Curvature approximation of circular arcs by low-degree parametric polynomials
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Boštjan Kovač
und
Emil Žagar
Abstract
In this paper some new methods for curvature approximation of circular arcs by low-degree Bézier curves are presented. Interpolation by geometrically continuous (G1) parametric polynomials is considered. All derived approximants are given explicitly and are therefore practically applicable. Moreover, obtained results indicate that G1 biarcs with at least G1 continuity at the junction have smaller curvature error as parametric polynomial counterparts of the same degree. It is also shown that all considered methods provide optimal asymptotic approximation order.
Acknowledgment
The authors are very grateful to the anonymous referees for their valuable suggestions which improved the paper.
References
[1] Y.J. Ahn and H.O. Kim, Approximation of circular arcs by Bézier curves, J. Comput. Appl. Math. 81 (1997), 145–163.10.1016/S0377-0427(97)00037-XSuche in Google Scholar
[2] T. Dokken, M. Dæhlen, T. Lyche, and K. Mørken, Good approximation of circles by curvature-continuous Bézier curves, Comput. Aided Geom. Design7 (1990), 33–41, Curves and surfaces in CAGD ’89 (Oberwolfach, 1989).10.1016/0167-8396(90)90019-NSuche in Google Scholar
[3] L. Fang, Circular arc approximation by quintic polynomial curves, Comput. Aided Geom. Design15 (1998), 843–861.10.1016/S0167-8396(98)00019-3Suche in Google Scholar
[4] M. Goldapp, Approximation of circular arcs by cubic polynomials, Comput. Aided Geom. Design8 (1991), 227–238.10.1016/0167-8396(91)90007-XSuche in Google Scholar
[5] J.A. Gregory, Mathematical methods in computer aided geometric design, Academic Press Professional, Inc., 1989, pp.353–371.10.1016/B978-0-12-460515-2.50028-7Suche in Google Scholar
[6] S. Hur and T. Kim, The best G1 cubic and G2 quartic Bézier approximations of circular arcs, J. Comput. Appl. Math. 236 (2011), 1183–1192.10.1016/j.cam.2011.08.002Suche in Google Scholar
[7] G. Jaklič and E. Žagar, Curvature variation minimizing cubic Hermite interpolants, Appl. Math. Comput. 218 (2011), 3918–3924.10.1016/j.amc.2011.09.039Suche in Google Scholar
[8] Z. Liu, J.Q. Tan, X.Y. Chen, and L. Zhang, An approximation method to circular arcs, Appl. Math. Comp. 219 (2012), 1306–1311.10.1016/j.amc.2012.07.038Suche in Google Scholar
© 2016 by Walter de Gruyter Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Research Article
- Qualitative analysis and numerical solution of burgers’ equation via B-spline collocation with implicit euler method on piecewise uniform mesh
- Research Article
- Curvature approximation of circular arcs by low-degree parametric polynomials
- Research Article
- Error analysis of finite element and finite volume methods for some viscoelastic fluids
- Research Article
- A priori error analysis for optimal distributed control problem governed by the first order linear hyperbolic equation: hp-streamline diffusion discontinuous galerkin method
Artikel in diesem Heft
- Frontmatter
- Research Article
- Qualitative analysis and numerical solution of burgers’ equation via B-spline collocation with implicit euler method on piecewise uniform mesh
- Research Article
- Curvature approximation of circular arcs by low-degree parametric polynomials
- Research Article
- Error analysis of finite element and finite volume methods for some viscoelastic fluids
- Research Article
- A priori error analysis for optimal distributed control problem governed by the first order linear hyperbolic equation: hp-streamline diffusion discontinuous galerkin method
