implemented inverse transform for Mollweide axes

Author: lpsinger

lib/matplotlib/projections/geo.py

@@ -476,8 +476,16 @@ def __init__(self, resolution):
             self._resolution = resolution
 
         def transform_non_affine(self, xy):
-            # MGDTODO: Math is hard ;(
-            return xy
+            x = xy[:, 0:1]
+            y = xy[:, 1:2]
+
+            # from Equations (7, 8) of
+            # http://mathworld.wolfram.com/MollweideProjection.html
+            theta = np.arcsin(y / np.sqrt(2))
+            lon = (np.pi / (2 * np.sqrt(2))) * x / np.cos(theta)
+            lat = np.arcsin((2 * theta + np.sin(2 * theta)) / np.pi)
+
+            return np.concatenate((lon, lat), 1)
         transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
 
         def inverted(self):