Table of Contents
ISRN Computer Graphics
Volume 2013, Article ID 434213, 8 pages
http://dx.doi.org/10.1155/2013/434213
Research Article

The Quaternary Interpolating Scheme for Geometric Design

1Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
2Centre for Undergraduate Studies, University of the Punjab, Lahore 54590, Pakistan

Received 18 February 2013; Accepted 27 March 2013

Academic Editors: A. Castelo, C. Cusano, F. Giannini, C. Joslin, G. Patanè, and C.-M. Wang

Copyright © 2013 Shahid S. Siddiqi and Muhammad Younis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A novel 4-point interpolating subdivision scheme is presented, which generates the family of limiting curves and its limiting function has support on . It behaves better than classical 4-point binary and ternary schemes with the same approximation order in many aspects that it has smaller support size, higher smoothness, and is computationally more efficient. The proposed nonstationary scheme can reproduce the functions of linear spaces spanned by for . Moreover, some examples are illustrated to show that the proposed scheme can also reproduce asteroids, cardioids, and conic sections as well.