Journal of the Korean Society for Industrial and Applied Mathematics

  • 제13권4호
  • /
  • Pages.307-314
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  • 2009
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
권호 표지

QUATNARY APPROXIMATING 4-POINT SUBDIVISION SCHEME

  • Ko, Kwan-Pyo (DIVISION OF COMPUTER & INFORMATION, DONGSEO UNIVERSITY)
  • 투고 : 2009.10.13
  • 심사 : 2009.12.01
  • 발행 : 2009.12.25
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초록

In this work, we introduce a new quatnary approximating subdivision scheme for curve and deal with its analysis (convergence and regularity) using Laurent polynomials method. We also discuss various properties, such as approximation order and support of basic limit function.

키워드

참고문헌

  1. N. Aspert, Non-linear subdivision of univariate signals and discrete surfaces, EPFL thesis, (2003).
  2. N. Cavaretta, W. Dahmen and C. Micchelli, Stationary Subdivision, Memoirs of the AMS., (1991).
  3. G. Deslauriers and S. Dubuc, Symmetric iterative interpolation processes, Constr. Approx. 5 (1989), 49-68. https://doi.org/10.1007/BF01889598
  4. S. Dubuc, Intepolation through an iterative scheme, J.Math.Anal and Appl. 114 (1986), 185-204. https://doi.org/10.1016/0022-247X(86)90077-6
  5. N. Dyn, Subdivision schemes in computer aided geometric design, Advances in Numerical Analysis, Subdivision algorithms and radial functions,W.A.Light (ed.), Oxford University Press, (1992), 36-104.
  6. M. Hassan, Multiresolution in Geometric Modelling: Subdivision Mark Points and Ternary Subdivision, Ph.D Thesis, Computer Laboratory, University of Cambridge, (2005).
  7. M. Hassan, I. Ivrissimitzis, N. Dodgson and M. Sabin, An Interpolating 4-point $C^2$ ternary stationary subdivision scheme, CAGD 19(1) (2002), 1-18.
  8. K. P. Ko, B. G. Lee and G. J. Yoon, A study on the mask of interpolatory symmetric subdivision schemes, Applied Mathematics and Computations, 187 (2007), 609-621. https://doi.org/10.1016/j.amc.2006.08.089
  9. K. P. Ko, B. G. Lee and G. J. Yoon, A ternary four-point approximating subdivision scheme, Applied Mathematics and Computation, 190 (2007), 1563-1573. https://doi.org/10.1016/j.amc.2007.02.032
  10. K. P. Ko, B. G. Lee and G. J. Yoon, A (2n+4)-point symmetric subdivision scheme with two parameters, preprint.