The representation of circular arc by using rational cubic Timmer curve
type: Item
instance of: scholarly article
title: The representation of circular arc by using rational cubic Timmer curve
zbMATH Open document ID: 1407.65024
DOI: 10.1155/2014/408492
author: Muhammad Abbas
author: Norhidayah Ramli
author: Ahmad Abd. Majid
author: Jamaludin Md. Ali
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: 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 \(4 \pi / 3\) and \(\pi\), 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.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 7016370
Wikidata QID: Q59066858
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/408492
OpenAlex ID: W2016431084
cites work: Q4178157
cites work: Higher order Bézier circles
cites work: A rational quartic Bézier representation for conics
cites work: The rational cubic Bézier representation of conics
cites work: Necessary and sufficient conditions for rational quartic representation of conic sections
cites work: Approximating conic sections by constrained Bézier curves of arbitrary degree
cites work: Approximation of circular arcs by Bézier curves
cites work: An approximation of circular arcs by quartic Bézier curves
cites work: Approximation of conic sections by curvature continuous quartic Bézier curves
cites work: Rational cubic/quartic Said-Ball conics
cites work: A generalized Ball curve and its recursive algorithm
description: scientific article; zbMATH DE number 7016370