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Approximation Theory and its Applications

, Volume 12, Issue 4, pp 67–80 | Cite as

Wave recursive interpolation

  • Cui Zhenwen
Article
  • 2 Downloads

Abstract

In this paper it is studied that the generated theory of wave recursive inter polation of uniform T-subdivision scheme include wave parameter.

The paper analyses the convergence of sequences of control polygons produced by wave recursive inter polation T-subdivision scheme of the form
$$\left\{ {\begin{array}{*{20}c} {P_{Tm}^{k + 1} = P_m^h ,} \\ {P_{Tm + j}^{k + 1} \left( \beta \right) = \sum\limits_{i = 1}^k {\left( {P_{m - i + 1}^k a_{i,j} \left( \beta \right) + P_{m + i}^k a_{i,T - j} \left( \beta \right)} \right)} } \\ \end{array} } \right.$$
, j=1,2,...,T−1; m=0,1,...,nTk; k=0,1,2,.... and differentiability of the limit curve.

Keywords

Limit Function Wave Parameter Subdivision Scheme Limit Curve Bernstein Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Qi Dongxu, Liang Zhenshen and Ma Siliang, Graph and Computer Explore. Jilin University Press. 1989.Google Scholar
  2. [2]
    Catmull, E., and Clark, J., Recursively Generated B-spline Surfaces an Arbitrary Topological Meshes. Comput Aided Design. 10 (1978) 350–355.CrossRefGoogle Scholar
  3. [3]
    Sato, M., Recursive Interpolation Science on Form, S. Ishizaka (eds.), KTK Scientific Publishers, Tokoy, (1987).Google Scholar
  4. [4]
    Dyn, N., Gregory, J. A. and Leven, D., a 4-point Interpolatory Subdivision Scheme for Curve Design. Comput. Aided. Geom. Disign, 4 (1987) 257–268.MATHCrossRefGoogle Scholar
  5. [5]
    Xing Liping and Qi Dongxu, A Recursive Subdivision Method Simulating Terrain, International Conference Proceedings Pacific Graphics’94/CADDM’94, Aug. 26–29, 1994.Google Scholar
  6. [6]
    Xing Liping, Natural Phenomena Modelling and Iterative Generation of Fractal, Jilin University thesis of doctor, 1992.Google Scholar
  7. [7]
    Cavaretta, A. S., Dahmen, W. and Micchelli, C. A., Stationary Subdivision, Memoir of Amer. Math. Soc., 93 (1991), 1–186.MathSciNetGoogle Scholar
  8. [8]
    Dyn, N., Gregory, J. A. and Leven, D., Analysis of Uniform Binary Subdivision Scheme for Curve Design Constructive Approx., 7 (1991) 127–147.MATHGoogle Scholar

Copyright information

© Springer 1996

Authors and Affiliations

  • Cui Zhenwen
    • 1
  1. 1.Department of MathematicsHenan Normal UniversityXinxian, HenanP. R. China

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