stereographic_plot.py

# -*- coding: utf-8 -*-
# Copyright 2018-2024 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/>.

"""Stereographic plot inheriting from :class:`~matplotlib.axes.Axes` for
plotting :class:`~orix.vector.Vector3d`.
"""

from copy import deepcopy
from typing import Any, List, Optional, Tuple, Union

from matplotlib import rcParams
import matplotlib.axes as maxes
import matplotlib.collections as mcollections
import matplotlib.patches as mpatches
import matplotlib.path as mpath
import matplotlib.projections as mprojections
import matplotlib.pyplot as plt
import numpy as np

# fmt: off
# isort: off
from orix.measure import pole_density_function
from orix.plot._symmetry_marker import (
    TwoFoldMarker,
    ThreeFoldMarker,
    FourFoldMarker,
    SixFoldMarker,
)
# isort: on
# fmt: on
from orix.projections import InverseStereographicProjection, StereographicProjection
from orix.vector import FundamentalSector, Vector3d
from orix.vector.fundamental_sector import _closed_edges_in_hemisphere

# This order determines which parts are plotted over other parts
ZORDER = dict(
    text=6,
    scatter=5,
    symmetry_marker=4,
    draw_circle=3,
    border=2,
    grid=1,
    mesh=0,
)


class StereographicPlot(maxes.Axes):
    """Stereographic plot for plotting :class:`~orix.vector.Vector3d`.

    Parameters
    ----------
    *args
        Arguments passed to :class:`matplotlib.axes.Axes`.
    hemisphere
        Which hemisphere to plot vectors in, either ``"upper"``
        (default) or ``"lower"``.
    azimuth_resolution
        Resolution of azimuth grid lines in degrees. Default is 10
        degrees.
    polar_resolution
        Resolution of polar grid lines in degrees. Default is 10
        degrees.
    **kwargs
        Keyword arguments passed to :class:`matplotlib.axes.Axes`.
    """

    name = "stereographic"
    _pad_xy = 0.05

    def __init__(
        self,
        *args,
        hemisphere: str = "upper",
        azimuth_resolution: Union[int, float] = 10,
        polar_resolution: Union[int, float] = 10,
        **kwargs,
    ):
        """Create an axis for plotting :class:`~orix.vector.Vector3d`."""
        self.hemisphere = hemisphere
        self._azimuth_resolution = azimuth_resolution
        self._polar_resolution = polar_resolution

        # Custom attribute to keep track of whether grid is on or off
        self._stereographic_grid = None

        super().__init__(*args, **kwargs)

        # Set ratio of y-unit to x-unit by adjusting the physical
        # dimension of the Axes (box), and centering the anchor (C)
        self.set_aspect("equal", adjustable="box", anchor="C")
        self.clear()

    def clear(self):
        super().clear()

        self.xaxis.set_ticks_position("none")
        self.yaxis.set_ticks_position("none")
        self.xaxis.set_tick_params(label1On=False)
        self.yaxis.set_tick_params(label1On=False)

        self.set_xlim(-1 - self._pad_xy, 1 + self._pad_xy)
        self.set_ylim(-1 - self._pad_xy, 1 + self._pad_xy)

        spines = self.spines
        for spine in spines.values():
            spine.set_visible(False)

        self.add_patch(
            mpatches.Circle(
                xy=(0, 0),
                radius=1,
                facecolor="none",
                edgecolor="k",
                label="sa_circle",
                zorder=ZORDER["border"],
            )
        )

        # Don't show rectangular grid
        self.grid(False)
        self.stereographic_grid(rcParams["axes.grid"])

    def format_coord(self, x, y):
        if np.sqrt(np.sum(np.square([x, y]))) > 1:
            return ""
        else:
            azimuth, polar = self._inverse_projection.xy2spherical(x, y)
            azimuth = azimuth[0]
            polar = polar[0]
            azimuth_deg = np.rad2deg(azimuth)
            polar_deg = np.rad2deg(polar)
            return (
                "\N{GREEK SMALL LETTER PHI}={:.2f}\N{GREEK SMALL LETTER PI} "
                "({:.2f}\N{DEGREE SIGN}), "
                "\N{GREEK SMALL LETTER theta}={:.2f}\N{GREEK SMALL LETTER PI} "
                "({:.2f}\N{DEGREE SIGN})"
            ).format(azimuth / np.pi, azimuth_deg, polar / np.pi, polar_deg)

    def plot(
        self,
        *args: Union[Vector3d, Tuple[float, float], Tuple[np.ndarray, np.ndarray]],
        **kwargs,
    ):
        """Draw straight lines between vectors.

        This method overwrites :meth:`matplotlib.axes.Axes.plot`, see
        that method's docstring for parameters.

        Parameters
        ----------
        *args
            Vector(s), or azimuth and polar angles, the latter two
            passed as separate arguments (not keyword arguments).
        **kwargs
            Keyword arguments passed to
            :meth:`matplotlib.axes.Axes.plot`.

        See Also
        --------
        matplotlib.axes.Axes.plot
        """
        new_kwargs = dict(clip_on=True, linewidth=2, color="k", linestyle="-")
        x, y, _, updated_kwargs = self._prepare_to_call_inherited_method(
            args, kwargs, new_kwargs, sort=True
        )
        if x.size == 0:
            return

        super().plot(x, y, **updated_kwargs)

    def scatter(
        self,
        *args: Union[Vector3d, Tuple[float, float], Tuple[np.ndarray, np.ndarray]],
        **kwargs,
    ):
        """A scatter plot of vectors.

        This method overwrites :meth:`matplotlib.axes.Axes.scatter`, see
        that method's docstring for parameters.

        Parameters
        ----------
        *args
            Vector(s), or azimuth and polar angles, the latter two
            passed as separate arguments (not keyword arguments).
        **kwargs
            Keyword arguments passed to
            :meth:`matplotlib.axes.Axes.scatter`.

        See Also
        --------
        matplotlib.axes.Axes.scatter
        """
        new_kwargs = dict(zorder=ZORDER["scatter"], clip_on=False)
        out = self._prepare_to_call_inherited_method(args, kwargs, new_kwargs)
        x, y, visible, updated_kwargs = out
        if x.size == 0:
            return

        # Color(s)
        if "color" in updated_kwargs.keys():
            key_color = "color"
        else:
            key_color = "c"
        c = updated_kwargs.pop(key_color, "C0")
        c = _get_array_of_values(value=c, visible=visible)

        # Size(s)
        if "sizes" in updated_kwargs.keys():
            key_size = "sizes"
        else:
            key_size = "s"
        s = updated_kwargs.pop(key_size, None)
        if s is not None:
            s = _get_array_of_values(value=s, visible=visible)

        super().scatter(x, y, c=c, s=s, **updated_kwargs)

    def text(
        self,
        *args: Union[Vector3d, Tuple[float, float], Tuple[np.ndarray, np.ndarray]],
        offset: Optional[Tuple[float, float]] = None,
        **kwargs,
    ):
        """Add text to the axes.

        This method overwrites :meth:`matplotlib.axes.Axes.text`, see
        that method's docstring for parameters.

        Parameters
        ----------
        *args
            Vector(s), or azimuth and polar angles, the latter two
            passed as separate arguments (not keyword arguments).
        offset
            Tuple of offsets in stereographic coordinates (X, Y). No
            offset is applied if not given.
        **kwargs
            Keyword arguments passed to
            :meth:`matplotlib.axes.Axes.text`.

        See Also
        --------
        matplotlib.axes.Axes.text
        """
        new_kwargs = dict(va="bottom", ha="center", zorder=ZORDER["text"])
        out = self._prepare_to_call_inherited_method(
            args, kwargs, new_kwargs, offset=offset
        )
        x, y, _, updated_kwargs = out
        if x.size == 0:
            return
        super().text(x, y, **updated_kwargs)

    # ----------- Custom attributes and methods below here ----------- #

    @property
    def hemisphere(self) -> str:
        """Return or set the hemisphere to plot, either ``"upper"`` or
        ``"lower"``.

        :attr:`pole` is derived from this attribute.

        Parameters
        ----------
        value : str
            Either ``"upper"`` or ``"lower"``.
        """
        return self._hemisphere

    @hemisphere.setter
    def hemisphere(self, value: str):
        """Set hemisphere to plot."""
        value = value.lower()
        if value in ["upper", "lower"]:
            self._hemisphere = value
        else:
            raise ValueError(f"Hemisphere must be 'upper' or 'lower', not {value}.")

    @property
    def pole(self) -> int:
        """Return the projection pole, either -1 or 1, where -1 (1)
        means the projection point of the stereographic transform is the
        lower (upper) pole [00-1] ([001]), i.e. only vectors with z > 0
        (z < 0) are plotted.

        Derived from :attr:`hemisphere`.
        """
        return {"upper": -1, "lower": 1}[self.hemisphere]

    @property
    def _projection(self):
        return StereographicProjection(self.pole)

    @property
    def _inverse_projection(self):
        return InverseStereographicProjection(self.pole)

    def pole_density_function(
        self,
        *args: Union[np.ndarray, Vector3d],
        resolution: float = 1,
        sigma: float = 5,
        log: bool = False,
        colorbar: bool = True,
        weights: Optional[np.ndarray] = None,
        **kwargs: Any,
    ):
        """Compute the Pole Density Function (PDF) of vectors in the
        stereographic projection. See :cite:`rohrer2004distribution`.

        Parameters
        ----------
        *args
            Vector(s), or azimuth and polar angles of the vectors, the
            latter passed as two separate arguments.
        resolution
            The angular resolution of the sampling grid in degrees.
            Default value is 1.
        sigma
            The angular resolution of the applied broadening in degrees.
            Default value is 5.
        log
            If ``True`` the log(PDF) is calculated. Default is ``True``.
        colorbar
            If ``True`` a colorbar is shown alongside the PDF plot.
            Default is ``True``.
        weights
            The weights for the individual vectors. If not given, the
            weight of each vector is 1.
        **kwargs
            Keyword arguments passed to
            :meth:`matplotlib.axes.Axes.pcolormesh`.

        See Also
        --------
        orix.measure.pole_density_function
        orix.plot.InversePoleFigurePlot.pole_density_function
        orix.vector.Vector3d.pole_density_function
        """
        hist, (x, y) = pole_density_function(
            *args,
            resolution=resolution,
            sigma=sigma,
            log=log,
            hemisphere=self.hemisphere,
            weights=weights,
        )

        new_kwargs = dict(zorder=ZORDER["mesh"], clip_on=True)
        updated_kwargs = {**kwargs, **new_kwargs}

        # plot mesh
        updated_kwargs.setdefault("cmap", "magma")
        # mpl.QuadMesh handles masked values by default
        pc = self.pcolormesh(x, y, hist, **updated_kwargs)

        if colorbar:
            label = "MRD"
            if log:
                label = f"log({label})"
            plt.colorbar(pc, label=label, ax=self)

    def draw_circle(
        self,
        *args: Union[Vector3d, Tuple[float, float], Tuple[np.ndarray, np.ndarray]],
        opening_angle: Union[float, np.ndarray] = np.pi / 2,
        steps: int = 100,
        reproject: bool = False,
        reproject_plot_kwargs: Optional[dict] = None,
        **kwargs,
    ):
        r"""Draw great or small circles with a given `opening_angle` to
        one or multiple vectors.

        A vector must be present in the current hemisphere for its
        circle to be drawn.

        Parameters
        ----------
        args
            Vector(s), or azimuth and polar angles defining vectors, the
            latter two passed as separate arguments (not keyword
            arguments). Circles are drawn perpendicular to these with a
            given ``opening_angle``.
        opening_angle
            Opening angle(s) around the vector(s). Default is
            :math:`\pi/2`, giving a great circle. If an array is passed,
            its size must be equal to the number of circles to draw.
        steps
            Number of vectors to describe each circle, default is 100.
        reproject
            Whether to reproject parts of the circle(s) visible on the
            other hemisphere. Re-projection is achieved by reflection of
            the circle(s) parts located on the other hemisphere in the
            projection plane. Ignored if ``hemisphere`` is ``"both"``.
            Default is ``False``.
        reproject_plot_kwargs
            Keyword arguments passed to
            :meth:`matplotlib.axes.Axes.plot` to alter the appearance of
            parts of the circle(s) visible on the other hemisphere if
            ``reproject=True``. These lines are dashed by default.
            Values used for circle(s) on the current hemisphere are used
            unless values are passed here.
        **kwargs
            Keyword arguments passed to
            :meth:`matplotlib.axes.Axes.plot` to alter the circles'
            appearance.

        See Also
        --------
        orix.vector.Vector3d.get_circle
        """
        out = self._prepare_to_call_inherited_method(args, kwargs)
        x, y, visible, updated_kwargs = out
        if x.size == 0:
            return

        if isinstance(opening_angle, np.ndarray) and opening_angle.size == visible.size:
            opening_angle = opening_angle[visible]

        # Get set of `steps` vectors delineating a circle per vector
        v = self._inverse_projection.xy2vector(x, y)
        circles = v.get_circle(opening_angle=opening_angle, steps=steps).unit

        # Enable using one color per circle
        color = kwargs.pop("color", "C0")
        color2 = _get_array_of_values(value=color, visible=visible)

        # Set above which plotting elements circles will appear (zorder)
        new_kwargs = dict(zorder=ZORDER["draw_circle"], clip_on=True)
        for k, v in new_kwargs.items():
            kwargs.setdefault(k, v)

        for i, c in enumerate(circles):
            self.plot(c.azimuth, c.polar, color=color2[i], **kwargs)

        if reproject:
            if reproject_plot_kwargs is None:
                reproject_plot_kwargs = {}
            reproject_plot_kwargs.setdefault("linestyle", "--")
            # Simulate reflection about the projection plane by
            # temporarily setting the hemisphere to the other one
            other_hemisphere = {"upper": "lower", "lower": "upper"}
            self._hemisphere = other_hemisphere[self._hemisphere]
            for i, c in enumerate(circles):
                self.plot(c.azimuth, c.polar, color=color2[i], **reproject_plot_kwargs)
            self._hemisphere = other_hemisphere[self._hemisphere]

    def restrict_to_sector(
        self,
        sector: FundamentalSector,
        pad: float = 1.3,
        show_edges: bool = True,
        **kwargs,
    ):
        """Restrict the stereographic axis to a
        :class:`~orix.vector.FundamentalSector`, typically obtained from
        :attr:`~orix.quaternion.Symmetry.fundamental_sector`.

        Parameters
        ----------
        sector
            Fundamental sector with edges delineating a fundamental
            sector.
        pad
            Padding outside the sector in the stereographic projection
            in degrees. Default is 1.3 degrees.
        show_edges
            Whether to draw the sector edges. Default is ``True``.
        **kwargs
            Keyword arguments passed to
            :class:`matplotlib.patches.PathPatch` if
            ``show_edges=True``.
        """
        original_pole = deepcopy(sector._pole)
        sector._pole = self.pole
        edges = sector.edges
        if edges.size == 0:
            return
        edges = _closed_edges_in_hemisphere(edges, sector, pole=self.pole)
        sector._pole = original_pole
        if edges.size == 0:
            return
        x, y, _ = self._pretransform_input((edges,))

        pad_angle = np.deg2rad(pad)
        verts = sector.vertices
        center = sector.center
        verts_normal = center.cross(verts)
        verts_rot = verts.rotate(verts_normal, pad_angle)
        x_pad, y_pad = self._projection.vector2xy(verts_rot)
        pad_min = 0.01
        if x_pad.size == 0:
            x_min, x_max = np.min(x) - pad_min, np.max(x) + pad_min
            y_min, y_max = np.min(y) - pad_min, np.max(y) + pad_min
        else:
            x_min = min([np.min(x) - pad_min, np.min(x_pad)])
            x_max = max([np.max(x) + pad_min, np.max(x_pad)])
            y_min = min([np.min(y) - pad_min, np.min(y_pad)])
            y_max = max([np.max(y) + pad_min, np.max(y_pad)])
        self.set(xlim=(x_min, x_max), ylim=(y_min, y_max))

        self.patches[0].set_visible(False)

        if show_edges:
            for k, v in [("facecolor", "none"), ("edgecolor", "k"), ("linewidth", 1)]:
                kwargs.setdefault(k, v)
            patch = mpatches.PathPatch(
                mpath.Path(np.column_stack([x, y]), closed=True),
                label="sa_sector",
                **kwargs,
            )
            self.add_patch(patch)
            self.set_clip_path(patch)
            labels = ["sa_azimuth_grid", "sa_polar_grid"]
            for c in self.collections:
                if c.get_label() in labels:
                    c.set_clip_path(patch)

    def show_hemisphere_label(self, **kwargs):
        """Add a hemisphere label (``"upper"``/``"lower"``) to the upper
        left of the plot.

        Parameters
        ----------
        **kwargs
            Keyword arguments passed to
            :func:`matplotlib.axes.Axes.text`.

        See Also
        --------
        hemisphere
        """
        new_kwargs = dict(ha="right", va="bottom")
        new_kwargs.update(kwargs)
        super().text(-0.71, 0.71, s=self.hemisphere, **new_kwargs)

    def set_labels(
        self,
        xlabel: Union[str, bool, None] = "x",
        ylabel: Union[str, bool, None] = "y",
        zlabel: Union[str, bool, None] = "z",
        **kwargs,
    ):
        """Set the reference frame's axes labels.

        Parameters
        ----------
        xlabel
            X axis label, default is ``"x"``. If ``False`` or ``None``,
            this label is not shown.
        ylabel
            Y axis label, default is ``"y"``. If ``False`` or ``None``,
            this label is not shown.
        zlabel
            Z axis label, default is ``"z"``. If ``False`` or ``None``,
            this label is not shown.
        """
        pos = [(1, 0), (0, 1), (0, 0)]
        for (x, y), label in zip(pos, [xlabel, ylabel, zlabel]):
            if label not in [None, False]:
                self._set_label(x=x, y=y, label=label, **kwargs)

    def stereographic_grid(
        self,
        show_grid: Optional[bool] = None,
        azimuth_resolution: Optional[float] = None,
        polar_resolution: Optional[float] = None,
    ):
        """Turn a stereographic grid on or off, and set the azimuth and
        polar grid resolution in degrees.

        Parameters
        ----------
        show_grid
            Whether to show grid lines. If any keyword arguments are
            passed, this is set to ``True``. If not given and there are
            no keyword arguments, the grid lines are toggled.
        azimuth_resolution
            Azimuth grid resolution in degrees. Default is 10 degrees.
            This can also be set upon initialization of the axes by
            passing ``azimuth_resolution`` to ``subplot_kw``.
        polar_resolution
            Polar grid resolution in degrees. Default is 10 degrees.
            This can also be set upon initialization of the axes by
            passing ``polar_resolution`` to ``subplot_kw``.

        See Also
        --------
        matplotlib.axes.Axes.grid
        """
        if (
            show_grid is None
            and self._stereographic_grid in [None, False]
            or show_grid is None
            and (azimuth_resolution is not None or polar_resolution is not None)
            or show_grid is True
        ) and hasattr(self, "patch"):
            self._azimuth_grid(azimuth_resolution)
            self._polar_grid(polar_resolution)
            self._stereographic_grid = True
        elif show_grid in [None, False] and self._stereographic_grid is True:
            # Remove grid
            has_azimuth, index_azimuth = self._has_collection(
                "sa_azimuth_grid", self.collections
            )
            has_polar, index_polar = self._has_collection(
                "sa_polar_grid", self.collections
            )
            if has_azimuth:
                if index_polar > index_azimuth:
                    index_polar -= 1
                self.collections[index_azimuth].remove()
            if has_polar:
                self.collections[index_polar].remove()
            self._stereographic_grid = False

    def symmetry_marker(self, v: Vector3d, fold: int, **kwargs):
        """Plot 2-, 3- 4- or 6-fold symmetry marker(s).

        Parameters
        ----------
        v
            Position of the marker(s) to plot.
        fold
            Which symmetry element to plot, can be either 2, 3, 4 or 6.
        **kwargs
            Keyword arguments passed to :meth:`scatter`.
        """
        if fold not in [2, 3, 4, 6]:
            raise ValueError("Can only plot 2-, 3-, 4- or 6-fold elements.")

        marker_classes = {
            "2": TwoFoldMarker,
            "3": ThreeFoldMarker,
            "4": FourFoldMarker,
            "6": SixFoldMarker,
        }
        marker = marker_classes[str(fold)](v, size=kwargs.pop("s", 1))

        new_kwargs = dict(zorder=ZORDER["symmetry_marker"], clip_on=False)
        for k, v in new_kwargs.items():
            kwargs.setdefault(k, v)

        for vec, marker, marker_size in marker:
            self.scatter(vec, marker=marker, s=marker_size, **kwargs)

        # TODO: Find a way to control padding, so that markers aren't
        #  clipped

    def _azimuth_grid(self, resolution: Optional[float] = None):
        """Set the azimuth grid resolution in degrees.

        Parameters
        ----------
        resolution
            Azimuth grid resolution in degrees. Default is 10 degrees.
            This can also be set upon initialization of the axes by
            passing ``azimuth_resolution`` to ``subplot_kw``.

        See Also
        --------
        polar_grid
        matplotlib.axes.Axes.grid
        """
        if resolution is not None:
            self._azimuth_resolution = resolution

        azimuth_start = np.arange(0, np.pi, np.radians(self._azimuth_resolution))
        polar = np.full(azimuth_start.size, np.pi / 2)
        if self.hemisphere == "lower":
            polar += 1e-9
        v_start = Vector3d.from_polar(azimuth_start, polar)
        x_start, y_start = self._projection.vector2xy(v_start)
        v_end = Vector3d.from_polar(azimuth_start + np.pi, polar)
        x_end, y_end = self._projection.vector2xy(v_end)

        kwargs = dict(
            linewidths=rcParams["grid.linewidth"],
            linestyle=rcParams["grid.linestyle"],
            alpha=rcParams["grid.alpha"],
            color=rcParams["grid.color"],
            antialiased=True,
            zorder=ZORDER["grid"],
        )

        label = "sa_azimuth_grid"
        lines = np.stack(((x_start, x_end), (y_start, y_end))).T
        lines_collection = mcollections.LineCollection(lines, label=label, **kwargs)
        has_collection, index = self._has_collection(label, self.collections)
        if has_collection:
            self.collections[index].remove()
        has_sector, sector_index = self._has_collection("sa_sector", self.patches)
        if has_sector:
            lines_collection.set_clip_path(self.patches[sector_index])
        self.add_collection(lines_collection)

    @staticmethod
    def _has_collection(label, collections):
        labels = [c.get_label() for c in collections]
        for i in range(len(labels)):
            if label == labels[i]:
                return True, i
        return False, -1

    def _polar_grid(self, resolution: Optional[float] = None):
        """Set the polar grid resolution in degrees.

        Parameters
        ----------
        resolution
            Polar grid resolution in degrees. Default is 15 degrees.
            This can also be set upon initialization of the axes by
            passing ``polar_resolution`` to ``subplot_kw``.

        See Also
        --------
        azimuth_grid
        matplotlib.axes.Axes.grid
        """
        if resolution is not None:
            self._polar_resolution = resolution

        res = np.radians(self._polar_resolution)

        polar = np.arange(res, np.pi, res)
        v = Vector3d.from_polar(np.zeros(polar.size), polar)
        radii, _ = self._projection.vector2xy(v)

        ec = rcParams["grid.color"]
        kwargs = dict(
            xy=(0, 0),
            linewidth=rcParams["grid.linewidth"],
            linestyle=rcParams["grid.linestyle"],
            alpha=rcParams["grid.alpha"],
            ec=ec,
            fc="none",
            antialiased=True,
            zorder=ZORDER["grid"],
        )

        circles = []
        for r in radii:
            circles.append(mpatches.Circle(radius=r, **kwargs))
        label = "sa_polar_grid"
        circles_collection = mcollections.PatchCollection(
            circles,
            label=label,
            edgecolors=kwargs["ec"],
            facecolors=kwargs["fc"],
            alpha=kwargs["alpha"],
        )
        has_collection, index = self._has_collection(label, self.collections)
        if has_collection:
            self.collections[index].remove()
        has_sector, sector_index = self._has_collection("sa_sector", self.patches)
        if has_sector:
            circles_collection.set_clip_path(self.patches[sector_index])
        self.add_collection(circles_collection)

    def _prepare_to_call_inherited_method(
        self,
        args: Union[Vector3d, Tuple[float, float], Tuple[np.ndarray, np.ndarray]],
        kwargs: dict,
        new_kwargs: Optional[dict] = None,
        sort: bool = False,
        offset: Tuple[float, float] = None,
    ) -> Tuple[np.ndarray, np.ndarray, np.ndarray, dict]:
        """Prepare arguments and keyword arguments passed to methods in
        :class:`StereographicPlot` inherited from
        :class:`matplotlib.axes.Axes`.

        Parameters
        ----------
        args
            Any arguments passed to the :class:`StereographicPlot`
            method.
        kwargs
            Any arguments passed to the :class:`StereographicPlot`
            method.
        new_kwargs
            Any default keyword arguments to be passed to the inherited
            method.
        sort
            Whether to sort vectors before passing them to Matplotlib.
            Default is ``False``.
        offset
            Tuple of offsets in (X, Y). No offset is applied if not
            given.

        Returns
        -------
        x
        y
        visible
        updated_kwargs
        """
        updated_kwargs = kwargs
        if new_kwargs is not None:
            for k, v in new_kwargs.items():
                updated_kwargs.setdefault(k, v)
        x, y, visible = self._pretransform_input(args, sort=sort, offset=offset)
        return x, y, visible, updated_kwargs

    def _pretransform_input(
        self,
        values: Union[Vector3d, Tuple[float, float], Tuple[np.ndarray, np.ndarray]],
        sort: bool = False,
        offset: Optional[Tuple[float, float]] = None,
    ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
        """Return arrays of (X, Y) from input data.

        Parameters
        ----------
        values
            Spherical coordinates (azimuth, polar) or vectors. If
            spherical coordinates are given, they are assumed to
            describe unit vectors. Vectors will be made into unit
            vectors if they are not already.
        sort
            Whether to sort vectors before passing them to Matplotlib.
            Default is ``False``.
        offset
            Tuple of offsets in (X, Y). No offset is applied if not
            given.

        Returns
        -------
        X
            Stereographic X coordinates of unit vectors.
        Y
            Stereographic Y coordinates of unit vectors.
        visible
            Whether these values are visible on the axes.
        """
        pole = self.pole
        if len(values) == 2:
            azimuth, polar = values[0], values[1]
            if sort:
                order = _order_in_hemisphere(polar, pole)
                azimuth = azimuth[order]
                polar = polar[order]
            x, y = self._projection.spherical2xy(azimuth=azimuth, polar=polar)
            v = self._inverse_projection.xy2vector(x, y)
        else:
            try:
                v = values[0].flatten().unit
                if sort:
                    order = _order_in_hemisphere(v.polar, pole)
                    v = v[order]
                x, y = self._projection.vector2xy(v)
            except (ValueError, AttributeError):
                raise ValueError(
                    "Accepts only one (Vector3d) or two (azimuth, polar) input "
                    "arguments."
                )

        visible = v <= self._projection.region

        if offset is not None:
            x += offset[0]
            y += offset[1]

        return x, y, visible

    def _set_label(self, x: float, y: float, label: str, **kwargs):
        bbox_dict = dict(boxstyle="round, pad=0.1", fc="w", ec="w")
        new_kwargs = dict(ha="center", va="center", bbox=bbox_dict)
        new_kwargs.update(kwargs)
        super().text(x=x, y=y, s=label, **new_kwargs)


mprojections.register_projection(StereographicPlot)


def _get_array_of_values(
    value: Union[str, float, List[str], List[float]], visible: np.ndarray
) -> np.ndarray:
    """Return a usable array of ``value`` with the correct size
    even though ``value`` doesn't have as many elements as
    ``visible.size``, to be iterated over along with ``True`` elements
    in ``visible``.

    Parameters
    ----------
    value
        Typically a keyword argument value to be passed to some
        Matplotlib routine.
    visible
        Boolean array with as many elements as input vectors, only some
        of which are visible in the hemisphere (``True``).

    Returns
    -------
    array
        An array populated with ``value`` of a size equal to the number
        of ``True`` elements in ``visible``.
    """
    n = visible.size
    if not isinstance(value, str) and hasattr(value, "__iter__") and len(value) != n:
        value = value[0]
    if isinstance(value, str) or not hasattr(value, "__iter__"):
        value = [value] * n
    return np.asarray(value)[visible]


def _is_visible(polar: np.ndarray, pole: int) -> np.ndarray:
    """Return a boolean array describing whether the vector which the
    polar angles belong to are visible in the current hemisphere.

    Parameters
    ----------
    polar
    pole

    Returns
    -------
    polar_visible
        Boolean array with ``True`` for polar angles corresponding to
        vectors visible in this hemisphere.
    """
    if pole == -1:
        return polar <= np.pi / 2
    else:  # pole == 1
        return polar >= np.pi / 2


def _order_in_hemisphere(polar: np.ndarray, pole: int) -> Union[np.ndarray, None]:
    """Return order of vectors based on polar angles, so that the ones
    corresponding to vectors visible in this hemisphere are shifted to
    the start of the arrays.

    Used in :meth:`StereographicPlot._pretransform_input` when
    ``sort=True``.

    Parameters
    ----------
    polar
    pole

    Returns
    -------
    out
        If no vectors are visible, ``None`` is returned.
    """
    visible = _is_visible(polar, pole)
    if visible.size == 0 or not np.any(visible):
        return

    indices = np.asarray(visible != visible[0]).nonzero()[0]
    order = np.arange(visible.size)
    if indices.size != 0:
        order = np.roll(order, shift=-(indices[-1] + 1))

    return order