New Proof of Dimension Formula of Spline Spaces over T-Meshes via Smoothing Cofactors

Abstract

A T-mesh is basically a rectangular grid that allows T-junctions. Recently, Deng $etal$ introduced splines over T-meshes, which are generalizations of T-splines invented by Sederberg $etal$, and proposed a dimension formula based on the B-net method. In this paper, we derive an equivalent dimension formula in a different form with the smoothing cofactor method.