129
Views
4
CrossRef citations to date
0
Altmetric
Section A

Approximating of conic sections by DP curves with endpoint interpolation

&
Pages 1-14 | Received 17 Sep 2012, Accepted 24 Jan 2014, Published online: 14 Apr 2014

References

  • Y.J. Ahn and H.O. Kim, Approximation of circular arcs by Bézier curves, J. Comput. Appl. Math. 81 (1997), pp. 145–163. doi: 10.1016/S0377-0427(97)00037-X
  • Y.J. Ahn, Y.S. Kim, and Y.S. Shin, Approximation of circular arcs and offset curves by Bézier curves of high degree, J. Comput. Appl. Math. 167(2) (2004), pp. 405–416. doi: 10.1016/j.cam.2003.10.008
  • C. Aphirukmatakun and N. Dejdumrong, Multiple degree elevation and constrained multiple degree reduction for DP curves and surfaces, Comput. Math. Appl. 61(8) (2011), pp. 2296–2299. doi: 10.1016/j.camwa.2010.09.052
  • J.M. Carnicer and J.M. Peña, Shape preserving representations and optimality of the Bernstein basis, Adv. Comput. Math. 1 (1993) pp. 173–196. doi: 10.1007/BF02071384
  • S. Coons, Surfaces for computer aided design, Tech. Rep, MIT (1964). Available as AD 663 504 from the National Technical Information service, Springfield, VA 22161.
  • J. Delgado and J.M. Peña, Monotonicity preservation of some polynomial and rational representations, in Information Visualisation, E. Banissi and M. Sarfraz, eds., IEEE Computer Society, Los Alamitos, CA, 2002, pp. 57–62.
  • J. Delgado and J.M. Peña, A shape preserving representation with an evaluation algorithm of linear complexity, Comput. Aided Geom. Design 20 (2003), pp. 1–10. doi: 10.1016/S0167-8396(02)00190-5
  • T. Dokken, M. Daehlen, T. Lyche, and K. Mørken, Good approximation of circles by curvature-continuous Bézier curves, Comput. Aided Geom. Design 7 (1990), pp. 33–41. doi: 10.1016/0167-8396(90)90019-N
  • L. Fang, Circular arc approximation by quintic polynomial curves, Comput. Aided Geom. Design 15 (1998), pp. 843–861. doi: 10.1016/S0167-8396(98)00019-3
  • G. Farin, Curves and Surfaces for Computer Aided Geometric Design, 4th ed., Academic Press, San Diego, 1996.
  • M. Floater, High order approximation of conic sections by quadratic splines, Comput. Aided Geom. Design 12 (1995), pp. 617–637. doi: 10.1016/0167-8396(94)00037-S
  • M. Goldapp, Approximation of circular arcs by cubic polynomials, Comput. Aided Geom. Design 8 (1991), pp. 227–238. doi: 10.1016/0167-8396(91)90007-X
  • T.N.T. Goodman and H.B. Said, Shape-preserving properties of the generalized Ball Basis, Comput. Aided Geom. Design 8 (1991), pp. 115–121. doi: 10.1016/0167-8396(91)90037-C
  • J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design, AK Peters, Wellesley, 1993.
  • Q.-Q. Hu, Approximating conic sections by constrained Bézier curves of arbitrary degree, J. Comput. Appl. Math. 236(11) (2012), pp. 2813–2821. doi: 10.1016/j.cam.2012.01.017
  • S.R. Jiang and G.J. Wang, Conversion and evaluation for two types of parametric surfaces constructed by NTP bases, Comput. Math. Appl. 49(2–3) (2005), pp. 321–329. doi: 10.1016/j.camwa.2004.06.031
  • S.H. Kim and Y.J. Ahn, An approximation of circular arcs by quartic Bézier curves, Comput. Aided Des. 39(6) (2007), pp. 490–493. doi: 10.1016/j.cad.2007.01.004
  • E.T.Y. Lee, The rational Bézier representation for conics, in Geometric. Modeling: Algorithms and New Trends, G. Farin, ed., SIAM, Philadelphia, 1987, pp. 3–20.
  • R. Liming, Mathematics for Computer Graphics, Aero Publishers, Fallbrook, CA, 1979.
  • R. Liming, Practical Analytical Geometry with Application to Aircraft, Macmillan, London, 1944.
  • K. Mørken, Best approximation of circle segments by quadratic Bézier curves, in Curves and Surfaces, P.J. Laurent, A. Le Méhauté, and L.L. Schumaker, eds., Academic Press, New York, 1991.
  • J.M. Peña, On the optimal stability of bases of univariate functions, Numer. Math. 91(2) (2002), pp. 305–318. doi: 10.1007/s002110100327
  • J.M. Peña (ed.), Shape Preserving Representations in Computer Aided Geometric Design, Nova Science Publishers, Commack, NY, 1999.
  • V.V. Williams, Breaking the Coppersmith-Winograd barrier, preprint (2011).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.