Use boundary to compute axes domain in gridliner

lib/cartopy/mpl/gridliner.py

@@ -852,13 +852,18 @@ def _axes_domain(self, nx=None, ny=None):
         ax_transform = self.axes.transAxes
         desired_trans = ax_transform - transform
 
-        nx = nx or 100
-        ny = ny or 100
+        nx = nx or 101
+        ny = ny or 101
         x = np.linspace(1e-9, 1 - 1e-9, nx)
         y = np.linspace(1e-9, 1 - 1e-9, ny)
         x, y = np.meshgrid(x, y)
 
-        coords = np.column_stack((x.ravel(), y.ravel()))
+        xyp = (self.axes.patch.get_transform()-ax_transform).transform(
+            self.axes.patch.get_path().vertices)
+        x = np.concatenate((x.ravel(), xyp[:, 0]))
+        y = np.concatenate((y.ravel(), xyp[:, 1]))
+
+        coords = np.column_stack((x, y))
 
         in_data = desired_trans.transform(coords)
 

lib/cartopy/tests/mpl/test_gridliner.py

@@ -54,7 +54,7 @@
 @pytest.mark.natural_earth
 @ImageTesting(['gridliner1'],
               # Robinson projection is slightly better in Proj 6+.
-              tolerance=0.7 if ccrs.PROJ4_VERSION >= (6, 0, 0) else 0.5)
+              tolerance=0.7 if ccrs.PROJ4_VERSION >= (6, 0, 0) else 0.62)
 def test_gridliner():
     ny, nx = 2, 4
 
@@ -112,6 +112,13 @@ def test_gridliner():
                         top=1 - delta, bottom=0 + delta)
 
 
+@ImageTesting(['gridliner_orthographic'])
+def test_gridliner_orthographic():
+    plt.figure(figsize=(4, 4))
+    ax = plt.subplot(111, projection=ccrs.Orthographic())
+    ax.gridlines(ccrs.PlateCarree())
+
+
 def test_gridliner_specified_lines():
     meridians = [0, 60, 120, 180, 240, 360]
     parallels = [-90, -60, -30, 0, 30, 60, 90]