SHEPPACK: a Fortran 95 package for interpolation using the modified Shepard algorithm

Scattered data interpolation and approximation problems arise in many applications. Shepard's method for constructing global interpolants by blending local interpolants using locally-supported weight functions usually creates reasonable approximations. This paper describes SHEPPACK, a Fortran 95 package containing five versions of the modified Shepard algorithm. These five versions include quadratic (TOMS Algorithm 660, 661, and 798), cubic (TOMS Algorithm 790), and linear variations of the original Shepard algorithm. The main goal of SHEPPACK is to provide users with a single consistent package consisting of all existing polynomial variations of Shepard's algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm is the only algorithm in the package that is applicable to arbitrary dimensional data. The motivation is to enable researchers to experiment with different algorithms using their data and select one (or more) that is best suited to their needs, and to support interpolation for sparse, high dimensional data sets.

[1]  I. J. Schoenberg.  Metric spaces and completely monotone functions , 1938 .

[2]  S. A. Coons.  SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS , 1967 .

[3]  D. Shepard.  A two-dimensional interpolation function for irregularly-spaced data , 1968, ACM National Conference.

[4]  P. C. Gehlen,et al.  Computer Experiments , 1996 .

[5]  Kenneth James Versprille.  Computer-aided design applications of the rational b-spline approximation form. , 1975 .

[6]  Richard Franke,et al.  Smooth interpolation of large sets of scattered data , 1980 .

[7]  C. Micchelli.  Interpolation of scattered data: Distance matrices and conditionally positive definite functions , 1986 .

[8]  R. H. Myers.  Classical and modern regression with applications , 1986 .

[9]  Robert J. Renka,et al.  Algorithm 660: QSHEP2D: Quadratic Shepard Method for Bivariate Interpolation of Scattered Data , 1988, TOMS.

[10]  Robert J. Renka,et al.  Multivariate interpolation of large sets of scattered data , 1988, TOMS.

[11]  L. Piegl.  Modifying the shape of rational B-splines. part2: surfaces , 1989 .

[12]  Glenn Stone,et al.  Computation of Thin-Plate Splines , 1991, SIAM J. Sci. Comput..

[13]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[14]  Cristina H. Amon,et al.  An engineering design methodology with multistage Bayesian surrogates and optimal sampling , 1996 .

[15]  Anthony A. Giunta,et al.  Aircraft Multidisciplinary Design Optimization using Design of Experiments Theory and Response Surface Modeling Methods , 1997 .

[16]  Ron Brown,et al.  Algorithm 792: accuracy test of ACM algorithms for interpolation of scattered data in the plane , 1999, TOMS.

[17]  Robert J. Renka,et al.  Algorithm 790: CSHEP2D: cubic Shepard method for bivariate interpolation of scattered data , 1988, TOMS.

[18]  Ron Brown,et al.  Algorithm 791: TSHEP2D: cosine series Shepard method for bivariate interpolation of scattered data , 1999, TOMS.

[19]  Ward Cheney,et al.  A course in approximation theory , 1999 .

[20]  Michael W. Berry,et al.  Algorithm 798: high-dimensional interpolation using the modified Shepard method , 1999, TOMS.

[21]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[22]  Layne T. Watson,et al.  Linear Shepard Interpolation for High Dimensional Piecewise Smooth Functions , 2004 .