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.

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)
        mid_xpt, mid_ypt = mids[:,0], mids[:,1]

        return mid_xpt, mid_ypt