Merge pull request #4 from hakonanes/Add-Rotation_from_path_ends

Suggestions for changes to path ends PR

Author: argerlt

CHANGELOG.rst

@@ -34,8 +34,8 @@ Added
   An example of a custom projection is the :class:`~orix.plot.StereographicPlot`.
   This function replaces the previous behavior of relying on a side-effect of importing
   the :mod:`orix.plot` module, which also registered the projections.
-- :func:`~orix.quaternion.Rotation.from_path_ends` returns evenly spaced points
-  mapping the shortest path betwen two or more rotations.
+- Method ``from_path_ends()`` to return quaternions, rotations, orientations, or
+  misorientations along the shortest path between two or more points.
 
 Changed
 -------

examples/plotting/visualizing_crystallographic_paths.py

@@ -0,0 +1,154 @@
+#
+# Copyright 2018-2025 the orix developers
+#
+# This file is part of orix.
+#
+# orix is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# orix is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with orix. If not, see <http://www.gnu.org/licenses/>.
+#
+
+"""
+===============================================
+Visualizing paths between rotations and vectors
+===============================================
+
+This example shows how define and plot paths through either rotation or vector space.
+This is akin to describing crystallographic fiber textures in metallurgy, or the
+shortest arcs connecting points on the surface of a unit sphere.
+
+In both cases, "shortest" is defined as the route that minimizes the movement required
+to transform from point to point, which is typically not a stright line when plotted
+into a euclidean projection (axis-angle, stereographic, etc.).
+"""
+
+import matplotlib as mpl
+import matplotlib.pyplot as plt
+import numpy as np
+
+from orix.plot import register_projections
+from orix.plot.direction_color_keys import DirectionColorKeyTSL
+from orix.quaternion import Orientation, Rotation
+from orix.quaternion.symmetry import C1, Oh
+from orix.sampling import sample_S2
+from orix.vector import Vector3d
+
+register_projections()  # Register our custom Matplotlib projections
+np.random.seed(2319)  # Reproducible random data
+
+# Number of steps along each path
+n_steps = 30
+
+########################################################################################
+# Example 1: Continuous path
+# ==========================
+#
+# This plot traces the path of an object rotated 90 degrees around the x-axis, then 90
+# degrees around the y-axis.
+
+oris1 = Orientation.from_axes_angles(
+    [[1, 0, 0], [1, 0, 0], [0, 1, 0]], [0, 90, 90], degrees=True
+)
+oris1[2] = oris1[1] * oris1[2]
+path = Orientation.from_path_ends(oris1, steps=n_steps)
+
+# Create a list of RGBA color values for a gradient red line and blue line
+colors1 = np.vstack(
+    [
+        mpl.colormaps["Reds"](np.linspace(0.5, 1, n_steps)),
+        mpl.colormaps["Blues"](np.linspace(0.5, 1, n_steps)),
+    ]
+)
+
+# Here, we use the built-in plotting method from Orientation.scatter to auto-generate
+# the plot.
+# This is especially handy when plotting only a single set of orientations.
+path.scatter(marker=">", c=colors1)
+_ = plt.gca().set_title("Axis-angle space, two 90\N{DEGREE SIGN} rotations")
+
+########################################################################################
+# Example 2: Multiple paths
+# =========================
+#
+# This plot 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 same paths are then also plotted in the inverse pole figure (IPF) for the sample
+# direction (0, 0, 1), IPF-Z.
+
+# Random orientations with the cubic *m3m* crystal symmetry, located inside the
+# fundamental zone of the proper point group (*432*)
+oris2 = Orientation.random(10, symmetry=Oh).reduce()
+
+# Rotation around the z-axis
+ori_shift = Orientation.from_axes_angles([0, 0, 1], -30, degrees=True)
+
+# Plot path for the first orientation (to get a figure to add to)
+rot_end = ori_shift * oris2[0]
+points = Orientation.stack([oris2[0], rot_end])
+path = Orientation.from_path_ends(points, steps=n_steps)
+path.symmetry = Oh
+
+colors2 = mpl.colormaps["inferno"](np.linspace(0, 1, n_steps))
+fig = path.scatter("rodrigues", position=121, return_figure=True, c=colors2)
+path.scatter("ipf", position=122, figure=fig, c=colors2)
+
+# Plot the rest
+rod_ax, ipf_ax = fig.axes
+rod_ax.set_title("Orientation paths in Rodrigues space")
+ipf_ax.set_title("Vector paths in IPF-Z", pad=15)
+
+for ori_start in oris2[1:]:
+    rot_end = ori_shift * ori_start
+    points = Orientation.stack([ori_start, rot_end])
+    path = Orientation.from_path_ends(points, steps=n_steps)
+    path.symmetry = Oh
+    rod_ax.scatter(path, c=colors2)
+    ipf_ax.scatter(path, c=colors2)
+
+########################################################################################
+# Example 3: Multiple vector paths
+# ================================
+#
+# Rotate vectors around the (1, 1, 1) axis on a stereographic plot.
+
+vec_ax = plt.subplot(projection="stereographic")
+vec_ax.set_title(r"Stereographic")
+vec_ax.set_labels("X", "Y")
+
+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 < np.deg2rad(80)]
+
+# Define a 15 degree rotation around (1, 1, 1)
+rot111 = Rotation.from_axes_angles([1, 1, 1], [0, 15], degrees=True)
+
+for vec in vecs:
+    path_ends = rot111 * vec
+
+    # Handle case where path start end end are the same vector
+    if np.isclose(path_ends[0].dot(path_ends[1]), 1):
+        vec_ax.scatter(path_ends[0], c=ipf_colormap.direction2color(path_ends[0]))
+        continue
+
+    # Color each path using a gradient pased on the IPF coloring
+    colors3 = ipf_colormap.direction2color(vec)
+    path = Vector3d.from_path_ends(path_ends, steps=100)
+    colors3_segment = colors3 * np.linspace(0.25, 1, path.size)[:, np.newaxis]
+    vec_ax.scatter(path, c=colors3_segment)

examples/plotting/visualizing_rotation_vector_paths.py

@@ -277,40 +277,43 @@ def from_scipy_rotation(
     def from_path_ends(
         cls, points: Misorientation, closed: bool = False, steps: int = 100
     ) -> Misorientation:
-        """Return misorientations tracing the shortest path between
-        two or more consecutive points.
+        """Return misorientations tracing the shortest path between two
+        or more consecutive points.
 
         Parameters
         ----------
         points
             Two or more misorientations that define points along the
             path.
         closed
-            Option to add a final trip from the last point back to
-            the first, thus closing the loop. The default is False.
+            Add a final trip from the last point back to the first, thus
+            closing the loop. Default is False.
         steps
-            Number of misorientations to return between each point
-            along the path defined by `points`. The default is 100.
+            Number of misorientations to return between each point along
+            the path given by *points*. Default is 100.
 
         Returns
         -------
         path
-            regularly spaced misorientations following the shortest
-            path.
+            Regularly spaced misorientations along the path.
+
+        See Also
+        --------
+        :class:`~orix.quaternion.Quaternion.from_path_ends`,
+        :class:`~orix.quaternion.Orientation.from_path_ends`
 
         Notes
         -----
         This function traces the shortest path between points without
-        any regard to symmetry. Concept of "shortest path" is not
+        considering symmetry. The concept of "shortest path" is not
         well-defined for misorientations, which can define multiple
         symmetrically equivalent points with non-equivalent paths.
         """
-        # Confirm `points` are misorientations.
-        if type(points) is not cls:
+        points_type = type(points)
+        if points_type is not cls:
             raise TypeError(
-                f"Points must be a Misorientation, not of type {type(points)}"
+                f"Points must be misorientations, not of type {points_type}"
             )
-        # Create a path through Quaternion space, then reapply the symmetry.
         out = Rotation.from_path_ends(points=points, closed=closed, steps=steps)
         return cls(out.data, symmetry=points.symmetry)