On Some Recent Methods for Bivariate Shape-Preserving Interpolation

The purpose of this paper is to give a brief illustration of two methods for the shape-preserving interpolation of 2-D data on rectangular grids, starting from their common univariate basis. In addition, their convergence properties will be discussed.

[1]  Paolo Costantini,et al.  On monotone and convex spline interpolation , 1986 .

[2]  R. Barnhill Blending Function Interpolation: A Survey and Some New Results , 1976 .

[3]  Florencio I. Utreras Constrained surface Construction , 1987, Topics in Multivariate Approximation.

[4]  Paolo Costantini An algorithm for computing shape-preserving interpolating splines of arbitrary degree , 1988 .

[5]  Wolfgang Böhm,et al.  A survey of curve and surface methods in CAGD , 1984, Comput. Aided Geom. Des..

[6]  Ferruccio Fontanella,et al.  Shape-preserving bivariate interpolation , 1990 .

[7]  Paolo Costantini Co-Monotone interpolating splines of arbitrary degree—a local approach , 1987 .

[8]  Paolo Costantini,et al.  An algorithm for computing shape-preserving cubic spline interpolation to data , 1984 .

[9]  E. Passow,et al.  MONOTONE AND CONVEX SPLINE INTERPOLATION , 1977 .

[10]  Carla Manni,et al.  A local scheme for bivariate co-monotone interpolation , 1991, Comput. Aided Geom. Des..

[11]  Garrett Birkhoff,et al.  Hermite Interpolation Errors for Derivatives , 1967 .

[12]  Edward Neuman Uniform approximation by some Hermite interpolating splines , 1978 .

[13]  Larry L. Schumaker,et al.  Topics in Multivariate Approximation , 1987 .

[14]  C. Micchelli,et al.  Admissible slopes for monotone and convex interpolation , 1987 .

[15]  G. Vainikko Numerische Methoden der Approximationstheorie: L. Collatz and G. Meinardus, Editors. Band 1. 246 p. Birkhauser, Basel-Stuttgart, 1972 , 1973 .

[16]  Paolo Costantini,et al.  Monotone and convex cubic spline interpolation , 1984 .

[17]  R. E. Carlson,et al.  Monotone Piecewise Cubic Interpolation , 1980 .