diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index 37cc3d5f89e8..8091c7939502 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -1269,7 +1269,7 @@ def _set_artist_props(self, a):
     def _update_ticks(self):
         """
         Update ticks (position and labels) using the current data interval of
-        the axes.  Return the list of ticks that will be drawn.
+        the axes.
         """
         major_locs = self.get_majorticklocs()
         major_labels = self.major.formatter.format_ticks(major_locs)
@@ -1285,7 +1285,7 @@ def _update_ticks(self):
             tick.update_position(loc)
             tick.label1.set_text(label)
             tick.label2.set_text(label)
-        ticks = [*major_ticks, *minor_ticks]
+        self._ticks = [*major_ticks, *minor_ticks]
 
         view_low, view_high = self.get_view_interval()
         if view_low > view_high:
@@ -1302,10 +1302,16 @@ def _update_ticks(self):
             view_high = view_high - delta * margin
             view_low = view_low + delta * margin
 
-        interval_t = self.get_transform().transform([view_low, view_high])
+        self._interval_t = self.get_transform().transform([view_low, view_high])
 
+    def _get_ticks_to_draw(self, update=True):
+        """
+        Return the list of ticks that will be drawn.
+        """
+        if update:
+            self._update_ticks()
         ticks_to_draw = []
-        for tick in ticks:
+        for tick in self._ticks:
             try:
                 loc_t = self.get_transform().transform(tick.get_loc())
             except AssertionError:
@@ -1313,7 +1319,7 @@ def _update_ticks(self):
                 # some scales might make them, so we need this try/except.
                 pass
             else:
-                if mtransforms._interval_contains_close(interval_t, loc_t):
+                if mtransforms._interval_contains_close(self._interval_t, loc_t):
                     ticks_to_draw.append(tick)
 
         return ticks_to_draw
@@ -1341,7 +1347,7 @@ def get_tightbbox(self, renderer=None, *, for_layout_only=False):
             return
         if renderer is None:
             renderer = self.get_figure(root=True)._get_renderer()
-        ticks_to_draw = self._update_ticks()
+        ticks_to_draw = self._get_ticks_to_draw(update=True)
 
         self._update_label_position(renderer)
 
@@ -1394,7 +1400,7 @@ def draw(self, renderer):
             return
         renderer.open_group(__name__, gid=self.get_gid())
 
-        ticks_to_draw = self._update_ticks()
+        ticks_to_draw = self._get_ticks_to_draw(update=True)
         tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
 
         for tick in ticks_to_draw:
@@ -2230,7 +2236,7 @@ def _get_tick_boxes_siblings(self, renderer):
         # If we want to align labels from other Axes:
         for ax in grouper.get_siblings(self.axes):
             axis = ax._axis_map[name]
-            ticks_to_draw = axis._update_ticks()
+            ticks_to_draw = axis._get_ticks_to_draw(update=True)
             tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
             bboxes.extend(tlb)
             bboxes2.extend(tlb2)
diff --git a/lib/matplotlib/spines.py b/lib/matplotlib/spines.py
index 7e77a393f2a2..b04ae3819f90 100644
--- a/lib/matplotlib/spines.py
+++ b/lib/matplotlib/spines.py
@@ -155,7 +155,7 @@ def get_window_extent(self, renderer=None):
         if self.axis is None or not self.axis.get_visible():
             return bb
         bboxes = [bb]
-        drawn_ticks = self.axis._update_ticks()
+        drawn_ticks = self.axis._get_ticks_to_draw(update=True)
 
         major_tick = next(iter({*drawn_ticks} & {*self.axis.majorTicks}), None)
         minor_tick = next(iter({*drawn_ticks} & {*self.axis.minorTicks}), None)
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 38857e846c55..504f12702265 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -3128,7 +3128,8 @@ def test_log_scales():
     ax.invert_yaxis()
     ax.set_xscale('log', base=9.0)
     xticks, yticks = (
-        [(t.get_loc(), t.label1.get_text()) for t in axis._update_ticks()]
+        [(t.get_loc(), t.label1.get_text())
+         for t in axis._get_ticks_to_draw(update=True)]
         for axis in [ax.xaxis, ax.yaxis]
     )
     assert xticks == [
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index b694bc827646..c82c8180e411 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -456,6 +456,9 @@ def draw(self, renderer):
                 artist.do_3d_projection()
 
         if self._axis3don:
+            # Update ticks
+            for axis in self._axis_map.values():
+                axis._update_ticks()
             # Draw panes first
             for axis in self._axis_map.values():
                 axis.draw_pane(renderer)
diff --git a/lib/mpl_toolkits/mplot3d/axis3d.py b/lib/mpl_toolkits/mplot3d/axis3d.py
index 4da5031b990c..4a1248dbdb4f 100644
--- a/lib/mpl_toolkits/mplot3d/axis3d.py
+++ b/lib/mpl_toolkits/mplot3d/axis3d.py
@@ -435,10 +435,9 @@ def _axmask(self):
 
     def _draw_ticks(self, renderer, edgep1, centers, deltas, highs,
                     deltas_per_point, pos):
-        ticks = self._update_ticks()
+        ticks = self._get_ticks_to_draw(update=False)  # We updated in Axes3D.draw()
         info = self._axinfo
         index = info["i"]
-        juggled = info["juggled"]
 
         mins, maxs, tc, highs = self._get_coord_info()
         centers, deltas = self._calc_centers_deltas(maxs, mins)
@@ -461,17 +460,28 @@ def _draw_ticks(self, renderer, edgep1, centers, deltas, highs,
             # Get tick line positions
             pos = edgep1.copy()
             pos[index] = tick.get_loc()
-            pos[tickdir] = out_tickdir
-            x1, y1, z1 = proj3d.proj_transform(*pos, self.axes.M)
-            pos[tickdir] = in_tickdir
-            x2, y2, z2 = proj3d.proj_transform(*pos, self.axes.M)
 
-            # Get position of label
-            labeldeltas = (tick.get_pad() + default_label_offset) * points
+            # Add out and in tickdir positions
+            positions = []
+            for td in (out_tickdir, in_tickdir):
+                p = pos.copy()
+                p[tickdir] = td
+                positions.append(p)
+
+            # Add label position
+            p = pos.copy()
+            p[tickdir] = edgep1_tickdir
+            positions.append(_move_from_center(
+                p, centers,
+                (tick.get_pad() + default_label_offset) * points,
+                self._axmask()
+            ))
+
+            xs, ys, zs = proj3d._proj_trans_points(np.array(positions), self.axes.M)
 
-            pos[tickdir] = edgep1_tickdir
-            pos = _move_from_center(pos, centers, labeldeltas, self._axmask())
-            lx, ly, lz = proj3d.proj_transform(*pos, self.axes.M)
+            x1, y1, z1 = xs[0], ys[0], zs[0]
+            x2, y2, z2 = xs[1], ys[1], zs[1]
+            lx, ly, lz = xs[2], ys[2], zs[2]
 
             _tick_update_position(tick, (x1, x2), (y1, y2), (lx, ly))
             tick.tick1line.set_linewidth(tick_lw[tick._major])
@@ -636,7 +646,7 @@ def draw_grid(self, renderer):
 
         renderer.open_group("grid3d", gid=self.get_gid())
 
-        ticks = self._update_ticks()
+        ticks = self._get_ticks_to_draw(update=False)  # We updated in Axes3D.draw()
         if len(ticks):
             # Get general axis information:
             info = self._axinfo