matplotlib
diff --git a/lib/matplotlib/tests/test_transforms.py b/lib/matplotlib/tests/test_transforms.py
@@ -142,6 +142,25 @@ def test_pcolormesh_pre_transform_limits():
     assert_almost_equal(expected, ax.dataLim.get_points())
 
 
+def test_pcolormesh_gouraud_nans():
+    np.random.seed(19680801)
+
+    values = np.linspace(0, 180, 3)
+    radii = np.linspace(100, 1000, 10)
+    z, y = np.meshgrid(values, radii)
+    x = np.radians(np.random.rand(*z.shape) * 100)
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111, projection="polar")
+    # Setting the limit to cause clipping of the r values causes NaN to be
+    # introduced; these should not crash but be ignored as in other path
+    # operations.
+    ax.set_rlim(101, 1000)
+    ax.pcolormesh(x, y, z, shading="gouraud")
+
+    fig.canvas.draw()
+
+
 def test_Affine2D_from_values():
     points = np.array([[0, 0],
                        [10, 20],

diff --git a/src/_backend_agg.h b/src/_backend_agg.h
@@ -1193,6 +1193,9 @@ inline void RendererAgg::_draw_gouraud_triangle(PointArray &points,
             tpoints[i][j] = points(i, j);
         }
         trans.transform(&tpoints[i][0], &tpoints[i][1]);
+        if(std::isnan(tpoints[i][0]) || std::isnan(tpoints[i][1])) {
+            return;
+        }
     }
 
     span_alloc_t span_alloc;