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Mathematical Problems in Engineering
Volume 2014, Article ID 408492, 6 pages
http://dx.doi.org/10.1155/2014/408492
Research Article

The Representation of Circular Arc by Using Rational Cubic Timmer Curve

1Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
2School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

Received 24 June 2013; Accepted 12 December 2013; Published 16 January 2014

Academic Editor: Metin O. Kaya

Copyright © 2014 Muhammad Abbas et al. 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

In CAD/CAM systems, rational polynomials, in particular the Bézier or NURBS forms, are useful to approximate the circular arcs. In this paper, a new representation method by means of rational cubic Timmer (RCT) curves is proposed to effectively represent a circular arc. The turning angle of a rational cubic Bézier and rational cubic Ball circular arcs without negative weight is still not more than and , respectively. The turning angle of proposed approach is more than Bézier and Ball circular arcs with easier calculation and determination of control points. The proposed method also provides the easier modification in the shape of circular arc showing in several numerical examples.