return points defining a refined triangulation obtained by bisection of all edges
        in the triangulation connected to any of the vertices in the list provided

def midpoint_refine_triangulation_by_vertices(self, vertices):
        """
        return points defining a refined triangulation obtained by bisection of all edges
        in the triangulation connected to any of the vertices in the list provided
        """

        mlons, mlats = self.segment_midpoints_by_vertices(vertices=vertices)

        lonv1 = np.concatenate((self.lons, mlons), axis=0)
        latv1 = np.concatenate((self.lats, mlats), axis=0)

        return lonv1, latv1