diff --git a/lib/matplotlib/projections/geo.py b/lib/matplotlib/projections/geo.py
index 926a22fa5de5..9f4730301761 100644
--- a/lib/matplotlib/projections/geo.py
+++ b/lib/matplotlib/projections/geo.py
@@ -269,24 +269,23 @@ def __init__(self, resolution):
             self._resolution = resolution
 
         def transform_non_affine(self, ll):
-            longitude = ll[:, 0:1]
-            latitude  = ll[:, 1:2]
+            longitude = ll[:, 0]
+            latitude = ll[:, 1]
 
             # Pre-compute some values
             half_long = longitude / 2.0
             cos_latitude = np.cos(latitude)
 
             alpha = np.arccos(cos_latitude * np.cos(half_long))
-            # Mask this array or we'll get divide-by-zero errors
-            alpha = ma.masked_where(alpha == 0.0, alpha)
-            # The numerators also need to be masked so that masked
-            # division will be invoked.
+            # Avoid divide-by-zero errors using same method as NumPy.
+            alpha[alpha == 0.0] = 1e-20
             # We want unnormalized sinc.  numpy.sinc gives us normalized
-            sinc_alpha = ma.sin(alpha) / alpha
+            sinc_alpha = np.sin(alpha) / alpha
 
-            x = (cos_latitude * ma.sin(half_long)) / sinc_alpha
-            y = (ma.sin(latitude) / sinc_alpha)
-            return np.concatenate((x.filled(0), y.filled(0)), 1)
+            xy = np.empty_like(ll, float)
+            xy[:, 0] = (cos_latitude * np.sin(half_long)) / sinc_alpha
+            xy[:, 1] = np.sin(latitude) / sinc_alpha
+            return xy
         transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
 
         def transform_path_non_affine(self, path):