diff --git a/lib/mpl_toolkits/mplot3d/art3d.py b/lib/mpl_toolkits/mplot3d/art3d.py
index 6c7a97b75cc1..9856138b2758 100644
--- a/lib/mpl_toolkits/mplot3d/art3d.py
+++ b/lib/mpl_toolkits/mplot3d/art3d.py
@@ -866,15 +866,21 @@ def do_3d_projection(self, renderer=None):
             else:
                 cedge = cedge.repeat(len(xyzlist), axis=0)
 
-        # sort by depth (furthest drawn first)
-        z_segments_2d = sorted(
-            ((self._zsortfunc(zs), np.column_stack([xs, ys]), fc, ec, idx)
-             for idx, ((xs, ys, zs), fc, ec)
-             in enumerate(zip(xyzlist, cface, cedge))),
-            key=lambda x: x[0], reverse=True)
-
-        zzs, segments_2d, self._facecolors2d, self._edgecolors2d, idxs = \
-            zip(*z_segments_2d)
+        if xyzlist:
+            # sort by depth (furthest drawn first)
+            z_segments_2d = sorted(
+                ((self._zsortfunc(zs), np.column_stack([xs, ys]), fc, ec, idx)
+                 for idx, ((xs, ys, zs), fc, ec)
+                 in enumerate(zip(xyzlist, cface, cedge))),
+                key=lambda x: x[0], reverse=True)
+
+            _, segments_2d, self._facecolors2d, self._edgecolors2d, idxs = \
+                zip(*z_segments_2d)
+        else:
+            segments_2d = []
+            self._facecolors2d = np.empty((0, 4))
+            self._edgecolors2d = np.empty((0, 4))
+            idxs = []
 
         if self._codes3d is not None:
             codes = [self._codes3d[idx] for idx in idxs]
diff --git a/lib/mpl_toolkits/tests/test_mplot3d.py b/lib/mpl_toolkits/tests/test_mplot3d.py
index 89c3ba63acd0..990509c2c4b4 100644
--- a/lib/mpl_toolkits/tests/test_mplot3d.py
+++ b/lib/mpl_toolkits/tests/test_mplot3d.py
@@ -233,6 +233,8 @@ def test_scatter3d():
     x = y = z = np.arange(10, 20)
     ax.scatter(x, y, z, c='b', marker='^')
     z[-1] = 0  # Check that scatter() copies the data.
+    # Ensure empty scatters do not break.
+    ax.scatter([], [], [], c='r', marker='X')
 
 
 @mpl3d_image_comparison(['scatter3d_color.png'])
@@ -625,6 +627,14 @@ def test_poly_collection_2d_to_3d_empty():
     assert isinstance(poly, art3d.Poly3DCollection)
     assert poly.get_paths() == []
 
+    fig, ax = plt.subplots(subplot_kw=dict(projection='3d'))
+    ax.add_artist(poly)
+    minz = poly.do_3d_projection()
+    assert np.isnan(minz)
+
+    # Ensure drawing actually works.
+    fig.canvas.draw()
+
 
 @mpl3d_image_comparison(['poly3dcollection_alpha.png'])
 def test_poly3dcollection_alpha():