Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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.

Keywords

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

Subject

MATHEMATICS & COMPUTER SCIENCE, Computational Mathematics

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