                "the last two dimensions of 'matrix' must be (3, 3)"
-            )
+            raise ValueError("the last two dimensions of 'matrix' must be (3, 3)")
 
         Q = _conversions.om2qu(om)
         Q = cls(Q)
@@ -752,9 +748,7 @@ def from_path_ends(
         return path
 
     @classmethod
-    def triple_cross(
-        cls, q1: Quaternion, q2: Quaternion, q3: Quaternion
-    ) -> Quaternion:
+    def triple_cross(cls, q1: Quaternion, q2: Quaternion, q3: Quaternion) -> Quaternion:
         """Pointwise cross product of three quaternions.
 
         Parameters
@@ -1201,9 +1195,7 @@ def outer(
                     qu12 = np.outer(qu1, qu2).reshape(*qu1.shape, *qu2.shape)
                     qu = quaternion.as_float_array(qu12)
                 else:  # pragma: no cover
-                    Q12 = Quaternion(self).reshape(-1, 1) * other.reshape(
-                        1, -1
-                    )
+                    Q12 = Quaternion(self).reshape(-1, 1) * other.reshape(1, -1)
                     qu = Q12.data.reshape(*self.shape, *other.shape, 4)
             return other.__class__(qu)
         elif isinstance(other, Vector3d):
@@ -1376,9 +1368,7 @@ def _outer_dask(
 
 
 @nb.guvectorize("(n)->(n)", cache=True)
-def qu_conj_gufunc(
-    qu: np.ndarray, qu2: np.ndarray
-) -> None:  # pragma: no cover
+def qu_conj_gufunc(qu: np.ndarray, qu2: np.ndarray) -> None:  # pragma: no cover
     qu2[0] = qu[0]
     qu2[1] = -qu[1]
     qu2[2] = -qu[2]
@@ -1389,23 +1379,13 @@ def qu_conj_gufunc(
 def qu_multiply_gufunc(
     qu1: np.ndarray, qu2: np.ndarray, qu12: np.ndarray
 ) -> None:  # pragma: no cover
-    qu12[0] = (
-        qu1[0] * qu2[0] - qu1[1] * qu2[1] - qu1[2] * qu2[2] - qu1[3] * qu2[3]
-    )
-    qu12[1] = (
-        qu1[1] * qu2[0] + qu1[0] * qu2[1] - qu1[3] * qu2[2] + qu1[2] * qu2[3]
-    )
-    qu12[2] = (
-        qu1[2] * qu2[0] + qu1[3] * qu2[1] + qu1[0] * qu2[2] - qu1[1] * qu2[3]
-    )
-    qu12[3] = (
-        qu1[3] * qu2[0] - qu1[2] * qu2[1] + qu1[1] * qu2[2] + qu1[0] * qu2[3]
-    )
-
-
-def qu_multiply(
-    qu1: np.ndarray, qu2: np.ndarray
-) -> np.ndarray:  # pragma: no cover
+    qu12[0] = qu1[0] * qu2[0] - qu1[1] * qu2[1] - qu1[2] * qu2[2] - qu1[3] * qu2[3]
+    qu12[1] = qu1[1] * qu2[0] + qu1[0] * qu2[1] - qu1[3] * qu2[2] + qu1[2] * qu2[3]
+    qu12[2] = qu1[2] * qu2[0] + qu1[3] * qu2[1] + qu1[0] * qu2[2] - qu1[1] * qu2[3]
+    qu12[3] = qu1[3] * qu2[0] - qu1[2] * qu2[1] + qu1[1] * qu2[2] + qu1[0] * qu2[3]
+
+
+def qu_multiply(qu1: np.ndarray, qu2: np.ndarray) -> np.ndarray:  # pragma: no cover
     shape = np.broadcast_shapes(qu1.shape, qu2.shape)
     if not np.issubdtype(qu1.dtype, np.float64):
         qu1 = qu1.astype(np.float64)
@@ -1430,9 +1410,7 @@ def qu_rotate_vec_gufunc(
     v2[2] = z - c * tx + b * ty + a * tz
 
 
-def qu_rotate_vec(
-    qu: np.ndarray, v: np.ndarray
-) -> np.ndarray:  # pragma: no cover
+def qu_rotate_vec(qu: np.ndarray, v: np.ndarray) -> np.ndarray:  # pragma: no cover
     qu = np.atleast_2d(qu)
     v = np.atleast_2d(v)
     shape = np.broadcast_shapes(qu.shape[:-1], v.shape[:-1]) + (3,)
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index 57a31139a..0645a135e 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -314,9 +314,7 @@ def test_symmetry_property_wrong_type_misorientation(error_type, value):
     "error_type, value",
     [(ValueError, (C1,)), (ValueError, (C1, C2, C1))],
 )
-def test_symmetry_property_wrong_number_of_values_misorientation(
-    error_type, value
-):
+def test_symmetry_property_wrong_number_of_values_misorientation(error_type, value):
     o = Misorientation.random((3, 2))
     with pytest.raises(error_type, match="Value must be a 2-tuple"):
         # less than 2 Symmetry
@@ -612,9 +610,7 @@ def test_from_path_ends(self):
 
 
 class TestOrientation:
-    @pytest.mark.parametrize(
-        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
-    )
+    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
     def test_get_distance_matrix(self, symmetry):
         q = [(0.5, 0.5, 0.5, 0.5), (0.5**0.5, 0, 0, 0.5**0.5)]
         o = Orientation(q, symmetry=symmetry)
@@ -641,15 +637,11 @@ def test_get_distance_matrix_lazy_parameters(self):
         o = Orientation(abcd)
 
         angle1 = o.get_distance_matrix(lazy=True, chunk_size=5)
-        angle2 = o.get_distance_matrix(
-            lazy=True, chunk_size=10, progressbar=False
-        )
+        angle2 = o.get_distance_matrix(lazy=True, chunk_size=10, progressbar=False)
 
         assert np.allclose(angle1.data, angle2.data)
 
-    @pytest.mark.parametrize(
-        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
-    )
+    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
     def test_angle_with_outer(self, symmetry):
         shape = (5,)
         o = Orientation.random(shape)
@@ -696,9 +688,7 @@ def test_angle_with_outer_shape(self):
         assert awo_o12s.shape == awo_r12.shape
         assert not np.allclose(awo_o12s, awo_r12)
 
-    @pytest.mark.parametrize(
-        "symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh]
-    )
+    @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
     def test_angle_with(self, symmetry):
         q = [(0.5, 0.5, 0.5, 0.5), (0.5**0.5, 0, 0, 0.5**0.5)]
         r = Rotation(q)
@@ -733,9 +723,7 @@ def test_scatter(self, orientation, pure_misorientation):
         )
         assert (fig_axangle.get_size_inches() == fig_size).all()
         assert isinstance(fig_axangle.axes[0], AxAnglePlot)
-        fig_rodrigues = orientation.scatter(
-            projection="rodrigues", return_figure=True
-        )
+        fig_rodrigues = orientation.scatter(projection="rodrigues", return_figure=True)
         assert isinstance(fig_rodrigues.axes[0], RodriguesPlot)
 
         # Add multiple axes to figure, one at a time
@@ -828,9 +816,7 @@ def test_in_fundamental_region(self):
         for pg in _proper_groups:
             ori.symmetry = pg
             region = np.radians(pg.euler_fundamental_region)
-            assert np.all(
-                np.max(ori.in_euler_fundamental_region(), axis=0) <= region
-            )
+            assert np.all(np.max(ori.in_euler_fundamental_region(), axis=0) <= region)
 
     def test_inverse(self):
         O1 = Orientation([np.sqrt(2) / 2, np.sqrt(2) / 2, 0, 0], D6)
diff --git a/orix/tests/quaternion/test_quaternion.py b/orix/tests/quaternion/test_quaternion.py
index c82483bca..332193a0a 100644
--- a/orix/tests/quaternion/test_quaternion.py
+++ b/orix/tests/quaternion/test_quaternion.py
@@ -78,9 +78,7 @@ def test_neg(self, quaternion):
         assert np.allclose((-quaternion).data, (-quaternion.data))
 
     def test_norm(self, quaternion):
-        assert np.allclose(
-            quaternion.norm, (quaternion.data**2).sum(axis=-1) ** 0.5
-        )
+        assert np.allclose(quaternion.norm, (quaternion.data**2).sum(axis=-1) ** 0.5)
 
     def test_unit(self, quaternion):
         assert np.allclose(quaternion.unit.norm, 1)
@@ -104,9 +102,7 @@ def test_mul(self, quaternion, something):
         assert np.allclose(q1.d, qa * sd + qb * sc - qc * sb + qd * sa)
 
     def test_mul_identity(self, quaternion):
-        assert np.allclose(
-            (quaternion * Quaternion.identity()).data, quaternion.data
-        )
+        assert np.allclose((quaternion * Quaternion.identity()).data, quaternion.data)
 
     def test_no_multiplicative_inverse(self, quaternion, something):
         q1 = quaternion * something
@@ -197,9 +193,7 @@ def test_antipodal(self, quaternion):
         assert qa.size == 2 * q.size
 
     def test_edgecase_outer(self, quaternion):
-        with pytest.raises(
-            NotImplementedError, match="This operation is currently "
-        ):
+        with pytest.raises(NotImplementedError, match="This operation is currently "):
             _ = quaternion.outer([3, 2])
 
     def test_failing_mul(self, quaternion):
@@ -304,9 +298,7 @@ def test_outer_dask_wrong_type_raises(self):
         q = Quaternion(abcd)
         # not Quaternion or Vector3d
         other = np.random.rand(7, 3)
-        with pytest.raises(
-            TypeError, match="Other must be Quaternion or Vector3d"
-        ):
+        with pytest.raises(TypeError, match="Other must be Quaternion or Vector3d"):
             q._outer_dask(other)
 
     def test_from_align_vectors(self):
@@ -326,12 +318,8 @@ def test_from_align_vectors(self):
         error = out[1]
         assert error == 0
 
-        _, sens_mat = Quaternion.from_align_vectors(
-            v1, v2, return_sensitivity=True
-        )
-        assert np.allclose(
-            sens_mat, np.array([[1, 0, 0], [0, 1, 0], [0, 0, 0.5]])
-        )
+        _, sens_mat = Quaternion.from_align_vectors(v1, v2, return_sensitivity=True)
+        assert np.allclose(sens_mat, np.array([[1, 0, 0], [0, 1, 0], [0, 0, 0.5]]))
 
         out = Quaternion.from_align_vectors(
             v1, v2, return_rmsd=True, return_sensitivity=True
@@ -405,9 +393,7 @@ def test_direction_values(self, eu):
         assert np.allclose((q_l2c * q_c2l).data, [1, 0, 0, 0])
 
     def test_direction_kwarg_dumb(self, eu):
-        with pytest.raises(
-            ValueError, match="The chosen direction is not one of "
-        ):
+        with pytest.raises(ValueError, match="The chosen direction is not one of "):
             _ = Quaternion.from_euler(eu, direction="dumb_direction")
 
     def test_edge_cases_to_euler(self):
@@ -418,25 +404,19 @@ def test_edge_cases_to_euler(self):
         _ = q.to_euler()
 
     def test_passing_degrees_warns(self):
-        with pytest.warns(
-            UserWarning, match="Angles are quite high, did you forget "
-        ):
+        with pytest.warns(UserWarning, match="Angles are quite high, did you forget "):
             q = Quaternion.from_euler([90, 0, 0])
             assert np.allclose(q.data, [0.5253, 0, 0, -0.8509], atol=1e-4)
 
 
 class TestFromToMatrix:
     def test_to_matrix(self):
-        q = Quaternion(
-            [[1, 0, 0, 0], [3, 0, 0, 0], [0, 1, 0, 0], [0, 2, 0, 0]]
-        )
+        q = Quaternion([[1, 0, 0, 0], [3, 0, 0, 0], [0, 1, 0, 0], [0, 2, 0, 0]])
         om = np.array(
             [np.eye(3), np.eye(3), np.diag([1, -1, -1]), np.diag([1, -1, -1])]
         )
         # Shapes are handled correctly
-        assert np.allclose(
-            q.reshape(2, 2).unit.to_matrix(), om.reshape(2, 2, 3, 3)
-        )
+        assert np.allclose(q.reshape(2, 2).unit.to_matrix(), om.reshape(2, 2, 3, 3))
 
         q2 = Quaternion(
             [
@@ -450,18 +430,13 @@ def test_to_matrix(self):
         # Inverse equal to transpose
         assert all(np.allclose(np.linalg.inv(i), i.T) for i in om_from_q2)
         # Cross product of any two rows gives the third
-        assert all(
-            np.allclose(np.cross(i[:, 0], i[:, 1]), i[:, 2])
-            for i in om_from_q2
-        )
+        assert all(np.allclose(np.cross(i[:, 0], i[:, 1]), i[:, 2]) for i in om_from_q2)
         # Sum of squares of any column or row equals unity
         assert np.allclose(np.sum(np.square(om_from_q2), axis=1), 1)  # Rows
         assert np.allclose(np.sum(np.square(om_from_q2), axis=2), 1)  # Columns
 
     def test_from_matrix(self):
-        q = Quaternion(
-            [[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0]]
-        )
+        q = Quaternion([[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0]])
         ident = np.identity(3)
         rot_180x = np.diag([1, -1, -1])
         om = np.array([ident, 2 * ident, rot_180x, 2 * rot_180x])
@@ -505,9 +480,7 @@ def test_get_rotation_matrix_from_diffpy(self):
         q = Quaternion.from_matrix([i.R for i in sg225.symop_list])
         assert not np.isnan(q.data).any()
 
-    def test_from_matrix_raises(
-        self, quaternions_conversions, orientation_matrices
-    ):
+    def test_from_matrix_raises(self, quaternions_conversions, orientation_matrices):
         qu = Quaternion.from_matrix(orientation_matrices).data
         assert np.allclose(qu, quaternions_conversions, atol=1e-4)
         with pytest.raises(ValueError, match="(3, 3)"):
@@ -527,16 +500,12 @@ def test_from_axes_angles(self, rotations, extra_dim):
             rotations = rotations.__class__(rotations.data[..., np.newaxis, :])
         ax = AxAngle.from_rotation(rotations)
         Q1 = Quaternion.from_axes_angles(ax.axis.data, ax.angle)
-        Q2 = Quaternion.from_axes_angles(
-            ax.axis, np.rad2deg(ax.angle), degrees=True
-        )
+        Q2 = Quaternion.from_axes_angles(ax.axis, np.rad2deg(ax.angle), degrees=True)
         assert np.allclose(Q1.data, Q2.data)
 
     def test_to_axes_angles(self, quaternions_conversions, axis_angle_pairs):
         ax = Quaternion(quaternions_conversions).to_axes_angles()
-        assert np.allclose(
-            np.deg2rad(ax.angle), axis_angle_pairs[:, 3], atol=4
-        )
+        assert np.allclose(np.deg2rad(ax.angle), axis_angle_pairs[:, 3], atol=4)
 
     def test_from_axes_angles_empty(self):
         q = Quaternion.from_axes_angles([], [])
@@ -548,16 +517,12 @@ class TestFromToRodrigues:
     Rodrigues and Rodrigues-Frank vectors.
     """
 
-    def test_from_to_rodrigues(
-        self, quaternions_conversions, rodrigues_vectors
-    ):
+    def test_from_to_rodrigues(self, quaternions_conversions, rodrigues_vectors):
         axes = rodrigues_vectors[..., :3]
         angles = rodrigues_vectors[..., 3]
 
         q1 = Quaternion(quaternions_conversions)
-        with pytest.warns(
-            UserWarning, match="Highest angle is greater than 179.999 "
-        ):
+        with pytest.warns(UserWarning, match="Highest angle is greater than 179.999 "):
             q2 = Quaternion.from_rodrigues(axes, angles)
         assert np.allclose(q1.data, q2.data, atol=1e-4)
         ro = q1.to_rodrigues(frank=True)
@@ -567,9 +532,7 @@ def test_from_to_rodrigues(
             _ = Quaternion.from_rodrigues([1e15, 1e15, 1e10])
         with pytest.warns(UserWarning, match="Max."):
             _ = Quaternion.from_rodrigues([0, 0, 1e-16])
-        with pytest.raises(
-            ValueError, match="Final dimension of vector array must be"
-        ):
+        with pytest.raises(ValueError, match="Final dimension of vector array must be"):
             Quaternion.from_rodrigues([1, 2, 3, 4])
 
     def test_from_rodrigues_empty(self):
@@ -582,9 +545,7 @@ class TestFromToHomochoric:
     homochoric vectors.
     """
 
-    def test_from_to_homochoric(
-        self, homochoric_vectors, quaternions_conversions
-    ):
+    def test_from_to_homochoric(self, homochoric_vectors, quaternions_conversions):
         ho1 = homochoric_vectors
         ho2 = Vector3d(ho1)
         ho3 = Homochoric(ho1)
@@ -598,9 +559,7 @@ def test_from_to_homochoric(
         assert np.allclose(q1.data, quaternions_conversions, atol=1e-4)
         assert np.allclose(q2.data, quaternions_conversions, atol=1e-4)
         assert np.allclose(q3.data, quaternions_conversions, atol=1e-4)
-        assert np.allclose(
-            q4.data, quaternions_conversions.reshape(2, 5, 4), atol=1e-4
-        )
+        assert np.allclose(q4.data, quaternions_conversions.reshape(2, 5, 4), atol=1e-4)
 
         assert np.allclose(ho1, q1.to_homochoric().data, atol=1e-4)
         assert np.allclose(ho1, q2.to_homochoric().data, atol=1e-4)
@@ -608,9 +567,7 @@ def test_from_to_homochoric(
         assert np.allclose(ho4, q4.to_homochoric().data, atol=1e-4)
 
     def test_from_homochoric_raises(self):
-        with pytest.raises(
-            ValueError, match="Final dimension of vector array must be"
-        ):
+        with pytest.raises(ValueError, match="Final dimension of vector array must be"):
             Quaternion.from_homochoric([1, 2])
 
     def test_from_homochoric_empty(self):

From fcdc166ed7be3ee32b7d311f618f3b100c69f5db Mon Sep 17 00:00:00 2001
From: Austin Gerlt <argerlt@gmail.com>
Date: Sun, 13 Jul 2025 04:29:15 -0600
Subject: [PATCH 15/23] adding requested changes fomr #558

---
 orix/quaternion/misorientation.py |  5 ----
 orix/quaternion/quaternion.py     | 46 ++++++++++++++-----------------
 2 files changed, 21 insertions(+), 30 deletions(-)

diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index c7cc140c4..c4710cf5c 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -388,11 +388,6 @@ def reduce(self) -> Misorientation:
         """Return equivalent transformations which have the smallest
         angle of rotation as a new misorientation.
 
-        Parameters
-        ----------
-        verbose
-            Whether to print a progressbar. Default is ``False``.
-
         Returns
         -------
         M
diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index f72d6b704..e321be0fd 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -247,15 +247,11 @@ def __eq__(self, other: Any | Quaternion) -> bool:
     # ------------------------ Class methods ------------------------- #
 
     @classmethod
-    def random(cls, shape: Union[int, tuple] = 1) -> Quaternion:
+    def random(cls, shape: int | tuple = 1) -> Quaternion:
         quat = super().random(shape)
         quat.data[:, 0] = np.abs(quat.data[:, 0])
         return quat
 
-        O = super().__invert__()
-        O.symmetry = self.symmetry
-        return O
-
     @classmethod
     def from_axes_angles(
         cls,
@@ -697,22 +693,22 @@ def from_align_vectors(
 
     @classmethod
     def from_path_ends(
-        cls, waypoints: Quaternion, close_loop: bool = False, steps: int = 100
+        cls, points: Quaternion, closed: bool = False, steps: int = 100
     ) -> Quaternion:
-        """Return Quaternions tracing the shortest path between two or more
-        consecutive waypoints.
+        """Return quaternions tracing the shortest path between two or more
+        consecutive points.
 
         Parameters
         ----------
-        waypoints : Quaternion
+        points
             Two or more quaternions that define waypoints along a path through
             rotation space (SO3).
-        close_loop : bool, optional
+        closed
             Option to add a final trip from the last waypoint back to the
-            first, thus closing the loop. Default is False.
-        steps : int, optional
-        Number of points to return along the path between each pair of
-        waypoints. The default is 100.
+            first, thus closing the loop. The default is False.
+        steps
+            Number of quaternions to return along the path between each
+            pair of waypoints. The default is 100.
 
         Returns
         -------
@@ -721,30 +717,30 @@ def from_path_ends(
 
         Notes
         -----
-        This method can use Orientations and Misorientations as inputs, and
-        will return an object of the same class. However, symmetry is ignored
-        when determining the shortest routes.
+        This method can use :class:Orientation and :class:Misorientation as
+        inputs and will return an object of the same class. However,
+        symmetry is ignored when determining the shortest routes.
         """
-        waypoints = waypoints.flatten()
-        n = waypoints.size
-        if not close_loop:
+        points = points.flatten()
+        n = points.size
+        if not closed:
             n = n - 1
 
         path_list = []
         for i in range(n):
             # get start and end for this leg of the trip
-            q1 = waypoints[i]
-            q2 = waypoints[(i + 1) % (waypoints.size)]
+            q1 = points[i]
+            q2 = points[(i + 1) % (points.size)]
             # find the ax/ang describing the trip between points
             ax, ang = _conversions.qu2ax((~q1 * q2).data)
             # get 'steps=n' steps along the trip and add them to the journey
             trip = Quaternion.from_axes_angles(ax, np.linspace(0, ang, steps))
             path_list.append((q1 * (trip.flatten())).data)
         path_data = np.concatenate(path_list, axis=0)
-        path = waypoints.__class__(path_data)
+        path = points.__class__(path_data)
         # copy the symmetry if it exists
-        if hasattr(waypoints, "_symmetry"):
-            path._symmetry = waypoints._symmetry
+        if hasattr(points, "_symmetry"):
+            path._symmetry = points._symmetry
         return path
 
     @classmethod

From 7704d641c96aa1ffb065f91355afd4e238fa30f0 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Thu, 17 Jul 2025 15:46:34 -0600
Subject: [PATCH 16/23] made Quaternion.from_path_ends blind to symmetry, and
 added symmetry-aware counterpart to Misorientation

---
 orix/quaternion/misorientation.py         | 32 +++++++++++++++++++++++
 orix/quaternion/quaternion.py             | 24 ++++++-----------
 orix/tests/quaternion/test_orientation.py | 28 ++++++++++++++++++++
 orix/tests/quaternion/test_quaternion.py  |  2 +-
 4 files changed, 69 insertions(+), 17 deletions(-)

diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index c4710cf5c..9175bd5e5 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -266,6 +266,38 @@ def from_scipy_rotation(
             M.symmetry = symmetry
         return M
 
+    @classmethod
+    def from_path_ends(
+        cls, points: Misorientation, closed: bool = False, steps: int = 100
+    ) -> Misorientation:
+        """Return (mis)orientations tracing the shortest path between
+        two or more consecutive points.
+
+        Parameters
+        ----------
+        points
+            Two or more (mis)orientations that define waypoints along
+            a path through rotation space (SO3).
+        closed
+            Option to add a final trip from the last waypoint back to
+            the first, thus closing the loop. The default is False.
+        steps
+            Number of (mis)orientations to return along the path
+            between each pair of waypoints. The default is 100.
+
+        Returns
+        -------
+        path :Quaternion
+            quaternions that map a path between the given waypoints.
+
+        """
+        out = super().from_path_ends(points=points, closed=closed, steps=steps)
+        path = cls(out.data)
+        # copy the symmetry if it exists.
+        if hasattr(points, "_symmetry"):
+            path._symmetry = points._symmetry
+        return path
+
     @classmethod
     def random(
         cls,
diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index e321be0fd..5e9db9f3b 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -695,17 +695,17 @@ def from_align_vectors(
     def from_path_ends(
         cls, points: Quaternion, closed: bool = False, steps: int = 100
     ) -> Quaternion:
-        """Return quaternions tracing the shortest path between two or more
-        consecutive points.
+        """Return quaternions tracing the shortest path between two or
+        more consecutive points.
 
         Parameters
         ----------
         points
-            Two or more quaternions that define waypoints along a path through
-            rotation space (SO3).
+            Two or more quaternions that define waypoints along a path
+            through rotation space (SO3).
         closed
-            Option to add a final trip from the last waypoint back to the
-            first, thus closing the loop. The default is False.
+            Option to add a final trip from the last waypoint back to
+            the first, thus closing the loop. The default is False.
         steps
             Number of quaternions to return along the path between each
             pair of waypoints. The default is 100.
@@ -713,13 +713,8 @@ def from_path_ends(
         Returns
         -------
         path :Quaternion
-            quaternions that map out a path between the given waypoints.
+            quaternions that map a path between the given waypoints.
 
-        Notes
-        -----
-        This method can use :class:Orientation and :class:Misorientation as
-        inputs and will return an object of the same class. However,
-        symmetry is ignored when determining the shortest routes.
         """
         points = points.flatten()
         n = points.size
@@ -737,10 +732,7 @@ def from_path_ends(
             trip = Quaternion.from_axes_angles(ax, np.linspace(0, ang, steps))
             path_list.append((q1 * (trip.flatten())).data)
         path_data = np.concatenate(path_list, axis=0)
-        path = points.__class__(path_data)
-        # copy the symmetry if it exists
-        if hasattr(points, "_symmetry"):
-            path._symmetry = points._symmetry
+        path = cls(path_data)
         return path
 
     @classmethod
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index 0645a135e..96677a507 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -441,6 +441,34 @@ def test_from_scipy_rotation(self):
         with pytest.raises(TypeError, match="Value must be a 2-tuple of"):
             _ = Misorientation.from_scipy_rotation(r_scipy, Oh)
 
+    def test_from_path_ends(self):
+        """check from_path_ends returns what you would expect and
+        preserves symmetry information."""
+        q = Quaternion.random(10)
+        r = Rotation.random(10)
+        o = Orientation.random(10, Oh)
+        m = Misorientation.random(10, [D3, Oh])
+
+        # make sure the result is the correct class.
+        a = Quaternion.from_path_ends(q)
+        b = Rotation.from_path_ends(q)
+        c = Orientation.from_path_ends(r)
+        d = Quaternion.from_path_ends(o)
+        e = Orientation.from_path_ends(q)
+        f = Misorientation.from_path_ends(m)
+        g = Orientation.from_path_ends(o)
+        assert isinstance(a, Quaternion)
+        assert isinstance(b, Rotation)
+        assert isinstance(c, Orientation)
+        assert isinstance(d, Quaternion)
+        assert isinstance(e, Orientation)
+        assert isinstance(f, Misorientation)
+        assert isinstance(g, Orientation)
+
+        # make sure symmetry information is preserved.
+        assert f.symmetry == m.symmetry
+        assert g.symmetry == o.symmetry
+
     def test_inverse(self):
         M1 = Misorientation([np.sqrt(2) / 2, np.sqrt(2) / 2, 0, 0], (Oh, D6))
         M2 = ~M1
diff --git a/orix/tests/quaternion/test_quaternion.py b/orix/tests/quaternion/test_quaternion.py
index 332193a0a..41a9e2605 100644
--- a/orix/tests/quaternion/test_quaternion.py
+++ b/orix/tests/quaternion/test_quaternion.py
@@ -352,7 +352,7 @@ def test_from_path_ends(self):
             )
         )
         path = Quaternion.from_path_ends(waypoints)
-        loop = Quaternion.from_path_ends(waypoints, close_loop=True, steps=11)
+        loop = Quaternion.from_path_ends(waypoints, closed=True, steps=11)
         # check the sizes are as expected
         assert path.shape == (1100,)
         assert loop.shape == (132,)

From 57b56885b14f916b652e051cd52f34954c6da670 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <argerlt@gmail.com>
Date: Fri, 18 Jul 2025 03:07:45 -0600
Subject: [PATCH 17/23] fixing docstring styling

---
 orix/quaternion/quaternion.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index 5e9db9f3b..249ead06e 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -701,7 +701,7 @@ def from_path_ends(
         Parameters
         ----------
         points
-            Two or more quaternions that define waypoints along a path
+            Two or more quaternions that define points along a path
             through rotation space (SO3).
         closed
             Option to add a final trip from the last waypoint back to
@@ -712,7 +712,7 @@ def from_path_ends(
 
         Returns
         -------
-        path :Quaternion
+        path
             quaternions that map a path between the given waypoints.
 
         """

From f842e0bb298b1edffc74884d7ff44e14f9a7f09b Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Fri, 18 Jul 2025 11:48:07 -0600
Subject: [PATCH 18/23] formatting and clarifying tests

---
 orix/quaternion/misorientation.py         |  3 +-
 orix/quaternion/quaternion.py             |  1 -
 orix/tests/quaternion/test_orientation.py | 75 +++++++++++++----------
 3 files changed, 42 insertions(+), 37 deletions(-)

diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index 9175bd5e5..eafd7b6db 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -287,9 +287,8 @@ def from_path_ends(
 
         Returns
         -------
-        path :Quaternion
+        path
             quaternions that map a path between the given waypoints.
-
         """
         out = super().from_path_ends(points=points, closed=closed, steps=steps)
         path = cls(out.data)
diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index 249ead06e..d11fa2b60 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -714,7 +714,6 @@ def from_path_ends(
         -------
         path
             quaternions that map a path between the given waypoints.
-
         """
         points = points.flatten()
         n = points.size
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index 96677a507..c4e93c661 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -321,6 +321,39 @@ def test_symmetry_property_wrong_number_of_values_misorientation(error_type, val
         o.symmetry = value
 
 
+def test_from_path_ends():
+    """check from_path_ends returns what you would expect and
+    preserves symmetry information.
+
+    In particular, ensure the class of the returned object matches the class
+    used for creating it, NOT the class of the object passed in.
+    """
+    q = Quaternion.random(10)
+    r = Rotation.random(10)
+    o = Orientation.random(10, Oh)
+    m = Misorientation.random(10, [D3, Oh])
+
+    # make sure the result is the correct class.
+    a = Quaternion.from_path_ends(q)
+    b = Rotation.from_path_ends(q)
+    c = Orientation.from_path_ends(r)
+    d = Quaternion.from_path_ends(o)
+    e = Orientation.from_path_ends(q)
+    f = Misorientation.from_path_ends(m)
+    g = Orientation.from_path_ends(o)
+    assert isinstance(a, Quaternion)
+    assert isinstance(b, Rotation)
+    assert isinstance(c, Orientation)
+    assert isinstance(d, Quaternion)
+    assert isinstance(e, Orientation)
+    assert isinstance(f, Misorientation)
+    assert isinstance(g, Orientation)
+
+    # make sure symmetry information is preserved.
+    assert f.symmetry == m.symmetry
+    assert g.symmetry == o.symmetry
+
+
 class TestMisorientation:
     def test_get_distance_matrix(self):
         """Compute distance between every misorientation in an instance
@@ -442,32 +475,9 @@ def test_from_scipy_rotation(self):
             _ = Misorientation.from_scipy_rotation(r_scipy, Oh)
 
     def test_from_path_ends(self):
-        """check from_path_ends returns what you would expect and
-        preserves symmetry information."""
-        q = Quaternion.random(10)
-        r = Rotation.random(10)
-        o = Orientation.random(10, Oh)
-        m = Misorientation.random(10, [D3, Oh])
-
-        # make sure the result is the correct class.
-        a = Quaternion.from_path_ends(q)
-        b = Rotation.from_path_ends(q)
-        c = Orientation.from_path_ends(r)
-        d = Quaternion.from_path_ends(o)
-        e = Orientation.from_path_ends(q)
-        f = Misorientation.from_path_ends(m)
-        g = Orientation.from_path_ends(o)
-        assert isinstance(a, Quaternion)
-        assert isinstance(b, Rotation)
-        assert isinstance(c, Orientation)
-        assert isinstance(d, Quaternion)
-        assert isinstance(e, Orientation)
-        assert isinstance(f, Misorientation)
-        assert isinstance(g, Orientation)
-
-        # make sure symmetry information is preserved.
-        assert f.symmetry == m.symmetry
-        assert g.symmetry == o.symmetry
+        # generate paths with misorientations to check symmetry copying
+        wp_m = Misorientation(data=np.eye(4)[2:], symmetry=[Oh, C3])
+        assert Misorientation.from_path_ends(wp_m)._symmetry == (Oh, C3)
 
     def test_inverse(self):
         M1 = Misorientation([np.sqrt(2) / 2, np.sqrt(2) / 2, 0, 0], (Oh, D6))
@@ -628,14 +638,6 @@ def test_from_scipy_rotation(self):
         with pytest.raises(TypeError, match="Value must be an instance of"):
             _ = Orientation.from_scipy_rotation(r_scipy, (Oh, Oh))
 
-    def test_from_path_ends(self):
-        # generate paths with misorientations and orientations to check
-        # symmetry copying
-        wp_o = Orientation(data=np.eye(4)[:2], symmetry=Oh)
-        wp_m = Misorientation(data=np.eye(4)[2:], symmetry=[Oh, C3])
-        assert Orientation.from_path_ends(wp_o)._symmetry == (C1, Oh)
-        assert Misorientation.from_path_ends(wp_m)._symmetry == (Oh, C3)
-
 
 class TestOrientation:
     @pytest.mark.parametrize("symmetry", [C1, C2, C3, C4, D2, D3, D6, T, O, Oh])
@@ -846,6 +848,11 @@ def test_in_fundamental_region(self):
             region = np.radians(pg.euler_fundamental_region)
             assert np.all(np.max(ori.in_euler_fundamental_region(), axis=0) <= region)
 
+    def test_from_path_ends(self):
+        # generate paths with orientations to check symmetry copying
+        wp_o = Orientation(data=np.eye(4)[:2], symmetry=Oh)
+        assert Orientation.from_path_ends(wp_o)._symmetry == (C1, Oh)
+
     def test_inverse(self):
         O1 = Orientation([np.sqrt(2) / 2, np.sqrt(2) / 2, 0, 0], D6)
         O2 = ~O1

From d089947707526fe82c38e514638d300c25d5058b Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Fri, 18 Jul 2025 12:38:21 -0600
Subject: [PATCH 19/23] clarifying tests and adding from_path_ends example

---
 examples/plotting/plot_non_euclidean_paths.py | 81 +++++++++++++++++++
 orix/tests/quaternion/test_quaternion.py      | 12 +++
 2 files changed, 93 insertions(+)
 create mode 100644 examples/plotting/plot_non_euclidean_paths.py

diff --git a/examples/plotting/plot_non_euclidean_paths.py b/examples/plotting/plot_non_euclidean_paths.py
new file mode 100644
index 000000000..3a3b6ca16
--- /dev/null
+++ b/examples/plotting/plot_non_euclidean_paths.py
@@ -0,0 +1,81 @@
+r"""
+========================
+Plot symmetry operations
+========================
+
+This example shows how to use the `from_path_ends` functions from
+:class:`~orix.vector.Vector3d`, :class:`~orix.quaternions.Rotation`, and
+:class:`~orix.quaternions.Orientation` to draw paths through thier
+respective non-Euclidean spaces.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from orix.quaternion import Orientation, Rotation
+from orix.quaternion.symmetry import Oh, D3
+from orix.vector import Vector3d
+
+
+fig = plt.figure()
+
+# plot a path in homochoric space with no symmetry
+rot_path = Rotation(
+    data=np.array(
+        [
+            [1, 0, 0, 0],
+            [1, 1, 0, 0],
+            [1, 0, 1, 0],
+            [1, 0, 0, 1],
+            [1, 0, -1, 0],
+            [1, 0, 0, -1],
+            [1, 0, 0, -1],
+        ]
+    )
+)
+rotation_path = Rotation.from_path_ends(rot_path, closed=True)
+# cast the rotation to a symmetry-less orientation for plotting purposes
+Orientation(rotation_path).scatter(
+    figure=fig, position=[2, 2, 1], marker=">", c=np.arange(700)
+)
+
+# plot a path in rodrigues space with m-3m (cubic) symmetry.
+m3m_path = Orientation(
+    data=np.array(
+        [
+            [1, 0, 0, 0],
+            [2, 1, 0, 0],
+            [3, 0, 1, 0],
+            [4, 0, 0, 1],
+            [5, 0, -1, 0],
+            [6, 0, 0, -1],
+            [7, 0, 0, -1],
+            [8, 1, 0, 0],
+            [9, 0, 1, 0],
+            [10, 0, 0, 1],
+            [11, 0, -1, 0],
+            [12, 0, 0, -1],
+            [13, 0, 0, -1],
+        ]
+    ),
+    symmetry=Oh,
+)
+orientation_path = Orientation.from_path_ends(m3m_path.reduce(), closed=True).reduce()
+orientation_path.scatter(figure=fig, position=[2, 2, 2], marker=">", c=np.arange(1300))
+
+# plot a second path in rodrigues space with symmetry, but while also crossing a
+# symmetry boundary
+fiber_start = Rotation.identity(1)
+fiber_middle = Rotation.from_axes_angles([1, 2, 3], np.pi)
+fiber_end = Rotation.from_axes_angles([1, 2, 3], 2 * np.pi)
+fiber_points = Orientation.stack([fiber_start, fiber_middle, fiber_end])
+fiber_points.symmetry = Oh
+fiber_path = Orientation.from_path_ends(fiber_points, closed=False).reduce()
+fiber_path.scatter(figure=fig, position=[2, 2, 3], marker=">", c=np.arange(200))
+
+
+# plot vectors
+ax4 = plt.subplot(2, 2, 4, projection="stereographic")
+vector_points = Vector3d(np.array([[-1,0,0],[0,1,0.1],[1,0,0.2],[0,-1,0.3],[-1,0,0.4]]))
+
+vector_path = Vector3d.from_path_ends(vector_points,steps = 200)
+ax4.scatter(vector_path, figure=fig, marker=">", c=np.arange(vector_path.size))
diff --git a/orix/tests/quaternion/test_quaternion.py b/orix/tests/quaternion/test_quaternion.py
index 41a9e2605..fea55e915 100644
--- a/orix/tests/quaternion/test_quaternion.py
+++ b/orix/tests/quaternion/test_quaternion.py
@@ -362,6 +362,18 @@ def test_from_path_ends(self):
         assert np.all(np.std(path_spacing, axis=1) < 1e-12)
         assert np.all(np.std(loop_spacing, axis=1) < 1e-12)
 
+    def test_from_path_ends_fiber(self):
+        # check that a linear path in quaternion space follows an explicitly defined
+        # fiber along the same path.
+        # this ensures the path is the shortest distance in SO3 space, (as opposed
+        # to rodrigues or quaternion space) and also evenly spaced along the path.
+        Q1 = Quaternion.identity()
+        Q2 = Quaternion.from_axes_angles([1, 1, 1], 60, degrees=True)
+        Q12 = Quaternion.stack((Q1, Q2))
+        Q_path1 = Quaternion.from_axes_angles([1, 1, 1], np.arange(59), degrees=True)
+        Q_path2 = Quaternion.from_path_ends(Q12, steps=Q_path1.size)
+        assert np.allclose(Q_path1.dot(Q_path2), 1, atol=1e-3)
+
     def test_equality(self):
         Q1 = Quaternion.from_axes_angles([1, 1, 1], -np.pi / 3)
         Q2 = Quaternion.from_axes_angles([1, 1, 1], np.pi / 3)

From ef9f77c8079b3cd353851bb381c651481b3283ea Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Fri, 18 Jul 2025 12:48:54 -0600
Subject: [PATCH 20/23] formatting

---
 examples/plotting/plot_non_euclidean_paths.py | 12 +++++++-----
 1 file changed, 7 insertions(+), 5 deletions(-)

diff --git a/examples/plotting/plot_non_euclidean_paths.py b/examples/plotting/plot_non_euclidean_paths.py
index 3a3b6ca16..50dbe2060 100644
--- a/examples/plotting/plot_non_euclidean_paths.py
+++ b/examples/plotting/plot_non_euclidean_paths.py
@@ -9,13 +9,13 @@
 respective non-Euclidean spaces.
 """
 
-import numpy as np
 import matplotlib.pyplot as plt
+import numpy as np
+
 from orix.quaternion import Orientation, Rotation
-from orix.quaternion.symmetry import Oh, D3
+from orix.quaternion.symmetry import D3, Oh
 from orix.vector import Vector3d
 
-
 fig = plt.figure()
 
 # plot a path in homochoric space with no symmetry
@@ -75,7 +75,9 @@
 
 # plot vectors
 ax4 = plt.subplot(2, 2, 4, projection="stereographic")
-vector_points = Vector3d(np.array([[-1,0,0],[0,1,0.1],[1,0,0.2],[0,-1,0.3],[-1,0,0.4]]))
+vector_points = Vector3d(
+    np.array([[-1, 0, 0], [0, 1, 0.1], [1, 0, 0.2], [0, -1, 0.3], [-1, 0, 0.4]])
+)
 
-vector_path = Vector3d.from_path_ends(vector_points,steps = 200)
+vector_path = Vector3d.from_path_ends(vector_points, steps=200)
 ax4.scatter(vector_path, figure=fig, marker=">", c=np.arange(vector_path.size))

From 03827e0f7543e177e14a0ae51f5bfa6f1af0b1fc Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Wed, 3 Sep 2025 19:56:12 -0600
Subject: [PATCH 21/23] including suggestions and updating example

---
 examples/plotting/plot_non_euclidean_paths.py | 138 +++++++++++-------
 orix/quaternion/misorientation.py             |  18 ++-
 orix/quaternion/orientation.py                |  35 +++++
 orix/tests/quaternion/test_orientation.py     |  53 +++++--
 4 files changed, 169 insertions(+), 75 deletions(-)

diff --git a/examples/plotting/plot_non_euclidean_paths.py b/examples/plotting/plot_non_euclidean_paths.py
index 50dbe2060..2768c0a2a 100644
--- a/examples/plotting/plot_non_euclidean_paths.py
+++ b/examples/plotting/plot_non_euclidean_paths.py
@@ -1,83 +1,115 @@
 r"""
-========================
-Plot symmetry operations
-========================
+========================================
+Plot Paths Through Non-Euclidean Spaces
+========================================
 
-This example shows how to use the `from_path_ends` functions from
-:class:`~orix.vector.Vector3d`, :class:`~orix.quaternions.Rotation`, and
-:class:`~orix.quaternions.Orientation` to draw paths through thier
-respective non-Euclidean spaces.
+This example shows three variations on how 'from_path_ends' can be
+used to plot paths between points in rotational and vector spaces.
+
+This functionality is available in :class:`~orix.vector.Vector3d`,
+:class:`~orix.quaternions.Rotation`,
+:class:`~orix.quaternions.Orientation`,
+and :class:`~orix.quaternions.Misorientation`.
 """
 
 import matplotlib.pyplot as plt
+from matplotlib import cm
 import numpy as np
 
-from orix.quaternion import Orientation, Rotation
+from orix.quaternion import Misorientation, Orientation, Rotation
 from orix.quaternion.symmetry import D3, Oh
 from orix.vector import Vector3d
 
-fig = plt.figure()
+fig = plt.figure(figsize=(4, 8))
 
-# plot a path in homochoric space with no symmetry
-rot_path = Rotation(
+# ========= #
+# Example 1: Plotting a path of rotations with no symmetry in homochoric space
+# ========= #
+rots_along_path = Rotation(
     data=np.array(
         [
             [1, 0, 0, 0],
-            [1, 1, 0, 0],
-            [1, 0, 1, 0],
             [1, 0, 0, 1],
-            [1, 0, -1, 0],
-            [1, 0, 0, -1],
-            [1, 0, 0, -1],
+            [1, 1, 1, 1],
         ]
     )
 )
-rotation_path = Rotation.from_path_ends(rot_path, closed=True)
-# cast the rotation to a symmetry-less orientation for plotting purposes
-Orientation(rotation_path).scatter(
-    figure=fig, position=[2, 2, 1], marker=">", c=np.arange(700)
-)
+n_steps = 20
+rotation_path = Rotation.from_path_ends(rots_along_path, steps=n_steps)
+# create an Orientation loop using this path with no symmetry elements
+ori_path = Orientation(rotation_path)
+# plot the path in homochoric space
+segment_colors = cm.inferno(np.linspace(0, 1, n_steps))
 
-# plot a path in rodrigues space with m-3m (cubic) symmetry.
-m3m_path = Orientation(
+path_colors = np.vstack([segment_colors for x in range(rots_along_path.size - 1)])
+ori_path.scatter(figure=fig, position=[3, 1, 1], marker=">", c=path_colors)
+fig.axes[0].set_title(r"$90^\circ$ rotation around X, then Y")
+
+# ========= #
+# Example 2: Plotting the rotation of several orientations in m3m Rodrigues
+# space around the z axis.
+# ========= #
+oris = Orientation(
     data=np.array(
         [
-            [1, 0, 0, 0],
-            [2, 1, 0, 0],
-            [3, 0, 1, 0],
-            [4, 0, 0, 1],
-            [5, 0, -1, 0],
-            [6, 0, 0, -1],
-            [7, 0, 0, -1],
-            [8, 1, 0, 0],
-            [9, 0, 1, 0],
-            [10, 0, 0, 1],
-            [11, 0, -1, 0],
-            [12, 0, 0, -1],
-            [13, 0, 0, -1],
+            [0.69, 0.24, 0.68, 0.01],
+            [0.26, 0.59, 0.32, 0.7],
+            [0.07, 0.17, 0.93, 0.31],
+            [0.6, 0.03, 0.61, 0.52],
+            [0.51, 0.38, 0.34, 0.69],
+            [0.31, 0.86, 0.22, 0.35],
+            [0.68, 0.67, 0.06, 0.31],
+            [0.01, 0.12, 0.05, 0.99],
+            [0.39, 0.45, 0.34, 0.72],
+            [0.65, 0.59, 0.46, 0.15],
         ]
     ),
     symmetry=Oh,
+).reduce()
+# define a 20 degree rotation around the z axis
+shift = Orientation.from_axes_angles([0, 0, 1], np.pi / 9)
+segment_colors = cm.inferno(np.linspace(0, 1, 10))
+
+ori_paths = []
+for ori in oris:
+    shifted = (shift * ori).reduce()
+    to_from = Orientation.stack([ori, shifted]).flatten()
+    ori_paths.append(Orientation.from_path_ends(to_from, steps=10))
+# plot a path in roddrigues space with m-3m (cubic) symmetry.
+ori_path = Orientation.stack(ori_paths).flatten()
+ori_path.symmetry = Oh
+ori_path.scatter(
+    figure=fig,
+    position=[3, 1, 2],
+    marker=">",
+    c=np.tile(segment_colors, [10, 1]),
+    projection="rodrigues",
 )
-orientation_path = Orientation.from_path_ends(m3m_path.reduce(), closed=True).reduce()
-orientation_path.scatter(figure=fig, position=[2, 2, 2], marker=">", c=np.arange(1300))
+fig.axes[1].set_title(r"$20^{\circ}$ rotations around X-axis in m3m")
 
-# plot a second path in rodrigues space with symmetry, but while also crossing a
-# symmetry boundary
-fiber_start = Rotation.identity(1)
-fiber_middle = Rotation.from_axes_angles([1, 2, 3], np.pi)
-fiber_end = Rotation.from_axes_angles([1, 2, 3], 2 * np.pi)
-fiber_points = Orientation.stack([fiber_start, fiber_middle, fiber_end])
-fiber_points.symmetry = Oh
-fiber_path = Orientation.from_path_ends(fiber_points, closed=False).reduce()
-fiber_path.scatter(figure=fig, position=[2, 2, 3], marker=">", c=np.arange(200))
+# ========= #
+# Example 3: creating a customized Wulf Plotting the rotation of several orientations in m3m Rodrigues
+# space around the z axis.
+# ========= #
 
 
 # plot vectors
-ax4 = plt.subplot(2, 2, 4, projection="stereographic")
-vector_points = Vector3d(
-    np.array([[-1, 0, 0], [0, 1, 0.1], [1, 0, 0.2], [0, -1, 0.3], [-1, 0, 0.4]])
-)
+ax_upper = plt.subplot(3, 1, 3, projection="stereographic", hemisphere="upper")
+r90x = Rotation.from_axes_angles([1, -1, -1], [0, 60], degrees=True)
+x_axis_points = r90x * Vector3d.xvector()
+y_axis_points = r90x * Vector3d.yvector()
+z_axis_points = r90x * Vector3d.zvector()
+
+x_axis_path = Vector3d.from_path_ends(x_axis_points.unique())
+y_axis_path = Vector3d.from_path_ends(y_axis_points.unique())
+z_axis_path = Vector3d.from_path_ends(z_axis_points.unique())
+cx = cm.Reds(np.linspace(0.1, 1, x_axis_path.size))
+cy = cm.Greens(np.linspace(0.1, 1, y_axis_path.size))
+cz = cm.Blues(np.linspace(0.1, 1, z_axis_path.size))
+
+spx = ax_upper.scatter(x_axis_path, figure=fig, marker=">", c=cx, label="X")
+spy = ax_upper.scatter(y_axis_path, figure=fig, marker=">", c=cy, label="Y")
+spz = ax_upper.scatter(z_axis_path, figure=fig, marker=">", c=cz, label="Z")
+ax_upper.legend(loc="lower center", ncols=3)
 
-vector_path = Vector3d.from_path_ends(vector_points, steps=200)
-ax4.scatter(vector_path, figure=fig, marker=">", c=np.arange(vector_path.size))
+plt.tight_layout()
diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index eafd7b6db..018d0d06c 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -270,31 +270,35 @@ def from_scipy_rotation(
     def from_path_ends(
         cls, points: Misorientation, closed: bool = False, steps: int = 100
     ) -> Misorientation:
-        """Return (mis)orientations tracing the shortest path between
+        """Return misorientations tracing the shortest path between
         two or more consecutive points.
 
         Parameters
         ----------
         points
-            Two or more (mis)orientations that define waypoints along
+            Two or more misorientations that define waypoints along
             a path through rotation space (SO3).
         closed
             Option to add a final trip from the last waypoint back to
             the first, thus closing the loop. The default is False.
         steps
-            Number of (mis)orientations to return along the path
+            Number of misorientations to return along the path
             between each pair of waypoints. The default is 100.
 
         Returns
         -------
         path
-            quaternions that map a path between the given waypoints.
+            misorientations that map a path between the given waypoints.
         """
+        # Confirm `points` are (mis)orientations.
+        if not isinstance(points, Misorientation):
+            raise TypeError(
+                f"Points must be a Misorientation, not of type {type(points)}"
+            )
+        # Create a path through Quaternion space, then reapply the symmetry.
         out = super().from_path_ends(points=points, closed=closed, steps=steps)
         path = cls(out.data)
-        # copy the symmetry if it exists.
-        if hasattr(points, "_symmetry"):
-            path._symmetry = points._symmetry
+        path._symmetry = points._symmetry
         return path
 
     @classmethod
diff --git a/orix/quaternion/orientation.py b/orix/quaternion/orientation.py
index 598208c75..d93b524d5 100644
--- a/orix/quaternion/orientation.py
+++ b/orix/quaternion/orientation.py
@@ -346,6 +346,41 @@ def from_scipy_rotation(
             O.symmetry = symmetry
         return O
 
+    @classmethod
+    def from_path_ends(
+        cls, points: Orientation, closed: bool = False, steps: int = 100
+    ) -> Misorientation:
+        """Return orientations tracing the shortest path between
+        two or more consecutive points.
+
+        Parameters
+        ----------
+        points
+            Two or more orientations that define waypoints along
+            a path through rotation space (SO3).
+        closed
+            Option to add a final trip from the last waypoint back to
+            the first, thus closing the loop. The default is False.
+        steps
+            Number of orientations to return along the path
+            between each pair of waypoints. The default is 100.
+
+        Returns
+        -------
+        path
+            orientations that map a path between the given waypoints.
+        """
+        # Confirm `points` are orientations.
+        if not isinstance(points, Orientation):
+            raise TypeError(
+                f"Points must be an Orientation instance, not of type {type(points)}"
+            )
+        # Create a path through Quaternion space, then reapply the symmetry.
+        out = super().from_path_ends(points=points, closed=closed, steps=steps)
+        path = cls(out.data)
+        path._symmetry = points._symmetry
+        return path
+
     @classmethod
     def random(
         cls, shape: Union[int, tuple] = 1, symmetry: Optional[Symmetry] = None
diff --git a/orix/tests/quaternion/test_orientation.py b/orix/tests/quaternion/test_orientation.py
index c4e93c661..a259fc998 100644
--- a/orix/tests/quaternion/test_orientation.py
+++ b/orix/tests/quaternion/test_orientation.py
@@ -333,25 +333,48 @@ def test_from_path_ends():
     o = Orientation.random(10, Oh)
     m = Misorientation.random(10, [D3, Oh])
 
-    # make sure the result is the correct class.
+    # Quaternion sanity checks
     a = Quaternion.from_path_ends(q)
-    b = Rotation.from_path_ends(q)
-    c = Orientation.from_path_ends(r)
-    d = Quaternion.from_path_ends(o)
-    e = Orientation.from_path_ends(q)
-    f = Misorientation.from_path_ends(m)
-    g = Orientation.from_path_ends(o)
     assert isinstance(a, Quaternion)
-    assert isinstance(b, Rotation)
-    assert isinstance(c, Orientation)
+    b = Quaternion.from_path_ends(r)
+    assert isinstance(b, Quaternion)
+    c = Quaternion.from_path_ends(o)
+    assert isinstance(c, Quaternion)
+    d = Quaternion.from_path_ends(m)
     assert isinstance(d, Quaternion)
-    assert isinstance(e, Orientation)
-    assert isinstance(f, Misorientation)
-    assert isinstance(g, Orientation)
 
-    # make sure symmetry information is preserved.
-    assert f.symmetry == m.symmetry
-    assert g.symmetry == o.symmetry
+    # Rotation sanity checks
+    a = Rotation.from_path_ends(q)
+    assert isinstance(a, Rotation)
+    b = Rotation.from_path_ends(r)
+    assert isinstance(b, Rotation)
+    c = Rotation.from_path_ends(o)
+    assert isinstance(c, Rotation)
+    d = Rotation.from_path_ends(m)
+    assert isinstance(d, Rotation)
+
+    # Misorientation sanity checks
+    with pytest.raises(TypeError, match="Points must be a Misorientation"):
+        a = Misorientation.from_path_ends(q)
+    with pytest.raises(TypeError, match="Points must be a Misorientation"):
+        b = Misorientation.from_path_ends(r)
+    c = Misorientation.from_path_ends(o)
+    assert isinstance(c, Misorientation)
+    d = Misorientation.from_path_ends(m)
+    assert isinstance(d, Misorientation)
+    assert c.symmetry[1] == o.symmetry
+    assert d.symmetry == m.symmetry
+
+    # Orientation sanity checks
+    with pytest.raises(TypeError, match="Points must be an Orientation"):
+        a = Orientation.from_path_ends(q)
+    with pytest.raises(TypeError, match="Points must be an Orientation"):
+        b = Orientation.from_path_ends(r)
+    c = Orientation.from_path_ends(o)
+    assert c.symmetry == o.symmetry
+    assert isinstance(c, Orientation)
+    with pytest.raises(TypeError, match="Points must be an Orientation"):
+        d = Orientation.from_path_ends(m)
 
 
 class TestMisorientation:

From 1aeb7a964985b1109d6654c0ed67d9bdd1216741 Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Thu, 4 Sep 2025 19:30:57 -0600
Subject: [PATCH 22/23] add HomochroicPlot, cleaned up examples, formatting

---
 ...across_fundamental_region_boundaries.ipynb |   4 +-
 .../clustering_misorientations.ipynb          |   8 +-
 doc/tutorials/clustering_orientations.ipynb   |   6 +-
 examples/plotting/plot_non_euclidean_paths.py | 115 --------------
 examples/plotting/plotting_paths.py           | 141 ++++++++++++++++++
 orix/plot/__init__.py                         |   7 +-
 orix/plot/rotation_plot.py                    |  14 +-
 orix/quaternion/misorientation.py             |   5 +-
 orix/quaternion/orientation.py                |   6 +-
 orix/tests/plot/test_rotation_plot.py         |   9 +-
 orix/tests/test_crystal_map.py                |   1 +
 11 files changed, 182 insertions(+), 134 deletions(-)
 delete mode 100644 examples/plotting/plot_non_euclidean_paths.py
 create mode 100644 examples/plotting/plotting_paths.py

diff --git a/doc/tutorials/clustering_across_fundamental_region_boundaries.ipynb b/doc/tutorials/clustering_across_fundamental_region_boundaries.ipynb
index 9131004df..ca6dd364b 100644
--- a/doc/tutorials/clustering_across_fundamental_region_boundaries.ipynb
+++ b/doc/tutorials/clustering_across_fundamental_region_boundaries.ipynb
@@ -89,7 +89,7 @@
     "# Stack and map into the Oh fundamental zone\n",
     "ori = Orientation.stack([cluster1, cluster2, cluster3]).flatten()\n",
     "ori.symmetry = Oh\n",
-    "ori = ori.map_into_symmetry_reduced_zone()"
+    "ori = ori.reduce()"
    ]
   },
   {
@@ -158,7 +158,7 @@
     "mori2 = (~ori).outer(ori)\n",
     "\n",
     "mori2.symmetry = Oh\n",
-    "mori2 = mori2.map_into_symmetry_reduced_zone()\n",
+    "mori2 = mori2.reduce()\n",
     "\n",
     "D2 = mori2.angle"
    ]
diff --git a/doc/tutorials/clustering_misorientations.ipynb b/doc/tutorials/clustering_misorientations.ipynb
index f13e66385..8845a33c7 100644
--- a/doc/tutorials/clustering_misorientations.ipynb
+++ b/doc/tutorials/clustering_misorientations.ipynb
@@ -163,7 +163,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "ori = ori.map_into_symmetry_reduced_zone()"
+    "ori = ori.reduce()"
    ]
   },
   {
@@ -213,7 +213,7 @@
    "outputs": [],
    "source": [
     "mori.symmetry = (D6, D6)\n",
-    "mori = mori.map_into_symmetry_reduced_zone()"
+    "mori = mori.reduce()"
    ]
   },
   {
@@ -305,7 +305,7 @@
     "\n",
     "    # Map into the fundamental zone\n",
     "    mori_i.symmetry = (D6, D6)\n",
-    "    mori_i = mori_i.map_into_symmetry_reduced_zone()\n",
+    "    mori_i = mori_i.reduce()\n",
     "\n",
     "    # Get the cluster mean\n",
     "    mori_i = mori_i.mean()\n",
@@ -318,7 +318,7 @@
     "\n",
     "# Map into the fundamental zone\n",
     "cluster_means.symmetry = (D6, D6)\n",
-    "cluster_means = cluster_means.map_into_symmetry_reduced_zone()\n",
+    "cluster_means = cluster_means.reduce()\n",
     "cluster_means"
    ]
   },
diff --git a/doc/tutorials/clustering_orientations.ipynb b/doc/tutorials/clustering_orientations.ipynb
index ed2c363fe..5b15d014b 100644
--- a/doc/tutorials/clustering_orientations.ipynb
+++ b/doc/tutorials/clustering_orientations.ipynb
@@ -198,7 +198,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "ori = ori.map_into_symmetry_reduced_zone()"
+    "ori = ori.reduce()"
    ]
   },
   {
@@ -320,7 +320,7 @@
     "\n",
     "# Map into the fundamental zone\n",
     "cluster_means.symmetry = D6\n",
-    "cluster_means = cluster_means.map_into_symmetry_reduced_zone()\n",
+    "cluster_means = cluster_means.reduce()\n",
     "cluster_means"
    ]
   },
@@ -393,7 +393,7 @@
     "\n",
     "# Map into the fundamental zone\n",
     "ori_recentered.symmetry = D6\n",
-    "ori_recentered = ori_recentered.map_into_symmetry_reduced_zone()\n",
+    "ori_recentered = ori_recentered.reduce()\n",
     "\n",
     "cluster_means_recentered = Orientation.stack(\n",
     "    [ori_recentered[all_labels == l].mean() for l in unique_cluster_labels]\n",
diff --git a/examples/plotting/plot_non_euclidean_paths.py b/examples/plotting/plot_non_euclidean_paths.py
deleted file mode 100644
index 2768c0a2a..000000000
--- a/examples/plotting/plot_non_euclidean_paths.py
+++ /dev/null
@@ -1,115 +0,0 @@
-r"""
-========================================
-Plot Paths Through Non-Euclidean Spaces
-========================================
-
-This example shows three variations on how 'from_path_ends' can be
-used to plot paths between points in rotational and vector spaces.
-
-This functionality is available in :class:`~orix.vector.Vector3d`,
-:class:`~orix.quaternions.Rotation`,
-:class:`~orix.quaternions.Orientation`,
-and :class:`~orix.quaternions.Misorientation`.
-"""
-
-import matplotlib.pyplot as plt
-from matplotlib import cm
-import numpy as np
-
-from orix.quaternion import Misorientation, Orientation, Rotation
-from orix.quaternion.symmetry import D3, Oh
-from orix.vector import Vector3d
-
-fig = plt.figure(figsize=(4, 8))
-
-# ========= #
-# Example 1: Plotting a path of rotations with no symmetry in homochoric space
-# ========= #
-rots_along_path = Rotation(
-    data=np.array(
-        [
-            [1, 0, 0, 0],
-            [1, 0, 0, 1],
-            [1, 1, 1, 1],
-        ]
-    )
-)
-n_steps = 20
-rotation_path = Rotation.from_path_ends(rots_along_path, steps=n_steps)
-# create an Orientation loop using this path with no symmetry elements
-ori_path = Orientation(rotation_path)
-# plot the path in homochoric space
-segment_colors = cm.inferno(np.linspace(0, 1, n_steps))
-
-path_colors = np.vstack([segment_colors for x in range(rots_along_path.size - 1)])
-ori_path.scatter(figure=fig, position=[3, 1, 1], marker=">", c=path_colors)
-fig.axes[0].set_title(r"$90^\circ$ rotation around X, then Y")
-
-# ========= #
-# Example 2: Plotting the rotation of several orientations in m3m Rodrigues
-# space around the z axis.
-# ========= #
-oris = Orientation(
-    data=np.array(
-        [
-            [0.69, 0.24, 0.68, 0.01],
-            [0.26, 0.59, 0.32, 0.7],
-            [0.07, 0.17, 0.93, 0.31],
-            [0.6, 0.03, 0.61, 0.52],
-            [0.51, 0.38, 0.34, 0.69],
-            [0.31, 0.86, 0.22, 0.35],
-            [0.68, 0.67, 0.06, 0.31],
-            [0.01, 0.12, 0.05, 0.99],
-            [0.39, 0.45, 0.34, 0.72],
-            [0.65, 0.59, 0.46, 0.15],
-        ]
-    ),
-    symmetry=Oh,
-).reduce()
-# define a 20 degree rotation around the z axis
-shift = Orientation.from_axes_angles([0, 0, 1], np.pi / 9)
-segment_colors = cm.inferno(np.linspace(0, 1, 10))
-
-ori_paths = []
-for ori in oris:
-    shifted = (shift * ori).reduce()
-    to_from = Orientation.stack([ori, shifted]).flatten()
-    ori_paths.append(Orientation.from_path_ends(to_from, steps=10))
-# plot a path in roddrigues space with m-3m (cubic) symmetry.
-ori_path = Orientation.stack(ori_paths).flatten()
-ori_path.symmetry = Oh
-ori_path.scatter(
-    figure=fig,
-    position=[3, 1, 2],
-    marker=">",
-    c=np.tile(segment_colors, [10, 1]),
-    projection="rodrigues",
-)
-fig.axes[1].set_title(r"$20^{\circ}$ rotations around X-axis in m3m")
-
-# ========= #
-# Example 3: creating a customized Wulf Plotting the rotation of several orientations in m3m Rodrigues
-# space around the z axis.
-# ========= #
-
-
-# plot vectors
-ax_upper = plt.subplot(3, 1, 3, projection="stereographic", hemisphere="upper")
-r90x = Rotation.from_axes_angles([1, -1, -1], [0, 60], degrees=True)
-x_axis_points = r90x * Vector3d.xvector()
-y_axis_points = r90x * Vector3d.yvector()
-z_axis_points = r90x * Vector3d.zvector()
-
-x_axis_path = Vector3d.from_path_ends(x_axis_points.unique())
-y_axis_path = Vector3d.from_path_ends(y_axis_points.unique())
-z_axis_path = Vector3d.from_path_ends(z_axis_points.unique())
-cx = cm.Reds(np.linspace(0.1, 1, x_axis_path.size))
-cy = cm.Greens(np.linspace(0.1, 1, y_axis_path.size))
-cz = cm.Blues(np.linspace(0.1, 1, z_axis_path.size))
-
-spx = ax_upper.scatter(x_axis_path, figure=fig, marker=">", c=cx, label="X")
-spy = ax_upper.scatter(y_axis_path, figure=fig, marker=">", c=cy, label="Y")
-spz = ax_upper.scatter(z_axis_path, figure=fig, marker=">", c=cz, label="Z")
-ax_upper.legend(loc="lower center", ncols=3)
-
-plt.tight_layout()
diff --git a/examples/plotting/plotting_paths.py b/examples/plotting/plotting_paths.py
new file mode 100644
index 000000000..0ba8cf9b2
--- /dev/null
+++ b/examples/plotting/plotting_paths.py
@@ -0,0 +1,141 @@
+r"""
+=========================================
+ Plot Paths In Rotation and Vector Space
+=========================================
+
+This example shows how paths though either rotation or vector space
+can be plotted using ORIX. These are the shortest paths through their
+respective spaces, and thus not always straight lines in euclidean
+projections (Rodrigues, stereographic, etc.).
+
+This functionality is available in :class:`~orix.vector.Vector3d`,
+:class:`~orix.quaternions.Rotation`,
+:class:`~orix.quaternions.Orientation`,
+and :class:`~orix.quaternions.Misorientation`.
+"""
+
+from matplotlib import cm
+import matplotlib.pyplot as plt
+import numpy as np
+
+from orix import plot
+from orix.plot.direction_color_keys import DirectionColorKeyTSL
+from orix.quaternion import Orientation, OrientationRegion, Quaternion
+from orix.quaternion.symmetry import C1, Oh
+from orix.sampling import sample_S2
+from orix.vector import Vector3d
+
+fig = plt.figure(figsize=(6, 6))
+n_steps = 30
+
+# ========= #
+# Example 1: Plotting multiple paths into a user defined axis
+# ========= #
+# This subplot shows several paths through the cubic (m3m) fundamental zone
+# created by rotating 20 randomly chosen points 30 degrees around the z axis.
+# these paths are drawn in rodrigues space, which is an equal-angle projection
+# of rotation space. As such, notice how all lines tracing out axial rotations
+# are straight, but lines starting closer to the center of the fundamental zone
+# appear shorter.
+# the sampe paths are then also plotted on an Inverse Pole Figure (IPF) plot.
+rod_ax = fig.add_subplot(2, 2, 1, projection="rodrigues", proj_type="ortho")
+ipf_ax = fig.add_subplot(2, 2, 2, projection="ipf", symmetry=Oh)
+
+# 10 random orientations with the cubic m3m ('Oh' in the schoenflies notation)
+# crystal symmetry.
+oris = Orientation(
+    data=np.array(
+        [
+            [0.69, 0.24, 0.68, 0.01],
+            [0.26, 0.59, 0.32, 0.7],
+            [0.07, 0.17, 0.93, 0.31],
+            [0.6, 0.03, 0.61, 0.52],
+            [0.51, 0.38, 0.34, 0.69],
+            [0.31, 0.86, 0.22, 0.35],
+            [0.68, 0.67, 0.06, 0.31],
+            [0.01, 0.12, 0.05, 0.99],
+            [0.39, 0.45, 0.34, 0.72],
+            [0.65, 0.59, 0.46, 0.15],
+        ]
+    ),
+    symmetry=Oh,
+)
+# reduce them to their crystallographically identical representations
+oris = oris.reduce()
+# define a 20 degree rotation around the z axis
+shift = Orientation.from_axes_angles([0, 0, 1], 30, degrees=True)
+# for each orientation, calculate and plot the path they would take during a
+# 45 degree shift.
+segment_colors = cm.inferno(np.linspace(0, 1, n_steps))
+for ori in oris:
+    points = Orientation.stack([ori, (shift * ori)]).reduce()
+    points.symmetry = Oh
+    path = Orientation.from_path_ends(points, steps=n_steps)
+    rod_ax.scatter(path, c=segment_colors)
+    ipf_ax.scatter(path, c=segment_colors)
+
+# add the wireframe and clean up the plot.
+fz = OrientationRegion.from_symmetry(path.symmetry)
+rod_ax.plot_wireframe(fz)
+rod_ax._correct_aspect_ratio(fz)
+rod_ax.axis("off")
+rod_ax.set_title(r"Rodrigues, multiple paths")
+ipf_ax.set_title(r"IPF, multiple paths        ")
+
+
+# %%
+# ========= #
+# Example 2: Plotting a path using `Rotation.scatter'
+# ========= #
+# This subplot traces the path of an object rotated 90 degrees around the
+# X axis, then 90 degrees around the Y axis. The path is plotted in
+# homochoric space, which is an equal-volume projection of rotation space
+rots = Orientation.from_axes_angles(
+    [[1, 0, 0], [1, 0, 0], [0, 1, 0]], [0, 90, 90], degrees=True, symmetry=C1
+)
+rots[2] = rots[1] * rots[2]
+path = Orientation.from_path_ends(rots, steps=n_steps)
+# create a list of RGBA color values for a gradient red line and blue line
+path_colors = np.vstack(
+    [cm.Reds(np.linspace(0.5, 1, n_steps)), cm.Blues(np.linspace(0.5, 1, n_steps))]
+)
+
+# Here, we instead use the in-built plotting tool from
+# Orientation.scatter to auto-generate the subplot. This is especially handy when
+# plotting only a single Orientation object.
+path.scatter(figure=fig, position=[2, 2, 3], marker=">", c=path_colors)
+fig.axes[2].set_title(r"Homochoric, two $90^\circ$ rotations")
+
+# %%
+
+# ========= #
+# Example 3: paths in stereographic plots
+# ========= #
+# This is similar to the second example, but now vectors are being rotated
+# 20 degrees around the [1,1,1] axis on a stereographic plot.
+
+vec_ax = plt.subplot(2, 2, 4, projection="stereographic", hemisphere="upper")
+ipf_colormap = DirectionColorKeyTSL(C1)
+
+# define a mesh of vectors with approximately 20 degree spacing, and
+# within 80 degrees of the Z axis
+vecs = sample_S2(20)
+vecs = vecs[vecs.polar < (80 * np.pi / 180)]
+
+# define a 15 degree rotation around [1,1,1]
+rots = Quaternion.from_axes_angles([1, 1, 1], [0, 15], degrees=True)
+
+for vec in vecs:
+    path_ends = rots * vec
+    # color each path using a gradient pased on the IPF coloring.
+    c = ipf_colormap.direction2color(vec)
+    if np.abs(path_ends.cross(path_ends[::-1])[0].norm) > 1e-12:
+        path = Vector3d.from_path_ends(path_ends, steps=100)
+        segment_c = c * np.linspace(0.25, 1, path.size)[:, np.newaxis]
+        vec_ax.scatter(path, c=segment_c)
+    else:
+        vec_ax.scatter(path_ends[0], c=c)
+
+vec_ax.set_title(r"Stereographic")
+vec_ax.set_labels("X", "Y")
+plt.tight_layout()
diff --git a/orix/plot/__init__.py b/orix/plot/__init__.py
index de90d82d4..b024b6cb2 100644
--- a/orix/plot/__init__.py
+++ b/orix/plot/__init__.py
@@ -29,7 +29,12 @@
 import lazy_loader
 
 from orix.plot.crystal_map_plot import CrystalMapPlot
-from orix.plot.rotation_plot import AxAnglePlot, RodriguesPlot, RotationPlot
+from orix.plot.rotation_plot import (
+    AxAnglePlot,
+    HomochoricPlot,
+    RodriguesPlot,
+    RotationPlot,
+)
 from orix.plot.stereographic_plot import StereographicPlot
 
 # Must be imported below StereographicPlot since it imports it
diff --git a/orix/plot/rotation_plot.py b/orix/plot/rotation_plot.py
index 0ba8891e4..99a5583a7 100644
--- a/orix/plot/rotation_plot.py
+++ b/orix/plot/rotation_plot.py
@@ -24,7 +24,7 @@
 import matplotlib.pyplot as plt
 from mpl_toolkits.mplot3d import Axes3D
 
-from orix.vector import AxAngle, Rodrigues
+from orix.vector import AxAngle, Homochoric, Rodrigues
 
 
 class RotationPlot(Axes3D):
@@ -62,7 +62,7 @@ def transform(
                 raise TypeError("fundamental_zone is not an OrientationRegion object.")
             # if any in xs are out of fundamental_zone, calculate symmetry reduction
             if not (xs < fundamental_zone).all():
-                xs = xs.map_into_symmetry_reduced_zone()
+                xs = xs.reduce()
 
         if isinstance(xs, Rotation):
             if isinstance(xs, OrientationRegion):
@@ -152,8 +152,16 @@ class AxAnglePlot(RotationPlot):
     transformation_class = AxAngle
 
 
+class HomochoricPlot(RotationPlot):
+    """Plot rotations in a axis-angle space."""
+
+    name = "homochoric"
+    transformation_class = Homochoric
+
+
 projections.register_projection(RodriguesPlot)
 projections.register_projection(AxAnglePlot)
+projections.register_projection(HomochoricPlot)
 
 
 def _setup_rotation_plot(
@@ -161,7 +169,7 @@ def _setup_rotation_plot(
     projection: str = "axangle",
     position: Union[int, tuple, SubplotSpec, None] = (1, 1, 1),
     figure_kwargs: Optional[dict] = None,
-) -> Tuple[plt.Figure, Union[AxAnglePlot, RodriguesPlot]]:
+) -> Tuple[plt.Figure, Union[AxAnglePlot, RodriguesPlot, HomochoricPlot]]:
     """Return a figure and rotation plot axis of the correct type.
 
     This is a convenience method used in e.g.
diff --git a/orix/quaternion/misorientation.py b/orix/quaternion/misorientation.py
index 018d0d06c..456af7248 100644
--- a/orix/quaternion/misorientation.py
+++ b/orix/quaternion/misorientation.py
@@ -397,7 +397,7 @@ def map_into_symmetry_reduced_zone(self, verbose: bool = False) -> Misorientatio
         >>> data = np.array([[0.5, 0.5, 0.5, 0.5], [0, 1, 0, 0]])
         >>> M = Misorientation(data)
         >>> M.symmetry = (C4, C2)
-        >>> M.map_into_symmetry_reduced_zone()
+        >>> M.reduce()
         Misorientation (2,) 4, 2
         [[-0.7071  0.7071  0.      0.    ]
         [ 0.      1.      0.      0.    ]]
@@ -479,7 +479,8 @@ def scatter(
         ----------
         projection
             Which misorientation space to plot misorientations in,
-            either ``"axangle"`` (default) or ``"rodrigues"``.
+            either ``"axangle"`` (default), ``"rodrigues"``, or
+            ``"homochoric"``.
         figure
             If given, a new plot axis :class:`~orix.plot.AxAnglePlot` or
             :class:`~orix.plot.RodriguesPlot` is added to the figure in
diff --git a/orix/quaternion/orientation.py b/orix/quaternion/orientation.py
index d93b524d5..50049a035 100644
--- a/orix/quaternion/orientation.py
+++ b/orix/quaternion/orientation.py
@@ -102,7 +102,7 @@ def __sub__(self, other: Orientation) -> Misorientation:
             # Call to Object3d.squeeze() doesn't carry over symmetry
             M = Misorientation(self * ~other).squeeze()
             M.symmetry = (self.symmetry, other.symmetry)
-            return M.map_into_symmetry_reduced_zone()
+            return M.reduce()
         return NotImplemented
 
     # ------------------------ Class methods ------------------------- #
@@ -772,8 +772,8 @@ def scatter(
         ----------
         projection
             Which orientation space to plot orientations in, either
-            "axangle" (default), "rodrigues" or "ipf" (inverse pole
-            figure).
+            "axangle" (default), ``"rodrigues"``, ``"homochoric"``,
+            or ``"ipf"`` (inverse pole figure).
         figure
             If given, a new plot axis :class:`~orix.plot.AxAnglePlot` or
             :class:`~orix.plot.RodriguesPlot` is added to the figure in
diff --git a/orix/tests/plot/test_rotation_plot.py b/orix/tests/plot/test_rotation_plot.py
index 93a1cb749..93adc22b9 100644
--- a/orix/tests/plot/test_rotation_plot.py
+++ b/orix/tests/plot/test_rotation_plot.py
@@ -21,7 +21,7 @@
 import numpy as np
 import pytest
 
-from orix.plot import AxAnglePlot, RodriguesPlot, RotationPlot
+from orix.plot import AxAnglePlot, HomochoricPlot, RodriguesPlot, RotationPlot
 from orix.quaternion import Misorientation, Orientation, OrientationRegion
 from orix.quaternion.symmetry import C1, D6
 
@@ -33,6 +33,13 @@ def test_creation(self):
         assert isinstance(ax, RodriguesPlot)
 
 
+class TestHomochoricPlot:
+    def test_creation(self):
+        fig = plt.figure()
+        ax = fig.add_subplot(projection="homochoric")
+        assert isinstance(ax, HomochoricPlot)
+
+
 class TestAxisAnglePlot:
     def test_creation(self):
         fig = plt.figure()
diff --git a/orix/tests/test_crystal_map.py b/orix/tests/test_crystal_map.py
index f880ad395..9052ab0d0 100644
--- a/orix/tests/test_crystal_map.py
+++ b/orix/tests/test_crystal_map.py
@@ -674,6 +674,7 @@ def test_orientations_symmetry(self, point_group, rotation, expected_orientation
 
         o = xmap.orientations
         o = o.map_into_symmetry_reduced_zone()
+        o = o.reduce()
 
         o1 = Orientation(r)
         o1.symmetry = point_group

From 3209fbc7e26795d3278a2b9c38553743aef9b66a Mon Sep 17 00:00:00 2001
From: Austin Gerlt <83073845+argerlt@users.noreply.github.com>
Date: Thu, 4 Sep 2025 19:36:44 -0600
Subject: [PATCH 23/23] Delete plot_non_euclidean_paths.py

---
 examples/plotting/plot_non_euclidean_paths.py | 115 ------------------
 1 file changed, 115 deletions(-)
 delete mode 100644 examples/plotting/plot_non_euclidean_paths.py

diff --git a/examples/plotting/plot_non_euclidean_paths.py b/examples/plotting/plot_non_euclidean_paths.py
deleted file mode 100644
index 2768c0a2a..000000000
--- a/examples/plotting/plot_non_euclidean_paths.py
+++ /dev/null
@@ -1,115 +0,0 @@
-r"""
-========================================
-Plot Paths Through Non-Euclidean Spaces
-========================================
-
-This example shows three variations on how 'from_path_ends' can be
-used to plot paths between points in rotational and vector spaces.
-
-This functionality is available in :class:`~orix.vector.Vector3d`,
-:class:`~orix.quaternions.Rotation`,
-:class:`~orix.quaternions.Orientation`,
-and :class:`~orix.quaternions.Misorientation`.
-"""
-
-import matplotlib.pyplot as plt
-from matplotlib import cm
-import numpy as np
-
-from orix.quaternion import Misorientation, Orientation, Rotation
-from orix.quaternion.symmetry import D3, Oh
-from orix.vector import Vector3d
-
-fig = plt.figure(figsize=(4, 8))
-
-# ========= #
-# Example 1: Plotting a path of rotations with no symmetry in homochoric space
-# ========= #
-rots_along_path = Rotation(
-    data=np.array(
-        [
-            [1, 0, 0, 0],
-            [1, 0, 0, 1],
-            [1, 1, 1, 1],
-        ]
-    )
-)
-n_steps = 20
-rotation_path = Rotation.from_path_ends(rots_along_path, steps=n_steps)
-# create an Orientation loop using this path with no symmetry elements
-ori_path = Orientation(rotation_path)
-# plot the path in homochoric space
-segment_colors = cm.inferno(np.linspace(0, 1, n_steps))
-
-path_colors = np.vstack([segment_colors for x in range(rots_along_path.size - 1)])
-ori_path.scatter(figure=fig, position=[3, 1, 1], marker=">", c=path_colors)
-fig.axes[0].set_title(r"$90^\circ$ rotation around X, then Y")
-
-# ========= #
-# Example 2: Plotting the rotation of several orientations in m3m Rodrigues
-# space around the z axis.
-# ========= #
-oris = Orientation(
-    data=np.array(
-        [
-            [0.69, 0.24, 0.68, 0.01],
-            [0.26, 0.59, 0.32, 0.7],
-            [0.07, 0.17, 0.93, 0.31],
-            [0.6, 0.03, 0.61, 0.52],
-            [0.51, 0.38, 0.34, 0.69],
-            [0.31, 0.86, 0.22, 0.35],
-            [0.68, 0.67, 0.06, 0.31],
-            [0.01, 0.12, 0.05, 0.99],
-            [0.39, 0.45, 0.34, 0.72],
-            [0.65, 0.59, 0.46, 0.15],
-        ]
-    ),
-    symmetry=Oh,
-).reduce()
-# define a 20 degree rotation around the z axis
-shift = Orientation.from_axes_angles([0, 0, 1], np.pi / 9)
-segment_colors = cm.inferno(np.linspace(0, 1, 10))
-
-ori_paths = []
-for ori in oris:
-    shifted = (shift * ori).reduce()
-    to_from = Orientation.stack([ori, shifted]).flatten()
-    ori_paths.append(Orientation.from_path_ends(to_from, steps=10))
-# plot a path in roddrigues space with m-3m (cubic) symmetry.
-ori_path = Orientation.stack(ori_paths).flatten()
-ori_path.symmetry = Oh
-ori_path.scatter(
-    figure=fig,
-    position=[3, 1, 2],
-    marker=">",
-    c=np.tile(segment_colors, [10, 1]),
-    projection="rodrigues",
-)
-fig.axes[1].set_title(r"$20^{\circ}$ rotations around X-axis in m3m")
-
-# ========= #
-# Example 3: creating a customized Wulf Plotting the rotation of several orientations in m3m Rodrigues
-# space around the z axis.
-# ========= #
-
-
-# plot vectors
-ax_upper = plt.subplot(3, 1, 3, projection="stereographic", hemisphere="upper")
-r90x = Rotation.from_axes_angles([1, -1, -1], [0, 60], degrees=True)
-x_axis_points = r90x * Vector3d.xvector()
-y_axis_points = r90x * Vector3d.yvector()
-z_axis_points = r90x * Vector3d.zvector()
-
-x_axis_path = Vector3d.from_path_ends(x_axis_points.unique())
-y_axis_path = Vector3d.from_path_ends(y_axis_points.unique())
-z_axis_path = Vector3d.from_path_ends(z_axis_points.unique())
-cx = cm.Reds(np.linspace(0.1, 1, x_axis_path.size))
-cy = cm.Greens(np.linspace(0.1, 1, y_axis_path.size))
-cz = cm.Blues(np.linspace(0.1, 1, z_axis_path.size))
-
-spx = ax_upper.scatter(x_axis_path, figure=fig, marker=">", c=cx, label="X")
-spy = ax_upper.scatter(y_axis_path, figure=fig, marker=">", c=cy, label="Y")
-spz = ax_upper.scatter(z_axis_path, figure=fig, marker=">", c=cz, label="Z")
-ax_upper.legend(loc="lower center", ncols=3)
-
-plt.tight_layout()