Full Text:   <2572>

CLC number: TP391

On-line Access: 

Received: 2003-02-27

Revision Accepted: 2003-07-07

Crosschecked: 0000-00-00

Cited: 1

Clicked: 4824

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.3 P.343-349


PH-spline approximation for Bézier curve and rendering offset

Author(s):  ZHENG Zhi-hao, WANG Guo-zhao

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

Corresponding email(s):   mathzzh@eyou.com

Key Words:  PH-spline, Bé, zier curve, Offset, Approximation, Error

Share this article to: More

ZHENG Zhi-hao, WANG Guo-zhao. PH-spline approximation for Bézier curve and rendering offset[J]. Journal of Zhejiang University Science A, 2004, 5(3): 343-349.

@article{title="PH-spline approximation for Bézier curve and rendering offset",
author="ZHENG Zhi-hao, WANG Guo-zhao",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T PH-spline approximation for Bézier curve and rendering offset
%A ZHENG Zhi-hao
%A WANG Guo-zhao
%J Journal of Zhejiang University SCIENCE A
%V 5
%N 3
%P 343-349
%@ 1869-1951
%D 2004
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2004.0343

T1 - PH-spline approximation for Bézier curve and rendering offset
A1 - ZHENG Zhi-hao
A1 - WANG Guo-zhao
J0 - Journal of Zhejiang University Science A
VL - 5
IS - 3
SP - 343
EP - 349
%@ 1869-1951
Y1 - 2004
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2004.0343

In this paper, a G1, C1, C2 PH-spline is employed as an approximation for a given ;zier curve within error bound and further renders offset which can be regarded as an approximate offset to the ;zier curve. The errors between PH-spline and the ;zier curve, the offset to PH-spline and the offset to the given ;zier curve are also estimated. A new algorithm for constructing offset to the ;zier curve is proposed.

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


[1] Bercovier, M., Jacobi, A., 1994. Minimization, constraints and composite Bézier curves.Computer Aided Geometric Design,11:533-563.

[2] Choi, H., Han, C.Y., 1999. Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves.Computer-Aided Design,31:59-72.

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

[4] Farouki, R.T., 1990. Pythagorean-Hodograph Curve in Practical use. IBM Research Report.

[5] Farouki, R.T., 1994. The conformal mapZ

[6] Hoschek, J., Wissel, N., 1988. Optimal approximation conversion of spline curve and spline approximation of offset curves.Computer-Aided Design,20(8):475-483.

[7] Klass, R., 1983. An offset spline approximation for plane cubic spline.Computer Aided Design,15(4):297-299.

[8] Li, Y.M., 1998. Curve offsetting base on Legendre series.Computer Aided Geometric Design,12:711-720.

[9] Lü, W., 1995. Offset-rational parametric plane curves.Computer Aided Geometric Design,12:601-616.

[10] Moon, H.P., Farouki, R.T., 2001. Construction and shape analysis of PH quintic Hermite interpolants.Computer Aided Geometric Design,18:93-115.

[11] Tiller, W., Hanson, E.G., 1984. Offsets of dimensional profiles.IEEE Compute Graph & Application,l4:36-46.

Open peer comments: Debate/Discuss/Question/Opinion


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 - 2024 Journal of Zhejiang University-SCIENCE