Store FloatingAxes "extremes" info in fewer places.

Make the value returned by ExtremeFinderFixed be the canonical place
to query the value of the extremes parameter.

This may make it easier to change the extremes post-facto (there's fewer
places to update).

Also deprecate the related get_data_boundary method, which doesn't exist
anywhere else and isn't really needed as a separate API: we can just
inline it into its only call site instead.

Author: anntzer

doc/api/next_api_changes/deprecations/25427-AL.rst

@@ -0,0 +1,4 @@
+``GridHelperCurveLinear.get_data_boundary``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+... is deprecated.  Use ``grid_finder.extreme_finder(*[None] * 5)`` to get the
+extremes of the grid.

lib/mpl_toolkits/axisartist/floating_axes.py

@@ -33,7 +33,10 @@ def __init__(self, grid_helper, side, nth_coord_ticks=None):
         nth_coord = along which coordinate value varies.
          nth_coord = 0 ->  x axis, nth_coord = 1 -> y axis
         """
-        value, nth_coord = grid_helper.get_data_boundary(side)
+        lon1, lon2, lat1, lat2 = grid_helper.grid_finder.extreme_finder(*[None] * 5)
+        value, nth_coord = _api.check_getitem(
+            dict(left=(lon1, 0), right=(lon2, 0), bottom=(lat1, 1), top=(lat2, 1)),
+            side=side)
         super().__init__(grid_helper, nth_coord, value, axis_direction=side)
         if nth_coord_ticks is None:
             nth_coord_ticks = nth_coord
@@ -58,7 +61,7 @@ def get_tick_iterators(self, axes):
         lon_levs, lon_n, lon_factor = self._grid_info["lon_info"]
         xx0 = lon_levs / lon_factor
 
-        extremes = self.grid_helper._extremes
+        extremes = self.grid_helper.grid_finder.extreme_finder(*[None] * 5)
         xmin, xmax = sorted(extremes[:2])
         ymin, ymax = sorted(extremes[2:])
 
@@ -137,20 +140,19 @@ def __init__(self, aux_trans, extremes,
                  tick_formatter1=None,
                  tick_formatter2=None):
         # docstring inherited
-        self._extremes = extremes
-        extreme_finder = ExtremeFinderFixed(extremes)
         super().__init__(aux_trans,
-                         extreme_finder,
+                         extreme_finder=ExtremeFinderFixed(extremes),
                          grid_locator1=grid_locator1,
                          grid_locator2=grid_locator2,
                          tick_formatter1=tick_formatter1,
                          tick_formatter2=tick_formatter2)
 
+    @_api.deprecated("3.8")
     def get_data_boundary(self, side):
         """
         Return v=0, nth=1.
         """
-        lon1, lon2, lat1, lat2 = self._extremes
+        lon1, lon2, lat1, lat2 = self.grid_finder.extreme_finder(*[None] * 5)
         return dict(left=(lon1, 0),
                     right=(lon2, 0),
                     bottom=(lat1, 1),
@@ -262,10 +264,7 @@ def __init__(self, *args, grid_helper, **kwargs):
 
     def _gen_axes_patch(self):
         # docstring inherited
-        # Using a public API to access _extremes.
-        (x0, _), (x1, _), (y0, _), (y1, _) = map(
-            self.get_grid_helper().get_data_boundary,
-            ["left", "right", "bottom", "top"])
+        x0, x1, y0, y1 = self.get_grid_helper().grid_finder.extreme_finder(*[None] * 5)
         patch = mpatches.Polygon([(x0, y0), (x1, y0), (x1, y1), (x0, y1)])
         patch.get_path()._interpolation_steps = 100
         return patch