The Representation of Circular Arc by Using Rational Cubic Timmer Curve-Reference-Cited by-同舟云学术

The Representation of Circular Arc by Using Rational Cubic Timmer Curve

Published:2014 Issue: Volume:2014 Page:1-6
ISSN:1024-123X
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Abbas Muhammad¹²^ORCID,Ramli Norhidayah²^ORCID,Majid Ahmad Abd.²,Ali Jamaludin Md.²

Affiliation:

1. Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan

2. School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

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 than4π/3andπ, 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.

Funder

Universiti Sains Malaysia

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2014/408492.pdf

Reference17 articles.

1. Rational cubic circular arcs and their application in CAD

2. Accurate parametrization of conics by NURBS

3. Higher order Bézier circles

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