From b8c55ea22efbf90d073af18cedb2ae882e383d2d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Ha=CC=8Akon=20Wiik=20A=CC=8Anes?= <hwaanes@xnovotech.com>
Date: Sun, 7 Apr 2024 15:27:36 +0200
Subject: [PATCH] Add new example showing the use of
 get_sample_reduced_fundamental()
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Signed-off-by: Håkon Wiik Ånes <hwaanes@xnovotech.com>
---
 .../rotations_mapping_fundamental_sector.py   | 57 +++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 examples/rotations/rotations_mapping_fundamental_sector.py

diff --git a/examples/rotations/rotations_mapping_fundamental_sector.py b/examples/rotations/rotations_mapping_fundamental_sector.py
new file mode 100644
index 00000000..66c9cf9f
--- /dev/null
+++ b/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)