diff --git a/lib/matplotlib/collections.py b/lib/matplotlib/collections.py
index d02607cc5..bcce49440 100644
--- a/lib/matplotlib/collections.py
+++ b/lib/matplotlib/collections.py
@@ -1977,34 +1977,38 @@ class QuadMesh(Collection):
     (*meshWidth* * *meshHeight*) quadrilaterals in the mesh.  The mesh
     need not be regular and the polygons need not be convex.
 
-    A quadrilateral mesh is represented by a (2 x ((*meshWidth* + 1) *
-    (*meshHeight* + 1))) numpy array *coordinates*, where each row is
-    the *x* and *y* coordinates of one of the vertices.  To define the
+    A quadrilateral mesh is represented by a ((*meshWidth* + 1),
+    (*meshHeight* + 1), 2) numpy array *coordinates*, where the final dimension
+    is the *x* and *y* coordinates of one of the vertices.  To define the
     function that maps from a data point to its corresponding color,
-    use the :meth:`set_cmap` method.  Each of these arrays is indexed in
-    row-major order by the mesh coordinates of the vertex (or the mesh
-    coordinates of the lower left vertex, in the case of the colors).
-
-    For example, the first entry in *coordinates* is the coordinates of the
-    vertex at mesh coordinates (0, 0), then the one at (0, 1), then at (0, 2)
-    .. (0, meshWidth), (1, 0), (1, 1), and so on.
+    use the :meth:`set_cmap` method.
 
     *shading* may be 'flat', or 'gouraud'
     """
-    def __init__(self, meshWidth, meshHeight, coordinates,
+    def __init__(self, coordinates, *args,
                  antialiased=True, shading='flat', **kwargs):
         super().__init__(**kwargs)
-        self._meshWidth = meshWidth
-        self._meshHeight = meshHeight
-        # By converting to floats now, we can avoid that on every draw.
-        self._coordinates = np.asarray(coordinates, float).reshape(
-            (meshHeight + 1, meshWidth + 1, 2))
+        if len(args):
+            _api.warn_deprecated("3.5", alternative=(
+                "The QuadMesh class now takes a 3-dimensional *coordinates* "
+                "array as input of shape (nx, ny, 2) that defines the shape "
+                "and size of the mesh."))
+            self._meshWidth = coordinates
+            self._meshHeight = args[0]
+            # By converting to floats now, we can avoid that on every draw.
+            self._coordinates = np.asarray(args[1], float).reshape(
+                (self._meshHeight + 1, self._meshWidth + 1, 2))
+        else:
+            # This will become standard after the deprecation
+            self._coordiantes = np.asarray(coordinates, float)
+            self._meshWidth = self._coordinates.shape[0] - 1
+            self._meshHeight = self._coordinates.shape[1] - 1
+
         self._antialiased = antialiased
         self._shading = shading
 
         self._bbox = transforms.Bbox.unit()
-        self._bbox.update_from_data_xy(coordinates.reshape(
-            ((meshWidth + 1) * (meshHeight + 1), 2)))
+        self._bbox.update_from_data_xy(self._coordinates.reshape(-1, 2))
 
     def get_paths(self):
         if self._paths is None: