This paper provides a general formula for the dimension of spline space over general planar T-meshes (having concave corners or holes) by using the smoothing cofactor-conformality method. We introduce a new notion, the diagonalizable T-mesh, where the dimension formula is only associated with the topological information of the T-mesh. A necessary and sufficient condition for characterization of the diagonalizable T-mesh is also provided. By this new notion, we obtain some new dimension results for the spline spaces over T-meshes.
Li, X., & Deng, J. (2016). On the dimension of spline spaces over T-meshes with smoothing cofactor-conformality method. Computer Aided Geometric Design, 41, 76–86. https://doi.org/10.1016/j.cagd.2015.12.002