Option to use euler fundamental region for mean orientation

orix/quaternion/orientation.py

@@ -30,6 +30,7 @@
 import numpy as np
 from tqdm import tqdm
 
+from orix.quaternion import Quaternion
 from orix.quaternion.orientation_region import OrientationRegion
 from orix.quaternion.rotation import Rotation
 from orix.quaternion.symmetry import C1, Symmetry, _get_unique_symmetry_elements
@@ -792,6 +793,39 @@ def dot_outer(self, other: Orientation) -> np.ndarray:
         )
         return highest_dot_products.transpose(*order)
 
+    def mean(self, mean_in_euler_fundamental_region=False) -> Orientation:
+        """Return the mean orientation with unitary weights.
+
+        Returns
+        -------
+        ori_mean
+            Mean orientation.
+
+        mean_in_euler_fundamental_region
+            Calculate mean orientation in euler fundamental region.
+
+        Notes
+        -----
+        The method used here corresponds to Equation (13) in
+        https://arc.aiaa.org/doi/pdf/10.2514/1.28949.
+
+        Examples
+        --------
+        >>> from orix.quaternion import Orientation, symmetry
+        >>> oris = Orientation.from_axes_angles([1, 0, 0], np.deg2rad([0, 45]), symmetry.Oh)
+        >>> oris.mean(mean_in_euler_fundamental_region=True)
+        Orientation (1,) m-3m
+        [[0.2469 0.     0.3708 0.8953]]
+        """
+        if mean_in_euler_fundamental_region:
+            quat = Quaternion.from_euler(self.in_euler_fundamental_region())
+        else:
+            quat = Quaternion(self)
+
+        mean = quat.mean()
+
+        return Orientation(mean, symmetry=self.symmetry)
+
     def plot_unit_cell(
         self,
         c: str = "tab:blue",

orix/tests/quaternion/test_orientation.py

@@ -698,3 +698,38 @@ def test_in_fundamental_region(self):
             ori.symmetry = pg
             region = np.radians(pg.euler_fundamental_region)
             assert np.all(np.max(ori.in_euler_fundamental_region(), axis=0) <= region)
+
+    def test_mean(self):
+        oris = Orientation(
+            [
+                [0.215, 0.9696, -0.1001, -0.0602],
+                [0.2132, 0.97, -0.0977, -0.0643],
+                [0.2154, 0.9693, -0.098, -0.067],
+                [0.2157, 0.9692, -0.0989, -0.0659],
+                [0.2141, 0.9693, -0.1012, -0.0668],
+                [0.2132, 0.9696, -0.1001, -0.0659],
+                [0.2083, 0.9715, -0.0952, -0.0605],
+                [0.1558, 0.7913, -0.569, -0.1608],
+                [0.1495, 0.79, -0.5704, -0.1681],
+                [0.1537, 0.7908, -0.5686, -0.1663],
+                [0.1552, 0.7918, -0.5677, -0.1634],
+                [0.1518, 0.792, -0.5679, -0.165],
+                [0.0484, 0.3993, -0.8886, -0.2203],
+                [0.0459, 0.4007, -0.888, -0.2209],
+            ],
+            symmetry=D6,
+        )
+        mean_not_fund_region = oris.mean()
+        mean_fund_region = oris.mean(mean_in_euler_fundamental_region=True)
+
+        assert np.allclose(
+            mean_not_fund_region.data,
+            Orientation([0.1835, 0.8938, -0.3888, -0.1277], symmetry=D6).data,
+            atol=0.0001,
+        )
+
+        assert np.allclose(
+            mean_fund_region.data,
+            Orientation([0.8887, -0.2184, 0.0502, -0.4], symmetry=D6).data,
+            atol=0.0001,
+        )