Discrete Smooth Interpolation

in: ACM Transactions on Graphics, 8:2 (121--144)

Abstract

Interpolation of a function ƒ (.) known at some data points of RP is a common problem. Many computer applications (e.g., automatic contouring) need to perform interpolation only at the nodes of a given grid. Whereas most classical methods solve the problem by finding a function defined everywhere, the proposed method avoids explicitly computing such a function and instead produces values only at the grid points. For two-dimensional regular grids, a special case of this method is identical to the Briggs method (see “Machine Contouring Using Minimum Curvature,” Geophysics 17, 1 (1974)), while another special case is equivalent to a discrete version of thin plate splines (see J. Duchon, Fonctions Splines du type Plaque Mince en Dimention 2, Séminaire d'analyse numérique, n 231, U.S.M.G., Grenoble, 1975; and J. Enriquez, J. Thomann, and M. Goupillot, Application of bidimensional spline functions to geophysics, Geophysics 48, 9 (1983)).

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BibTeX Reference

@ARTICLE{Mallet89,
    author = { Mallet, Jean-Laurent },
     title = { Discrete Smooth Interpolation },
   journal = { ACM Transactions on Graphics },
    volume = { 8 },
    number = { 2 },
   chapter = { 0 },
      year = { 1989 },
     pages = { 121--144 },
       doi = { 10.1145/62054.62057 },
  abstract = { Interpolation of a function ƒ (.) known at some data points of RP is a common problem. Many computer applications (e.g., automatic contouring) need to perform interpolation only at the nodes of a given grid. Whereas most classical methods solve the problem by finding a function defined everywhere, the proposed method avoids explicitly computing such a function and instead produces values only at the grid points. For two-dimensional regular grids, a special case of this method is identical to the Briggs method (see “Machine Contouring Using Minimum Curvature,” Geophysics 17, 1 (1974)), while another special case is equivalent to a discrete version of thin plate splines (see J. Duchon, Fonctions Splines du type Plaque Mince en Dimention 2, Séminaire d'analyse numérique, n 231, U.S.M.G., Grenoble, 1975; and J. Enriquez, J. Thomann, and M. Goupillot, Application of bidimensional spline functions to geophysics, Geophysics 48, 9 (1983)). }
}