Merge branch 'adopt-reduce-and-other-updates-from-pyxem#442' of https://github.com/argerlt/orix into adopt-reduce-and-other-updates-from-pyxem#442

Author: argerlt

examples/plotting/plot_non_euclidean_paths.py

@@ -0,0 +1,115 @@
+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()