diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
index b83714bdcd7b..544a626b8abe 100644
--- a/lib/matplotlib/patches.py
+++ b/lib/matplotlib/patches.py
@@ -806,6 +806,18 @@ def get_xy(self):
         """Return the left and bottom coords of the rectangle as a tuple."""
         return self._x0, self._y0
 
+    def get_corners(self):
+        """
+        Return the corners of the rectangle, moving anti-clockwise from
+        (x0, y0).
+        """
+        return self.get_patch_transform().transform(
+            [(0, 0), (1, 0), (1, 1), (0, 1)])
+
+    def get_center(self):
+        """Return the centre of the rectangle."""
+        return self.get_patch_transform().transform((0.5, 0.5))
+
     def get_width(self):
         """Return the width of the rectangle."""
         return self._width
@@ -1657,6 +1669,16 @@ def get_angle(self):
 
     angle = property(get_angle, set_angle)
 
+    def get_corners(self):
+        """
+        Return the corners of the ellipse bounding box.
+
+        The bounding box orientation is moving anti-clockwise from the
+        lower left corner defined before rotation.
+        """
+        return self.get_patch_transform().transform(
+            [(-1, -1), (1, -1), (1, 1), (-1, 1)])
+
 
 class Annulus(Patch):
     """
diff --git a/lib/matplotlib/tests/test_patches.py b/lib/matplotlib/tests/test_patches.py
index 9487758c8aef..6a8ddc87f3ae 100644
--- a/lib/matplotlib/tests/test_patches.py
+++ b/lib/matplotlib/tests/test_patches.py
@@ -6,7 +6,7 @@
 import pytest
 
 import matplotlib as mpl
-from matplotlib.patches import (Annulus, Patch, Polygon, Rectangle,
+from matplotlib.patches import (Annulus, Ellipse, Patch, Polygon, Rectangle,
                                 FancyArrowPatch)
 from matplotlib.testing.decorators import image_comparison, check_figures_equal
 from matplotlib.transforms import Bbox
@@ -54,6 +54,54 @@ def test_Polygon_close():
     assert_array_equal(p.get_xy(), xyclosed)
 
 
+def test_corner_center():
+    loc = [10, 20]
+    width = 1
+    height = 2
+
+    # Rectangle
+    # No rotation
+    corners = ((10, 20), (11, 20), (11, 22), (10, 22))
+    rect = Rectangle(loc, width, height)
+    assert_array_equal(rect.get_corners(), corners)
+    assert_array_equal(rect.get_center(), (10.5, 21))
+
+    # 90 deg rotation
+    corners_rot = ((10, 20), (10, 21), (8, 21), (8, 20))
+    rect.set_angle(90)
+    assert_array_equal(rect.get_corners(), corners_rot)
+    assert_array_equal(rect.get_center(), (9, 20.5))
+
+    # Rotation not a multiple of 90 deg
+    theta = 33
+    t = mtransforms.Affine2D().rotate_around(*loc, np.deg2rad(theta))
+    corners_rot = t.transform(corners)
+    rect.set_angle(theta)
+    assert_almost_equal(rect.get_corners(), corners_rot)
+
+    # Ellipse
+    loc = [loc[0] + width / 2,
+           loc[1] + height / 2]
+    ellipse = Ellipse(loc, width, height)
+
+    # No rotation
+    assert_array_equal(ellipse.get_corners(), corners)
+
+    # 90 deg rotation
+    corners_rot = ((11.5, 20.5), (11.5, 21.5), (9.5, 21.5), (9.5, 20.5))
+    ellipse.set_angle(90)
+    assert_array_equal(ellipse.get_corners(), corners_rot)
+    # Rotation shouldn't change ellipse center
+    assert_array_equal(ellipse.get_center(), loc)
+
+    # Rotation not a multiple of 90 deg
+    theta = 33
+    t = mtransforms.Affine2D().rotate_around(*loc, np.deg2rad(theta))
+    corners_rot = t.transform(corners)
+    ellipse.set_angle(theta)
+    assert_almost_equal(ellipse.get_corners(), corners_rot)
+
+
 def test_rotate_rect():
     loc = np.asarray([1.0, 2.0])
     width = 2