<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Two-dimensional interpolation – or surface fitting – is an approximation tool with applications in geodetic datum transformations, terrain modelling 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 other methods 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 by means 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.</p>
</abstract>

Two-dimensional interpolation – or surface fitting – is an approximation tool with applications in geodetic datum transformations, terrain modelling 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 other methods 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 by means 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.

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

University of East London, Docklands Campus, University Way

Reports on Geodesy and Geoinformatics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Two-dimensional interpolation – or surface fitting – is an approximation tool with applications in geodetic datum transformations, terrain modelling and geoid...

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

Published Online: Aug 25, 2023

Page range: 9 - 14

Received: May 22, 2023

Accepted: Jul 25, 2023

DOI: https://doi.org/10.2478/rgg-2023-0006

Keywords
surface-fitting, inverse-distance weighting, 2D interpolation, accelerated decline

© 2023 Andrew Carey Ruffhead, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Aug 25, 2023

Page range: 9 - 14

Received: May 22, 2023

Accepted: Jul 25, 2023

DOI: https://doi.org/10.2478/rgg-2023-0006

Keywordssurface-fitting, inverse-distance weighting, 2D interpolation, accelerated decline

© 2023 Andrew Carey Ruffhead, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
surface-fitting, inverse-distance weighting, 2D interpolation, accelerated decline