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Received: 2003-02-27

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

http://doi.org/10.1631/jzus.2004.0343


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


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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.

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author="ZHENG Zhi-hao, WANG Guo-zhao",
journal="Journal of Zhejiang University Science A",
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pages="343-349",
year="2004",
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TY - JOUR
T1 - PH-spline approximation for Bézier curve and rendering offset
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A1 - WANG Guo-zhao
J0 - Journal of Zhejiang University Science A
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2004.0343


Abstract: 
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

Reference

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[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.

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