matplotlib
diff --git a/‎doc/users/next_whats_new/2019-03-25-mplot3d-projection.rst
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diff --git a/‎lib/matplotlib/axes/_base.py
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diff --git a/‎lib/matplotlib/tests/baseline_images/test_collections/polycollection_close.png
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diff --git a/‎lib/mpl_toolkits/mplot3d/axes3d.py
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diff --git a/‎lib/mpl_toolkits/mplot3d/proj3d.py
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diff --git a/‎lib/mpl_toolkits/tests/baseline_images/test_mplot3d/axes3d_cla.png
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diff --git a/‎lib/mpl_toolkits/tests/baseline_images/test_mplot3d/axes3d_labelpad.png
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diff --git a/‎lib/mpl_toolkits/tests/baseline_images/test_mplot3d/axes3d_ortho.png
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diff --git a/‎lib/mpl_toolkits/tests/baseline_images/test_mplot3d/axes3d_rotated.png
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diff --git a/‎lib/mpl_toolkits/tests/baseline_images/test_mplot3d/bar3d.png
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@@ -1499,9 +1499,9 @@ def apply_aspect(self, position=None):
         """
         Adjust the Axes for a specified data aspect ratio.
 
-        Depending on `.get_adjustable` this will modify either the Axes box
-        (position) or the view limits. In the former case, `.get_anchor`
-        will affect the position.
+        Depending on `.get_adjustable` this will modify either the
+        Axes box (position) or the view limits. In the former case,
+        `~matplotlib.axes.Axes.get_anchor` will affect the position.
 
         Notes
         -----
 
@@ -255,6 +255,20 @@ def tunit_edges(self, vals=None, M=None):
                  (tc[7], tc[4])]
         return edges
 
+    def apply_aspect(self, position=None):
+        if position is None:
+            position = self.get_position(original=True)
+
+        # in the superclass, we would go through and actually deal with axis
+        # scales and box/datalim. Those are all irrelevant - all we need to do
+        # is make sure our coordinate system is square.
+        figW, figH = self.get_figure().get_size_inches()
+        fig_aspect = figH / figW
+        box_aspect = 1
+        pb = position.frozen()
+        pb1 = pb.shrunk_to_aspect(box_aspect, pb, fig_aspect)
+        self.set_position(pb1.anchored(self.get_anchor(), pb), 'active')
+
     @artist.allow_rasterization
     def draw(self, renderer):
         # draw the background patch
@@ -950,6 +964,9 @@ def get_proj(self):
 
         dist is the distance of the eye viewing point from the object point.
         """
+        # chosen for similarity with the initial view before gh-8896
+        pb_aspect = np.array([4, 4, 3]) / 3.5
+
         relev, razim = np.pi * self.elev/180, np.pi * self.azim/180
 
         xmin, xmax = self.get_xlim3d()
@@ -959,10 +976,10 @@ def get_proj(self):
         # transform to uniform world coordinates 0-1, 0-1, 0-1
         worldM = proj3d.world_transformation(xmin, xmax,
                                              ymin, ymax,
-                                             zmin, zmax)
+                                             zmin, zmax, pb_aspect=pb_aspect)
 
         # look into the middle of the new coordinates
-        R = np.array([0.5, 0.5, 0.5])
+        R = pb_aspect / 2
 
         xp = R[0] + np.cos(razim) * np.cos(relev) * self.dist
         yp = R[1] + np.sin(razim) * np.cos(relev) * self.dist
 
@@ -30,8 +30,20 @@ def _line2d_seg_dist(p1, p2, p0):
 
 def world_transformation(xmin, xmax,
                          ymin, ymax,
-                         zmin, zmax):
-    dx, dy, dz = (xmax-xmin), (ymax-ymin), (zmax-zmin)
+                         zmin, zmax, pb_aspect=None):
+    """
+    produce a matrix that scales homogenous coords in the specified ranges
+    to [0, 1], or [0, pb_aspect[i]] if the plotbox aspect ratio is specified
+    """
+    dx = xmax - xmin
+    dy = ymax - ymin
+    dz = zmax - zmin
+    if pb_aspect is not None:
+        ax, ay, az = pb_aspect
+        dx /= ax
+        dy /= ay
+        dz /= az
+
     return np.array([[1/dx, 0,    0,    -xmin/dx],
                      [0,    1/dy, 0,    -ymin/dy],
                      [0,    0,    1/dz, -zmin/dz],