Enhancement of inverse-distance-weighting 2D interpolation using accelerated decline

Article


Ruffhead, A. 2023. Enhancement of inverse-distance-weighting 2D interpolation using accelerated decline. Reports on Geodesy and Geoinformatics. 116 (1), pp. 9-14. https://doi.org/10.2478/rgg-2023-0006
AuthorsRuffhead, A.
Abstract

Two-dimensional interpolation – or surface fitting – is an approximation tool with applications in geodetic datum transformations, terrainmodelling and geoid determination. It can also be applied to many other forms of geographic point data, including rainfall, chemical concentrations and noise levels. The problem of fitting of a smooth continuous interpolant to a bivariate function is particularly difficult if the dataset of control points is scattered irregularly. A typical approach is a weighted sum of data values where the sum of the weights is always unity. Weighting by inverse distance to a power is one approach, although a power greater than 1 is needed to ensure smooth results. One advantage over othermethods is that data values can be incorporated into the interpolated surface. One disadvantage is the influence of distant points. A simple cut-off limit on distance would affect continuity. This study proposes a transition range of accelerated decline bymeans of an adjoining polynomial. This preserves smoothness and continuity in the interpolating surface. Case studies indicate accuracy advantages over standard versions of inverse-distance weighting.

JournalReports on Geodesy and Geoinformatics
Journal citation116 (1), pp. 9-14
ISSN2391-8152
Year2023
PublisherDe Gruyter
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Anyone
Digital Object Identifier (DOI)https://doi.org/10.2478/rgg-2023-0006
Publication dates
Online25 Aug 2023
Publication process dates
Accepted25 Jul 2023
Deposited14 Dec 2023
Copyright holder© 2023 Andrew Carey Ruffhead
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