code: import numpy as np
  from vispy.scene.visuals import Compound, Line, Mesh, Text
  from vispy.visuals.transforms import STTransform
  
  from ...layers.shapes._shapes_utils import triangulate_ellipse
  from ...utils.colormaps.standardize_color import transform_color
  from ...utils.theme import get_theme
  from ...utils.translations import trans
  
  
  def make_dashed_line(num_dashes, axis):
      """Make a dashed line.
  
      Parameters
      ----------
      num_dashes : int
          Number of dashes in the line.
      axis : int
          Axis which is dashed.
  
      Returns
      -------
      np.ndarray
          Dashed line, of shape (num_dashes, 3) with zeros in
          the non dashed axes and line segments in the dashed
          axis.
      """
      dashes = np.linspace(0, 1, num_dashes * 2)
      dashed_line_ends = np.concatenate(
          [[dashes[2 * i], dashes[2 * i + 1]] for i in range(num_dashes)], axis=0
      )
      dashed_line = np.zeros((2 * num_dashes, 3))
      dashed_line[:, axis] = np.array(dashed_line_ends)
      return dashed_line
  
  
  def make_arrow_head(num_segments, axis):
      """Make an arrowhead line.
  
      Parameters
      ----------
      num_segments : int
          Number of segments in the arrowhead.
      axis
          Arrowhead direction.
  
      Returns
      -------
      np.ndarray, np.ndarray
          Vertices and faces of the arrowhead.
      """
      corners = np.array([[-1, -1], [-1, 1], [1, 1], [1, -1]]) * 0.1
      vertices, faces = triangulate_ellipse(corners, num_segments)
      full_vertices = np.zeros((num_segments + 1, 3))
      inds = list(range(3))
      inds.pop(axis)
      full_vertices[:, inds] = vertices
      full_vertices[:, axis] = 0.9
      full_vertices[0, axis] = 1.02
      return full_vertices, faces
  
  
  def color_lines(colors):
      if len(colors) == 2:
          return np.concatenate(
              [[colors[0]] * 2, [colors[1]] * 2],
              axis=0,
          )
      elif len(colors) == 3:
          return np.concatenate(
              [[colors[0]] * 2, [colors[1]] * 2, [colors[2]] * 2],
              axis=0,
          )
      else:
          return ValueError(
              trans._(
                  'Either 2 or 3 colors must be provided, got {number}.',
                  deferred=True,
                  number=len(colors),
              )
          )
  
  
  def color_dashed_lines(colors):
      if len(colors) == 2:
          return np.concatenate(
              [[colors[0]] * 2, [colors[1]] * 4 * 2],
              axis=0,
          )
      elif len(colors) == 3:
          return np.concatenate(
              [[colors[0]] * 2, [colors[1]] * 4 * 2, [colors[2]] * 8 * 2],
              axis=0,
          )
      else:
          return ValueError(
              trans._(
                  'Either 2 or 3 colors must be provided, got {number}.',
                  deferred=True,
                  number=len(colors),
              )
          )
  
  
  def color_arrowheads(colors, num_segments):
      if len(colors) == 2:
          return np.concatenate(
              [[colors[0]] * num_segments, [colors[1]] * num_segments],
              axis=0,
          )
      elif len(colors) == 3:
          return np.concatenate(
              [
                  [colors[0]] * num_segments,
                  [colors[1]] * num_segments,
                  [colors[2]] * num_segments,
              ],
              axis=0,
          )
      else:
          return ValueError(
              trans._(
                  'Either 2 or 3 colors must be provided, got {number}.',
                  deferred=True,
                  number=len(colors),
              )
          )
  
  
  class VispyAxesOverlay:
      """Axes indicating world coordinate origin and orientation."""
  
      _NUM_SEGMENTS_ARROWHEAD = 100
  
      def __init__(self, viewer, parent=None, order=0):
          self._viewer = viewer
          self._scale = 1
  
          # Target axes length in canvas pixels
          self._target_length = 80
          # CMYRGB for 6 axes data in x, y, z, ... ordering
          self._default_color = [
              [0, 1, 1, 1],
              [1, 0, 1, 1],
              [1, 1, 0, 1],
              [1, 0, 0, 1],
              [0, 1, 0, 1],
              [0, 0, 1, 1],
          ]
          # Text offset from line end position
          self._text_offsets = 0.1 * np.array([1, 1, 1])
  
          # note order is x, y, z for VisPy
          self._line_data2D = np.array(
              [[0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 1, 0]]
          )
          self._line_data3D = np.array(
              [[0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 1, 0], [0, 0, 0], [0, 0, 1]]
          )
  
          # note order is x, y, z for VisPy
          self._dashed_line_data2D = np.concatenate(
              [[[1, 0, 0], [0, 0, 0]], make_dashed_line(4, axis=1)],
              axis=0,
          )
          self._dashed_line_data3D = np.concatenate(
              [
                  [[1, 0, 0], [0, 0, 0]],
                  make_dashed_line(4, axis=1),
                  make_dashed_line(8, axis=2),
              ],
              axis=0,
          )
  
          # note order is x, y, z for VisPy
          vertices = np.empty((0, 3))
          faces = np.empty((0, 3))
          for axis in range(2):
              v, f = make_arrow_head(self._NUM_SEGMENTS_ARROWHEAD, axis)
              faces = np.concatenate([faces, f + len(vertices)], axis=0)
              vertices = np.concatenate([vertices, v], axis=0)
          self._default_arrow_vertices2D = vertices
          self._default_arrow_faces2D = faces.astype(int)
  
          vertices = np.empty((0, 3))
          faces = np.empty((0, 3))
          for axis in range(3):
              v, f = make_arrow_head(self._NUM_SEGMENTS_ARROWHEAD, axis)
              faces = np.concatenate([faces, f + len(vertices)], axis=0)
              vertices = np.concatenate([vertices, v], axis=0)
          self._default_arrow_vertices3D = vertices
          self._default_arrow_faces3D = faces.astype(int)
  
          self.node = Compound(
              [Line(connect='segments', method='gl', width=3), Mesh(), Text()],
              parent=parent,
          )
          self.node.transform = STTransform()
          self.node.order = order
  
          # Add a text node to display axes labels
          self.text_node = self.node._subvisuals[2]
          self.text_node.font_size = 10
          self.text_node.anchors = ('center', 'center')
          self.text_node.text = f'{1}'
  
          self.node.canvas._backend.destroyed.connect(self._set_canvas_none)
          # End Note
  
          self._viewer.events.theme.connect(self._on_data_change)
          self._viewer.axes.events.visible.connect(self._on_visible_change)
          self._viewer.axes.events.colored.connect(self._on_data_change)
          self._viewer.axes.events.dashed.connect(self._on_data_change)
          self._viewer.axes.events.labels.connect(self._on_data_change)
          self._viewer.axes.events.arrows.connect(self._on_data_change)
          self._viewer.dims.events.order.connect(self._on_data_change)
          self._viewer.dims.events.range.connect(self._on_data_change)
          self._viewer.dims.events.ndisplay.connect(self._on_data_change)
          self._viewer.dims.events.axis_labels.connect(self._on_data_change)
          self._viewer.camera.events.zoom.connect(self._on_zoom_change)
  
          self._on_visible_change(None)
          self._on_data_change(None)
  
      def _set_canvas_none(self):
          self.node._set_canvas(None)
          self.text_node._set_canvas(None)
  
      def _on_visible_change(self, event):
          """Change visibiliy of axes."""
          self.node.visible = self._viewer.axes.visible
          self._on_zoom_change(event)
          self._on_data_change(event)
  
      def _on_data_change(self, event):
          """Change style of axes."""
          if not self._viewer.axes.visible:
              return
  
          # Determine which axes are displayed
          axes = self._viewer.dims.displayed
  
          # Actual number of displayed dims
          ndisplay = len(self._viewer.dims.displayed)
  
          # Determine the labels of those axes
          axes_labels = [self._viewer.dims.axis_labels[a] for a in axes[::-1]]
          # Counting backwards from total number of dimensions
          # determine axes positions. This is done as by default
          # the last NumPy axis corresponds to the first Vispy axis
          reversed_axes = [self._viewer.dims.ndim - 1 - a for a in axes[::-1]]
  
          # Determine colors of axes based on reverse position
          if self._viewer.axes.colored:
              axes_colors = [
                  self._default_color[ra % len(self._default_color)]
                  for ra in reversed_axes
              ]
          else:
              # the reason for using the `as_hex` here is to avoid
              # `UserWarning` which is emitted when RGB values are above 1
              background_color = get_theme(
                  self._viewer.theme, False
              ).canvas.as_hex()
              background_color = transform_color(background_color)[0]
              color = np.subtract(1, background_color)
              color[-1] = background_color[-1]
              axes_colors = [color] * ndisplay
  
          # Determine data based on number of displayed dimensions and
          # axes visualization parameters
          if self._viewer.axes.dashed and ndisplay == 2:
              data = self._dashed_line_data2D
              color = color_dashed_lines(axes_colors)
              text_data = self._line_data2D[1::2]
          elif self._viewer.axes.dashed and ndisplay == 3:
              data = self._dashed_line_data3D
              color = color_dashed_lines(axes_colors)
              text_data = self._line_data3D[1::2]
          elif not self._viewer.axes.dashed and ndisplay == 2:
              data = self._line_data2D
              color = color_lines(axes_colors)
              text_data = self._line_data2D[1::2]
          elif not self._viewer.axes.dashed and ndisplay == 3:
              data = self._line_data3D
              color = color_lines(axes_colors)
              text_data = self._line_data3D[1::2]
          else:
              raise ValueError(
                  trans._(
                      'Axes dash status and ndisplay combination not supported',
                      deferred=True,
                  )
              )
  
          if self._viewer.axes.arrows and ndisplay == 2:
              arrow_vertices = self._default_arrow_vertices2D
              arrow_faces = self._default_arrow_faces2D
              arrow_color = color_arrowheads(
                  axes_colors, self._NUM_SEGMENTS_ARROWHEAD
              )
          elif self._viewer.axes.arrows and ndisplay == 3:
              arrow_vertices = self._default_arrow_vertices3D
              arrow_faces = self._default_arrow_faces3D
              arrow_color = color_arrowheads(
                  axes_colors, self._NUM_SEGMENTS_ARROWHEAD
              )
          else:
              arrow_vertices = np.zeros((3, 3))
              arrow_faces = np.array([[0, 1, 2]])
              arrow_color = [[0, 0, 0, 0]]
  
          self.node._subvisuals[0].set_data(data, color)
          self.node._subvisuals[1].set_data(
              vertices=arrow_vertices,
              faces=arrow_faces,
              face_colors=arrow_color,
          )
  
          # Set visibility status of text
          self.text_node.visible = (
              self._viewer.axes.visible and self._viewer.axes.labels
          )
          self.text_node.text = axes_labels
          self.text_node.color = axes_colors
          self.text_node.pos = text_data + self._text_offsets
  
      def _on_zoom_change(self, event):
          """Update axes length based on zoom scale."""
          if not self._viewer.axes.visible:
              return
  
          scale = 1 / self._viewer.camera.zoom
  
          # If scale has not changed, do not redraw
          if abs(np.log10(self._scale) - np.log10(scale)) < 1e-4:
              return
          self._scale = scale
          scale_canvas2world = self._scale
          target_canvas_pixels = self._target_length
          scale = target_canvas_pixels * scale_canvas2world
          # Update axes scale
          self.node.transform.scale = [scale, scale, scale, 1]
  
apis: numpy.empty numpy.zeros numpy.subtract numpy.log10 numpy.array numpy.concatenate numpy.linspace