A family of univariate ternary subdivision schemes with 5 parameters

Abstract

In this paper, we propose an efficient strategy for the construction of a family of ternary subdivision schemes with five parameters. These five parameters allow us to increase the choices when drawing and designing different models from the same initial control points. Moreover, by choosing appropriate values of parameters, we can get many existing ternary approximating subdivision schemes. Some of the existing ternary interpolatory and many new ternary approximating/interpolatory subdivision schemes with arbitrary order of regularities can also be obtained.