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Bivariate interpolatory rational splines

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Abstract

Smoothing conditions in terms of Bézier coefficients of piecewise rational functions on an arbitrary triangulation are derived. This facilitates the solution of the problem of bivariate rational spline interpolation, with or without convexity constraints, particularly on the three and four-directional meshes. For such a triangulation, we also derive the conformality condition that a bivariate rationale spline function must satisfy, and we demonstrate the interpolation scheme with a low-degree example.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA

    C. K. Chui

  2. Department of Mathematics, Illinois Wesleyan University, 61702, Bloomington, IL, USA

    T. X. He

Authors
  1. C. K. Chui
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  2. T. X. He
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Additional information

Communicated by P. J. Laurent

The research of this author was supported by NSF Grant # DMS-92-06928.

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Chui, C.K., He, T.X. Bivariate interpolatory rational splines. Numer Algor 9, 277–291 (1995). https://doi.org/10.1007/BF02141592

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  • DOI: https://doi.org/10.1007/BF02141592

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