matplotlib · ksunden · Jun 12, 2023 · Apr 27, 2023 · Apr 27, 2023 · Apr 27, 2023
diff --git a/doc/users/next_whats_new/get_vertices_co_vertices.rst b/doc/users/next_whats_new/get_vertices_co_vertices.rst
@@ -0,0 +1,7 @@
+``Ellipse.get_vertices()``, ``Ellipse.get_co_vertices()``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+These methods return the coordinates of ellipse vertices of
+major and minor axis. Additionally, an example gallery demo is added which
+shows how to add an arrow to an ellipse showing a clockwise or counter-clockwise
+rotation of the ellipse. To place the arrow exactly on the ellipse,
+the coordinates of the vertices are used.
diff --git a/galleries/examples/shapes_and_collections/ellipse_arrow.py b/galleries/examples/shapes_and_collections/ellipse_arrow.py
@@ -0,0 +1,53 @@
+"""
+===================================
+Ellipse with orientation arrow demo
+===================================
+
+This demo shows how to draw an ellipse with
+an orientation arrow (clockwise or counterclockwise).
+Compare this to the :doc:`Ellipse collection example
+</gallery/shapes_and_collections/ellipse_collection>`.
+"""
+
+import matplotlib.pyplot as plt
+
+from matplotlib.markers import MarkerStyle
+from matplotlib.patches import Ellipse
+from matplotlib.transforms import Affine2D
+
+# Create a figure and axis
+fig, ax = plt.subplots(subplot_kw={"aspect": "equal"})
+
+ellipse = Ellipse(
+    xy=(2, 4),
+    width=30,
+    height=20,
+    angle=35,
+    facecolor="none",
+    edgecolor="b"
+)
+ax.add_patch(ellipse)
+
+# Plot an arrow marker at the end point of minor axis
+vertices = ellipse.get_co_vertices()
+t = Affine2D().rotate_deg(ellipse.angle)
+ax.plot(
+    vertices[0][0],
+    vertices[0][1],
+    color="b",
+    marker=MarkerStyle(">", "full", t),
+    markersize=10
+)
+# Note: To reverse the orientation arrow, switch the marker type from > to <.
+
+plt.show()
+
+# %%
+#
+# .. admonition:: References
+#
+#    The use of the following functions, methods, classes and modules is shown
+#    in this example:
+#
+#    - `matplotlib.patches`
+#    - `matplotlib.patches.Ellipse`
diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
@@ -1654,6 +1654,37 @@ def get_corners(self):
         return self.get_patch_transform().transform(
             [(-1, -1), (1, -1), (1, 1), (-1, 1)])
 
+    def _calculate_length_between_points(self, x0, y0, x1, y1):
+        return np.sqrt((x1 - x0)**2 + (y1 - y0)**2)
+
+    def get_vertices(self):
+        """
+        Return the vertices coordinates of the ellipse.
+
+        The definition can be found `here <https://en.wikipedia.org/wiki/Ellipse>`_
+
+        .. versionadded:: 3.8
+        """
+        if self.width < self.height:
+            ret = self.get_patch_transform().transform([(0, 1), (0, -1)])
+        else:
+            ret = self.get_patch_transform().transform([(1, 0), (-1, 0)])
+        return [tuple(x) for x in ret]
+
+    def get_co_vertices(self):
+        """
+        Return the co-vertices coordinates of the ellipse.
+
+        The definition can be found `here <https://en.wikipedia.org/wiki/Ellipse>`_
+
+        .. versionadded:: 3.8
+        """
+        if self.width < self.height:
+            ret = self.get_patch_transform().transform([(1, 0), (-1, 0)])
+        else:
+            ret = self.get_patch_transform().transform([(0, 1), (0, -1)])
+        return [tuple(x) for x in ret]
+
 
 class Annulus(Patch):
     """

diff --git a/lib/matplotlib/patches.pyi b/lib/matplotlib/patches.pyi
@@ -259,6 +259,10 @@ class Ellipse(Patch):
 
     def get_corners(self) -> np.ndarray: ...
 
+    def get_vertices(self) -> list[tuple[float, float]]: ...
+    def get_co_vertices(self) -> list[tuple[float, float]]: ...
+
+
 class Annulus(Patch):
     a: float
     b: float

diff --git a/lib/matplotlib/tests/test_patches.py b/lib/matplotlib/tests/test_patches.py
@@ -104,6 +104,57 @@ def test_corner_center():
     assert_almost_equal(ellipse.get_corners(), corners_rot)
 
 
+def test_ellipse_vertices():
+    # expect 0 for 0 ellipse width, height
+    ellipse = Ellipse(xy=(0, 0), width=0, height=0, angle=0)
+    assert_almost_equal(
+        ellipse.get_vertices(),
+        [(0.0, 0.0), (0.0, 0.0)],
+    )
+    assert_almost_equal(
+        ellipse.get_co_vertices(),
+        [(0.0, 0.0), (0.0, 0.0)],
+    )
+
+    ellipse = Ellipse(xy=(0, 0), width=2, height=1, angle=30)
+    assert_almost_equal(
+        ellipse.get_vertices(),
+        [
+            (
+                ellipse.center[0] + ellipse.width / 4 * np.sqrt(3),
+                ellipse.center[1] + ellipse.width / 4,
+            ),
+            (
+                ellipse.center[0] - ellipse.width / 4 * np.sqrt(3),
+                ellipse.center[1] - ellipse.width / 4,
+            ),
+        ],
+    )
+    assert_almost_equal(
+        ellipse.get_co_vertices(),
+        [
+            (
+                ellipse.center[0] - ellipse.height / 4,
+                ellipse.center[1] + ellipse.height / 4 * np.sqrt(3),
+            ),
+            (
+                ellipse.center[0] + ellipse.height / 4,
+                ellipse.center[1] - ellipse.height / 4 * np.sqrt(3),
+            ),
+        ],
+    )
+    v1, v2 = np.array(ellipse.get_vertices())
+    np.testing.assert_almost_equal((v1 + v2) / 2, ellipse.center)
+    v1, v2 = np.array(ellipse.get_co_vertices())
+    np.testing.assert_almost_equal((v1 + v2) / 2, ellipse.center)
+
+    ellipse = Ellipse(xy=(2.252, -10.859), width=2.265, height=1.98, angle=68.78)
+    v1, v2 = np.array(ellipse.get_vertices())
+    np.testing.assert_almost_equal((v1 + v2) / 2, ellipse.center)
+    v1, v2 = np.array(ellipse.get_co_vertices())
+    np.testing.assert_almost_equal((v1 + v2) / 2, ellipse.center)
+
+
 def test_rotate_rect():
     loc = np.asarray([1.0, 2.0])
     width = 2