Preprint Article Version 1 This version is not peer-reviewed

Shape Preservation of Tension Controlled Ternary 4-point Non-Stationary Interpolating Subdivision Scheme

Version 1 : Received: 10 August 2018 / Approved: 16 August 2018 / Online: 16 August 2018 (12:14:35 CEST)

How to cite: Pervez, K.; Shah, S.H. Shape Preservation of Tension Controlled Ternary 4-point Non-Stationary Interpolating Subdivision Scheme. Preprints 2018, 2018080282 (doi: 10.20944/preprints201808.0282.v1). Pervez, K.; Shah, S.H. Shape Preservation of Tension Controlled Ternary 4-point Non-Stationary Interpolating Subdivision Scheme. Preprints 2018, 2018080282 (doi: 10.20944/preprints201808.0282.v1).

Abstract

The aim of this work is to analyze and investigate the shape preserving properties of ternary 4-point non-stationary interpolating subdivision schemes constructed by Beccari et al. [1] with a tension parameter !k+1 which can reproducing exponential. Moreover, the conditions on the initial control points are developed that allow user to generate shape preserving limit curves after a nite number of subdivision steps and generalize these results in limiting case. Signicance of derived conditions are illustrated through graphs and the whole discussion is followed by examples.

Subject Areas

Ternary; subdivision scheme; Non-stationary, Tension controlled, shape preservation

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