## Scattered Data Interpolation in Three or More Variables (1989)

Venue: | Mathematical Methods in Computer Aided Geometric Design |

Citations: | 47 - 0 self |

### BibTeX

@INPROCEEDINGS{Alfeld89scattereddata,

author = {Peter Alfeld},

title = {Scattered Data Interpolation in Three or More Variables},

booktitle = {Mathematical Methods in Computer Aided Geometric Design},

year = {1989},

pages = {1--33},

publisher = {Academic Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

This is a survey of techniques for the interpolation of scattered data in three or more independent variables. It covers schemes that can be used for any number of variables as well as schemes specifically designed for three variables. Emphasis is on breadth rather than depth, but there are explicit illustrations of different techniques used in the solution of multivariate interpolation problems. List of Contents 1. Introduction 2. Rendering of Trivariate Functions 3. Tensor Product Schemes 4. Point Schemes 4.1 Shepard's Methods 4.2 Radial Interpolants 4.2.1 Hardy Multiquadrics 4.2.2 Duchon Thin Plate Splines 5. Natural Neighbor Interpolation 6. k-dimensional Triangulations 7. Tetrahedral Schemes 7.1 Polynomial Schemes 7.2 Rational Schemes 8. Simplicial Schemes 8.1 Polynomial Schemes 8.2 Rational Schemes 8.3 A Transfinite Scheme 9. Multivariate Splines 10. Transfinite Hypercubal Methods 11. Derivative Generation 12. Interpolation on the sphere and other surfa...