diff --git a/lib/matplotlib/delaunay/_delaunay.cpp b/lib/matplotlib/delaunay/_delaunay.cpp
index 074ca139ca2c..ab10b8b3998d 100644
--- a/lib/matplotlib/delaunay/_delaunay.cpp
+++ b/lib/matplotlib/delaunay/_delaunay.cpp
@@ -289,8 +289,8 @@ static PyObject *linear_interpolate_grid(double x0, double x1, int xsteps,
     if (!z) return NULL;
     z_ptr = (double*)PyArray_DATA(z);
 
-    dx = (x1 - x0) / (xsteps-1);
-    dy = (y1 - y0) / (ysteps-1);
+    dx = ( xsteps==1 ? 0 : (x1 - x0) / (xsteps-1) );
+    dy = ( ysteps==1 ? 0 : (y1 - y0) / (ysteps-1) );
 
     rowtri = 0;
     for (iy=0; iy<ysteps; iy++) {
diff --git a/lib/matplotlib/tests/baseline_images/test_delaunay/delaunay-1d-interp.png b/lib/matplotlib/tests/baseline_images/test_delaunay/delaunay-1d-interp.png
new file mode 100644
index 000000000000..a2c19c85bff3
Binary files /dev/null and b/lib/matplotlib/tests/baseline_images/test_delaunay/delaunay-1d-interp.png differ
diff --git a/lib/matplotlib/tests/test_delaunay.py b/lib/matplotlib/tests/test_delaunay.py
index 629816127f13..93e8114d46b7 100644
--- a/lib/matplotlib/tests/test_delaunay.py
+++ b/lib/matplotlib/tests/test_delaunay.py
@@ -159,7 +159,7 @@ def interpolator(self, func):
         z = func(self.x, self.y)
         return self.tri.nn_extrapolator(z, bbox=self.xrange+self.yrange)
 
-def make_all_testfuncs(allfuncs=allfuncs):
+def make_all_2d_testfuncs(allfuncs=allfuncs):
     def make_test(func):
         filenames = [
             '%s-%s' % (func.func_name, x) for x in
@@ -186,4 +186,27 @@ def reference_test():
     for func in allfuncs:
         globals()['test_%s' % func.func_name] = make_test(func)
 
-make_all_testfuncs()
+make_all_2d_testfuncs()
+
+# 1d and 0d grid tests
+
+ref_interpolator = Triangulation([0,10,10,0],
+                                 [0,0,10,10]).linear_interpolator([1,10,5,2.0])
+
+def test_1d_grid():
+    res = ref_interpolator[3:6:2j,1:1:1j]
+    assert np.allclose(res, [[1.6],[1.9]], rtol=0)
+
+def test_0d_grid():
+    res = ref_interpolator[3:3:1j,1:1:1j]
+    assert np.allclose(res, [[1.6]], rtol=0)
+
+@image_comparison(baseline_images=['delaunay-1d-interp'], extensions=['png'])
+def test_1d_plots():
+    x_range = slice(0.25,9.75,20j)
+    x = np.mgrid[x_range]
+    ax = plt.gca()
+    for y in xrange(2,10,2):
+        plt.plot(x, ref_interpolator[x_range,y:y:1j])
+    ax.set_xticks([])
+    ax.set_yticks([])