Shape-Controlled Ternary Interpolating Subdivision Scheme Based on Approximating Subdivision

Abstract

In this paper a shape-controlled interpolating subdivision scheme is presented. It is derived by directly performing operations on geometric rules on approximating subdivision. The behavior of the limit curve produced by the proposed subdivision scheme is analyzed by the Laurent polynomial and attains C2 degree of smoothness. Furthermore, a non-uniform shape-controlled subdivision with shape control parameters is introduced. It allows a different tension value for every edge of the original control polygon.