def face_midpoints(self, simplices=None):
        """
        Identify the centroid of every simplex in the triangulation. If an array of
        simplices is given then the centroids of only those simplices is returned.
        """

        if type(simplices) == type(None):
            simplices = self.simplices

        mids = self.points[simplices].mean(axis=1)
        mids /= np.linalg.norm(mids, axis=1).reshape(-1,1)

        midlons, midlats = xyz2lonlat(mids[:,0], mids[:,1], mids[:,2])

        return midlons, midlats
Identify the centroid of every simplex in the triangulation. If an array of
        simplices is given then the centroids of only those simplices is returned.