호남수학학술지 (Honam Mathematical Journal)

  • 제27권4호
  • /
  • Pages.665-672
  • /
  • 2005
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지

REGULARITY CRITERIA FOR TERNARY INTERPOLATORY SUBDIVISION

  • JEON, MYUNGJIN (Department of Computer aided Mathematical Information Science Semyung University) ;
  • CHOI, GUNDON (Department of Mathematics Duksung Women's University)
  • 투고 : 2005.09.21
  • 심사 : 2005.11.02
  • 발행 : 2005.12.25
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초록

By its simplicity and efficiency, subdivision is a widely used technique in computer graphics, computer aided design and data compression. In this paper we prove a regularity theorem for ternary interpolatory subdivision scheme that can be applied to non-stationary subdivision. This theorem converts the convergence of the limit curve of a ternary interpolatory subdivision to the analysis of the rate of the contraction of differences of the polygons.

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참고문헌

  1. The College Mathematics Journal v.30-2 The trinomial triangle Chappell, J.;Osler, T.
  2. Ternary and 3-point univariate subdivision schemes, University of Cambridge Computer Laboratory Technical Report No. 520 Hassan, M.F.;Dodgson, N.A.
  3. Comput. Aided Geom. Design v.19 An interpolating 4-point C2 ternary stationary subdivision scheme Hassan, M.F.;Ivrissimitzis, I.P.;Dodgson, N.A.;Sabin, M.A.
  4. J. of Appl. Math. and Computing v.18 no.1-2 Ternary univariate curvature-preserving subdivision Jeon, M.;Han, D.;Park, K.;Choi, G.
  5. Comput. Aided Geom. Design v.13 A variational approach to subdivision Kobbelt, L.
  6. Applied and computational harmonic analysis v.5 Using the Discrete Fourier Transform to Analyze the Convergence of Subdivision Schemes Kobbelt, L.
  7. J. of Integral Sequences v.6 Some formulas for the central trinomial and Motzkin numbers Romik, D.
  8. Advances in Multiresolution for Geometric Modelling Recent progress in subdivision - a survey Sabin, Malcolm
  9. Subdivision methods for geometric design Warren, Joe
  10. SIGGRAPH 2000 Course Notes Subdivision for Modeling and Animation Zorin, Denis;Schroder, Peter;DeRose, Tony;Kobbelt, Leif;Levin, Adi;Sweldens, Wim
  11. WolframMathWorld the web's most extensive mathmatics resource