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 centroid_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
        """

        triangles = self.identify_vertex_triangles(vertices)

        return self.centroid_refine_triangulation_by_triangles(triangles)