Discrete smooth interpolation

@article{mallet:hal-04025873,
 abstract = {Interpolation of a function ƒ (.) known at some data points of R P 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)).},
 author = {Mallet, Jean-Laurent},
 doi = {10.1145/62054.62057},
 hal_id = {hal-04025873},
 hal_version = {v1},
 journal = {{ACM Transactions on Graphics}},
 month = {April},
 number = {2},
 pages = {121-144},
 publisher = {{Association for Computing Machinery}},
 title = {{Discrete smooth interpolation}},
 url = {https://hal.univ-lorraine.fr/hal-04025873},
 volume = {8},
 year = {1989}
}