Scattered data interpolation: tests of some methods

Absract. This paper is concerned with the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods. The process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation. To indicate the flavor of the type of results obtained, we give a summary table and representative perspective plots of several surfaces.

[1]  James Ferguson,et al.  Multivariable Curve Interpolation , 1964, JACM.

[2]  I. K Crain,et al.  Treatment of non-equispaced two-dimensional data with a digital computer , 1967 .

[3]  C. Pelto,et al.  AUTOMATIC CONTOURING OF IRREGULARLY SPACED DATA , 1968 .

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

[5]  G. Matheron Random Functions and their Application in Geology , 1970 .

[6]  R. L. Hardy Multiquadric equations of topography and other irregular surfaces , 1971 .

[7]  R. N. Desmarais,et al.  Interpolation using surface splines. , 1972 .

[8]  John L. Junkins,et al.  A weighting function approach to modeling of irregular surfaces , 1973 .

[9]  G. Matheron The intrinsic random functions and their applications , 1973, Advances in Applied Probability.

[10]  A. D. Maude Interpolation - Mainly for Graph Plotters , 1973, Comput. J..

[11]  D. H. McLain,et al.  Drawing Contours from Arbitrary Data Points , 1974, Comput. J..

[12]  John L. Junkins,et al.  Modeling in n dimensions using a weighting function approach , 1974 .

[13]  R. Olea Optimal contour mapping using universal kriging , 1974 .

[14]  Ian Briggs Machine contouring using minimum curvature , 1974 .

[15]  Hiroshi Akima Comments on ‘Optimal contour mapping using universal kriging’ by Ricardo A. Olea , 1975 .

[16]  R L Hardy RESEARCH RESULTS IN THE APPLICATION OF MULTIQUADRATIC EQUATIONS TO SURVEYING AND MAPPING PROBLEMS , 1975 .

[17]  R. L. Hardy,et al.  Least squares prediction of gravity anomalies, geoidal undulations, and deflections of the vertical with multiquadric harmonic functions , 1975 .

[18]  Jean Duchon,et al.  Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces , 1976 .

[19]  D. H. McLain,et al.  Two Dimensional Interpolation from Random Data , 1976, Comput. J..

[20]  Jean Duchon,et al.  Splines minimizing rotation-invariant semi-norms in Sobolev spaces , 1976, Constructive Theory of Functions of Several Variables.

[21]  L. Schumaker Fitting surfaces to scattered data , 1976 .

[22]  C. M. Gold,et al.  Automated contour mapping using triangular element data structures and an interpolant over each irregular triangular domain , 1977, SIGGRAPH '77.

[23]  Robert E. Barnhill,et al.  Representation and Approximation of Surfaces , 1977 .

[24]  C. Lawson Software for C1 Surface Interpolation , 1977 .

[25]  R. Franke Locally Determined Smooth Interpolation at Irregularly Spaced Points in Several Variables , 1977 .

[26]  R. L. Hardy,et al.  LEAST SQUARES PREDICTION , 1977 .

[27]  Malcolm A. Sabin,et al.  Piecewise Quadratic Approximations on Triangles , 1977, TOMS.

[28]  Rolland Lee Hardy The application of multiquadric equations and point mass anomaly models to crustal movement studies , 1978 .

[29]  Hiroshi Akima,et al.  A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points , 1978, TOMS.

[30]  Smooth Surface Approximation by a Local Method of Interpolation at Scattered Points. , 1978 .

[31]  W. J. Gordon,et al.  Shepard’s method of “metric interpolation” to bivariate and multivariate interpolation , 1978 .

[32]  J. Meinguet Multivariate interpolation at arbitrary points made simple , 1979 .

[33]  R. Franke A Critical Comparison of Some Methods for Interpolation of Scattered Data , 1979 .

[34]  P. Lancaster Moving Weighted Least-Squares Methods , 1979 .

[35]  J. Meinguet An Intrinsic Approach to Multivariate Spline Interpolation at Arbitrary Points , 1979 .

[36]  K. Brodlie Mathematical Methods in Computer Graphics and Design , 1980 .

[37]  J. Rendu,et al.  Disjunctive kriging: Comparison of theory with actual results , 1980 .

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

[39]  G. Nielson Minimum Norm Interpolation in Triangles , 1980 .

[40]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

[41]  G. Nielson A method for interpolating scattered data based upon a minimum norm network , 1983 .