Complete characterization of the regions of C2C2 and C3C3 convergence of combined ternary 4-point subdivision schemes

We present a 3-parameter combined ternary 4-point subdivision scheme that provides a unifying framework for several independent proposals appeared in the literature. For such a scheme we completely characterize the regions of C2C2 and C3C3 convergence, that is the sets of parameters that fulfill the necessary and sufficient conditions for C2C2 and C3C3 convergence, respectively. The identified region of C2C2 convergence improves a recent result obtained by other authors by considering only sufficient conditions for C2C2 convergence.