Multinode Shepard Functions and Tensor Product Polynomial Interpolation: Applications to Digital Elevation Models
Domingo Barrera, Francesco Dell'Accio, Filomena Di Tommaso, Salah Eddargani, Mar\'ia Jos\'e Ib\'a\~nez, Francesco Larosa, Federico Nudo, Juan F. Reinoso
TL;DR
This paper investigates multinode Shepard interpolation on regular grids for digital elevation models, analyzing its approximation properties, proposing a reconstruction algorithm, and validating its effectiveness through numerical tests.
Contribution
It introduces a detailed algorithm for surface reconstruction using multinode Shepard functions and analyzes their approximation order for DEM data.
Findings
Effective surface reconstruction from DEM data
The proposed algorithm achieves accurate results
The interpolation method has favorable approximation properties
Abstract
The paper presents an in-depth exploration of the multinode Shepard interpolant on a regular rectangular grid, demonstrating its efficacy in reconstructing surfaces from DEM data. Additionally, we study the approximation order associated to this interpolant and present a detailed algorithm for reconstructing surfaces. Numerical tests showcase the effectiveness of the proposed algorithm.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Digital Image Processing Techniques · Soil Geostatistics and Mapping