Point control of the interpolating curve with a rational cubic spline

被引：23

作者：

Bao, Fangxun ^{[1
]}

Sun, Qinghua ^{[1
]}

Duan, Qi ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

来源：

JOURNAL OF VISUAL COMMUNICATION AND IMAGE REPRESENTATION | 2009年 / 20卷 / 04期

关键词：

Rational spline; Value control; Convexity control; Error estimate; Cubic interpolation; Curve design; Local shape control; Inflection point control; FUNCTION VALUES;

D O I：

10.1016/j.jvcir.2009.03.003

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A rational cubic spline, a kind of smoothness interpolation with quadratic denominator, is constructed using the values of a function only. In order to meet the needs of practical design, an interpolation technique is employed to control the shape of curves. The method of value control, inflection-point control and convexity control of the interpolation at a point is also developed. The advantage of this new control method is that it can be applied to modify the local shape of an interpolating curve by selecting suitable parameters simply. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：275 / 280

页数：6

共 19 条

[1] PRESERVING CONVEXITY USING PIECEWISE CUBIC INTERPOLATION [J].

BRODLIE, KW ;

BUTT, S .

COMPUTERS & GRAPHICS, 1991, 15 (01) :15-23

[2]

Dierckx P., 1989, Computer-Aided Geometric Design, V6, P279, DOI 10.1016/0167-8396(89)90029-0

[3] Weighted rational cubic spline interpolation and its application [J].

Duan, Q ;

Djidjeli, K ;

Price, WG ;

Twizell, EH .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 117 (02) :121-135

[4] A rational cubic spline based on function values [J].

Duan, Q ;

Djidjeli, K ;

Price, WG ;

Twizell, EH .

COMPUTERS & GRAPHICS, 1998, 22 (04) :479-486

[5] A new C2 rational interpolation based on function values and constrained control of the interpolant curves [J].

Duan, Q ;

Wang, LQ ;

Twizell, EH .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 161 (01) :311-322

[6] The approximation properties of some rational cubic splines [J].

Duan, Q ;

Djidjeli, K ;

Price, WG ;

Twizell, EH .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1999, 72 (02) :155-166

[7] A novel approach to the convexity control of interpolant curves [J].

Duan, Q ;

Wang, LQ ;

Twizell, EH .

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 2003, 19 (10) :833-845

[8] Error estimation of a kind of rational spline [J].

Duan, Qi ;

Zhang, Huanling ;

Zhang, Yunfeng ;

Twizell, E. H. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 200 (01) :1-11

[9]

Foley T. A., 1986, Computer-Aided Geometric Design, V3, P281, DOI 10.1016/0167-8396(86)90004-X

[10]

FRITSCH FN, 1984, SIAM J SCI STAT COMP, V5, P303

← 1 2 →