Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-27T06:44:47.785Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximate conversion of Bézier curves

Published online by Cambridge University Press:  17 April 2009

Yungeom Park ,
U Jin Choi  and
Ha-Jine Kimn
Yungeom Park
Affiliation:
Department of Mathematics Korea AdvancedInstitute of Science and TechnologyGu-sung Dong, Yu-sung Gu Taejon 305-701 Republic of Korea
U Jin Choi
Affiliation:
Department of MathematicsKorea Advanced Institute of Science and TechnologyGu-sung Dong, Yu-sung Gu Taejon 305-701 Republic of Korea
Ha-Jine Kimn
Affiliation:
Department of Computer ScienceA-Jou UniversitySuwon Republic of Korea
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The methods for generating a polynomial Bézier approximation of degree n − 1 to an nth degree Bézier curve, and error analysis, are presented. The methods are based on observations of the geometric properties of Bézier curves. The approximation agrees at the two endpoints up to a preselected smoothness order. The methods allow a detailed error analysis, providing a priori bounds of the point-wise approximation error. The error analysis for other authors’ methods is also presented.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 1 , February 1995 , pp. 153 - 162
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Degen, W.L.F., ‘Best approximation of parametric curve by splines’, in Mathematical methods in computer aided design II, (Lyche, T. and Schumaker, L. L., Editors) (Academic Press, New York, 1992).Google Scholar
[2]Eck, M., ‘Degree reduction of Bézier curves’, Comput. Aided Geom. Design 10 (1993), 237–251.CrossRefGoogle Scholar
[3]Eisele, E., ‘Chebyshev approximation of planar curves by splines’, J. Approx. Theory 76 (1994), 133–148.CrossRefGoogle Scholar
[4]Farin, G., ‘Algorithms for rational Bézier curves’, Comput. Aided Design 15 (1983), 73–77.CrossRefGoogle Scholar
[5]Farin, G., Curves and surfaces for computer aided geometric design (Academic Press, New York, 1988).Google Scholar
[6]Forrest, A.R., ‘Interactive interpolation and approximation by Bézier polynomials’, Comput. Aided Design 22 (1988), 527–537.CrossRefGoogle Scholar
[7]Lachance, M.A., ‘Chebyshev economization for parametric surfaces’, Comput. Aided Geom. Design 5 (1988), 195–208.CrossRefGoogle Scholar
[8]Park, Y. and Choi, U.J., ‘Degree reduction of Bézier curves and its error analysis’, J. Austral. Math. Soc., Ser. B (to appear).Google Scholar
[9]Watkins, M.A. and Worsey, J.A., ‘Degree reduction of Bézier curves, Comput. Aided Des. 20 (1988), 398–405.CrossRefGoogle Scholar