Full Text:   <1943>

CLC number: TP391

On-line Access: 

Received: 2006-03-20

Revision Accepted: 2006-05-21

Crosschecked: 0000-00-00

Cited: 0

Clicked: 4100

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.9 P.1561-1565

http://doi.org/10.1631/jzus.2006.A1561


Rational offset approximation of rational Bézier curves


Author(s):  CHENG Min, WANG Guo-jin

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   gjwang@hzcnc.com

Key Words:  Rational Bé, zier curve, Parametric speed, Offset, Rational approximation


CHENG Min, WANG Guo-jin. Rational offset approximation of rational Bézier curves[J]. Journal of Zhejiang University Science A, 2006, 7(9): 1561-1565.

@article{title="Rational offset approximation of rational Bézier curves",
author="CHENG Min, WANG Guo-jin",
journal="Journal of Zhejiang University Science A",
volume="7",
number="9",
pages="1561-1565",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A1561"
}

%0 Journal Article
%T Rational offset approximation of rational Bézier curves
%A CHENG Min
%A WANG Guo-jin
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 9
%P 1561-1565
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A1561

TY - JOUR
T1 - Rational offset approximation of rational Bézier curves
A1 - CHENG Min
A1 - WANG Guo-jin
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 9
SP - 1561
EP - 1565
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A1561


Abstract: 
The problem of parametric speed approximation of a rational curve is raised in this paper. offset curves are widely used in various applications. As for the reason that in most cases the offset curves do not preserve the same polynomial or rational polynomial representations, it arouses difficulty in applications. Thus approximation methods have been introduced to solve this problem. In this paper, it has been pointed out that the crux of offset curve approximation lies in the approximation of parametric speed. Based on the Jacobi polynomial approximation theory with endpoints interpolation, an algebraic rational approximation algorithm of offset curve, which preserves the direction of normal, is presented.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Chiang, C.S., Hoffmann, C.M., Lynch, R.E., 1991. How to Compute Offsets without Self-intersection. In: Silbermann, M.J., Tagare, D. (Eds.), Proceedings of SPIE Conference on Curves and Surfaces in Computer Vision and Graphics II, Boston, p.76-87.

[2] Cobb, E.S., 1984. Design of Sculptured Surfaces Using the B-spline Representation. Ph.D Thesis, University of Utah.

[3] Coquillart, S., 1987. Computing offsets of B-spline curves. Computer-Aided Design, 19(6):305-309.

[4] Elber, G., Cohen, E., 1991. Error bounded variable distance offset operator for free form curves and surfaces. International Journal of Computational Geometry & Applications, 1(1):67-78.

[5] Farouki, R.T., 1992. Pythagorean-hodograph Curves in Practical Use. In: Barnhill, R.E. (Ed.), Geometry Processing For Design and Manufacturing. SIAM, Philadelphia, p.3-33.

[6] Farouki, R.T., Neff, 1990. Analytic properties of plane offset curves. Computer Aided Geometric Design, 7(1-4):83-99.

[7] Farouki, R.T., Shah, S., 1996. Real-time CNC interpolators for Pythagorean hodograph curves. Computer Aided Geometric Design, 13(7):583-600.

[8] Hoschek, J., 1988. Spline approximation of offset curves. Computer Aided Geometric Design, 20(1):33-40.

[9] Lee, I.K., Kim, M.S., Elber, G., 1996. Planar curve offset based on circle approximation. Computer-Aided Design, 28(8):617-630.

[10] Lü, W., 1995. Offsets-rational parametric plane curves. Computer Aided Geometric Design, 12(6):601-616.

[11] Maekawa, T., 1999. An overview of offset curves and surfaces. Computer-Aided Design, 31(3):165-173.

[12] Pham, B., 1988. Offset approximation of uniform B-splines. Computer-Aided design, 20(8):471-474.

[13] Piegl, L.A., Tiller, W., 1999. Computing offsets of NURBS curves and surfaces. Computer-Aided Design, 31(2):147-156.

[14] Sederberg, T.W., Buehler, D.B., 1992. Offsets of Polynomial Bézier Curves: Hermite Approximation with Error Bounds. In: Lyche, T., Schumaker, L.L. (Eds.), Mathematical Methods in Computer Aided Geometric Design II. Academic Press, Boston, p.549-558.

[15] Szego, G., 1975. Orthogonal Polynomials (4th Ed.). Amer. Math. Soc., Providence, RI.

[16] Tiller, W., Hanson, E.G., 1984. Offsets of two-dimensional profiles. IEEE Comput. Graph. & Applic., 4(9):36-46.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2022 Journal of Zhejiang University-SCIENCE