A new subdivision method for bivariate splines on the four-directional mesh

We present a new bivariate subdivision scheme based on two generators of a four-directional spline space. In particular, we are dealing with piecewise linear, continuous splines, and with piecewise cubic, continuously differentiable splines. The subdivision schemes rely on a matrix mask of small support. In addition, we present some results on related quasi-interpolating operators, and on approximation order of the underlying shift-invariant spaces.