Add new example showing the use of get_sample_reduced_fundamental()

Signed-off-by: Håkon Wiik Ånes <[email protected]>

examples/rotations/rotations_mapping_fundamental_sector.py

@@ -0,0 +1,57 @@
+"""
+================================================
+Rotations mapping the fundamental sector on *S2*
+================================================
+
+This example shows how to sample rotations :math:`\mathbf{R}` that when
+rotating the vector :math:`\mathbf{v_z} = (0, 0, 1)`, the resulting
+vectors cover the fundamental sector of a given Laue class.
+
+We show this by comparing the vectors we get by: 
+
+1. sampling rotations for *4/mmm* and then rotating :math:`\mathbf{v_z}`
+2. sampling all of *S2* but only keeping those within the corresponding
+   fundamental sector.
+
+Apart from the first rotation, all rotations have a Euler angle
+:math:`\phi = 0^{\circ}`.
+These "reduced" rotations are useful in template matching of spot
+patterns from the transmission electron microscope.
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+from orix import plot, sampling
+from orix.quaternion import symmetry
+from orix.vector import Vector3d
+
+# Sample rotations with an average misorientation
+res = 2
+pg = symmetry.D4h  # 4/mmm
+
+R = sampling.get_sample_reduced_fundamental(res, point_group=pg)
+print(np.allclose(R.to_euler()[1:, 0], 0))
+
+########################################################################
+# Get vectors within the fundamental sector following the two routes
+v1 = R * Vector3d.zvector()
+
+v2 = sampling.sample_S2(res)
+v2 = v2[v2 <= pg.fundamental_sector]
+
+# Only equivalent for the same S2 sampling method
+print(np.allclose(v1.data, v2.data))
+print(v1)
+print(v2)
+
+########################################################################
+# Plot the vectors in the fundamental sector of 4/mmm
+fig, (ax0, ax1) = plt.subplots(
+    ncols=2, subplot_kw={"projection": "ipf", "symmetry": pg}, layout="tight"
+)
+ax0.scatter(v1, s=5)
+ax1.scatter(v2, c="C1", s=5)
+ax0.set_title("Rotated Z vectors", loc="left")
+ax1.set_title("Directly sampled", loc="left")
+_ = fig.suptitle("Vectors in the fundamental sector of 4/mmm", y=0.8)