Multivariate interpolation of large sets of scattered data

✍ Scribed by Renka, Robert J.

• Book ID: 111927086
• Publisher: Association for Computing Machinery
• Year: 1988
• Tongue: English
• Weight: 662 KB
• Volume: 14
• Category: Article
• ISSN: 0098-3500
• DOI: 10.1145/45054.45055

✦ Synopsis

This paper presents a method of constructing a smooth function of two or more variables that interpolates data values at arbitrarily distributed points. Shepard's method for fitting a surface to data values at scattered points in the plane has the advantages of a small storage requirement and an easy generalization to more than two independent variables, but suffers from low accuracy and a high computational cost relative to some alternative methods. Localizations of this method have reasonably low computational costs, but remain relatively inaccurate. We describe a modified Shepard's method that, without sacrificing the advantages, has accuracy comparable to other local methods. Computational efficiency is also improved by using a cell method for nearest-neighbor searching. Test results for two and three independent variables are presented.