The Representation of Circular Arc by Using Rational Cubic Timmer Curve

被引：12

作者：

Abbas, Muhammad ^{[1
,2
]}

Ramli, Norhidayah ^{[2
]}

Majid, Ahmad Abd. ^{[2
]}

Ali, Jamaludin Md. ^{[2
]}

机构：

[1] Univ Sargodha, Dept Math, Sargodha 40100, Pakistan

[2] Univ Sains Malaysia, Sch Math Sci, George Town 11800, Malaysia

来源：

MATHEMATICAL PROBLEMS IN ENGINEERING | 2014年 / 2014卷

关键词：

BEZIER; APPROXIMATION;

D O I：

10.1155/2014/408492

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In CAD/CAM systems, rational polynomials, in particular the Bezier 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 Bezier 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 Bezier 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.

引用

页数：6

共 17 条

[1] Approximation of circular arcs by Bezier curves [J].

Ahn, YJ ;

Kim, HO .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 81 (01) :145-163

[2] Approximation of conic sections by curvature continuous quartic Bezier curves [J].

Ahn, Young Joon .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (07) :1986-1993

[3]

Ali J.M., 1994, SAINS MALAYS, V23, P42

[4] Accurate parametrization of conics by NURBS [J].

Blanc, C ;

Schlick, C .

IEEE COMPUTER GRAPHICS AND APPLICATIONS, 1996, 16 (06) :64-71

[5] HIGHER-ORDER BEZIER CIRCLES [J].

CHOU, JJ .

COMPUTER-AIDED DESIGN, 1995, 27 (04) :303-309

[6] A rational quartic Bezier representation for conics [J].

Fang, L .

COMPUTER AIDED GEOMETRIC DESIGN, 2002, 19 (05) :297-312

[7]

Farin G., 2001, CURVES SURFACES CAGD

[8]

FAUX I.D., 1979, COMPUTATIONAL GEOMET

[9]

Guo-Jin Wang, 1992, Computer-Aided Geometric Design, V9, P447, DOI 10.1016/0167-8396(92)90043-O

[10] Necessary and sufficient conditions for rational quartic representation of conic sections [J].

Hu, Qian-Qian ;

Wang, Guo-Jin .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 203 (01) :190-208

← 1 2 →