diff --git a/doc/api/api_changes/2017-07-14-IT_qhull_large_offset.rst b/doc/api/api_changes/2017-07-14-IT_qhull_large_offset.rst
new file mode 100644
index 000000000000..c60c56c0ff6b
--- /dev/null
+++ b/doc/api/api_changes/2017-07-14-IT_qhull_large_offset.rst
@@ -0,0 +1,10 @@
+Improved Delaunay triangulations with large offsets
+```````````````````````````````````````````````````
+
+Delaunay triangulations now deal with large x,y offsets in a better
+way. This can cause minor changes to any triangulations calculated
+using Matplotlib, i.e. any use of `matplotlib.tri.Triangulation` that
+requests that a Delaunay triangulation is calculated, which includes
+`matplotlib.pyplot.tricontour`, `matplotlib.pyplot.tricontourf`,
+`matplotlib.pyplot.tripcolor`, `matplotlib.pyplot.triplot`,
+`mlab.griddata` and `mpl_toolkits.mplot3d.plot_trisurf`.
diff --git a/lib/matplotlib/tests/baseline_images/test_triangulation/tri_smooth_contouring.png b/lib/matplotlib/tests/baseline_images/test_triangulation/tri_smooth_contouring.png
index d6d2b993fd80..80ea47079014 100644
Binary files a/lib/matplotlib/tests/baseline_images/test_triangulation/tri_smooth_contouring.png and b/lib/matplotlib/tests/baseline_images/test_triangulation/tri_smooth_contouring.png differ
diff --git a/lib/matplotlib/tests/baseline_images/test_triangulation/tri_smooth_gradient.png b/lib/matplotlib/tests/baseline_images/test_triangulation/tri_smooth_gradient.png
index 52b0d21362e4..956eadf30c59 100644
Binary files a/lib/matplotlib/tests/baseline_images/test_triangulation/tri_smooth_gradient.png and b/lib/matplotlib/tests/baseline_images/test_triangulation/tri_smooth_gradient.png differ
diff --git a/lib/matplotlib/tests/test_triangulation.py b/lib/matplotlib/tests/test_triangulation.py
index 18969afacf39..6dc2078f1384 100644
--- a/lib/matplotlib/tests/test_triangulation.py
+++ b/lib/matplotlib/tests/test_triangulation.py
@@ -745,7 +745,7 @@ def z(x, y):
 
 
 @image_comparison(baseline_images=['tri_smooth_contouring'],
-                  extensions=['png'], remove_text=True)
+                  extensions=['png'], remove_text=True, tol=0.07)
 def test_tri_smooth_contouring():
     # Image comparison based on example tricontour_smooth_user.
     n_angles = 20
@@ -786,8 +786,7 @@ def z(x, y):
 
 
 @image_comparison(baseline_images=['tri_smooth_gradient'],
-                  extensions=['png'], remove_text=True,
-                  tol=0.03 if on_win else 0)
+                  extensions=['png'], remove_text=True, tol=0.035)
 def test_tri_smooth_gradient():
     # Image comparison based on example trigradient_demo.
 
@@ -1123,3 +1122,14 @@ def test_internal_cpp_api():
     with pytest.raises(ValueError) as excinfo:
         trifinder.find_many([0], [0, 1])
     excinfo.match(r'x and y must be array_like with same shape')
+
+
+def test_qhull_large_offset():
+    # github issue 8682.
+    x = np.asarray([0, 1, 0, 1, 0.5])
+    y = np.asarray([0, 0, 1, 1, 0.5])
+
+    offset = 1e10
+    triang = mtri.Triangulation(x, y)
+    triang_offset = mtri.Triangulation(x + offset, y + offset)
+    assert len(triang.triangles) == len(triang_offset.triangles)
diff --git a/src/qhull_wrap.c b/src/qhull_wrap.c
index 38779441b4fd..e71afc7e3700 100644
--- a/src/qhull_wrap.c
+++ b/src/qhull_wrap.c
@@ -108,6 +108,8 @@ delaunay_impl(int npoints, const double* x, const double* y,
     PyArrayObject* neighbors = NULL;
     int* triangles_ptr;
     int* neighbors_ptr;
+    double x_mean = 0.0;
+    double y_mean = 0.0;
 
     QHULL_LIB_CHECK
 
@@ -119,10 +121,18 @@ delaunay_impl(int npoints, const double* x, const double* y,
         goto error_before_qhull;
     }
 
+    /* Determine mean x, y coordinates. */
+    for (i = 0; i < npoints; ++i) {
+        x_mean += x[i];
+        y_mean += y[i];
+    }
+    x_mean /= npoints;
+    y_mean /= npoints;
+
     /* Prepare points array to pass to qhull. */
     for (i = 0; i < npoints; ++i) {
-        points[2*i  ] = x[i];
-        points[2*i+1] = y[i];
+        points[2*i  ] = x[i] - x_mean;
+        points[2*i+1] = y[i] - y_mean;
     }
 
     /* qhull expects a FILE* to write errors to. */