On the dimension of splines spaces over T-meshes with smoothing cofactor-conformality method

Abstract: The present paper provides a general formula for the dimension of spline space over T-meshes using smoothing cofactor-conformality method. And we introduce a new notion, Diagonalizable T-mesh, over which the dimension formula is only associated with the topological information of the T-mesh. A necessary and sufficient condition for characterization a diagonalizable T-mesh is also provided. Using this technique, we find that the dimension is possible instable under the condition of [1] and we also provide a new correction theorem.