A Modified Local Distance-weighted (MLD) Method of Interpolation and Its Numerical Performances for Large Scattered Datasets
Article Sidebar
Main Article Content
Abstract
The purpose of this study was to propose a new interpolation scheme that was designed to remedy the shortcomings encountered in two popular interpolation methods; the triangle-based blending (TBB) method and the inverse distance weighted (IDW) method. At the same time, the proposed method combines their desirable aspects, which are the local nature and non-use of quadratic surface construction, making it comparatively less time-consuming and more independent of the global effect. Because of these properties, the new scheme was named the ‘Modified Local Distance-Weighted (MLD)’ method, and it was tested in detail with different sizes of datasets. The datasets involved in this investigation were of two types; uniformly and non-uniformly distributed. The performances were carefully monitored and assessed via several criteria; accuracy, sensitivity to parameters, CPU-time, storage requirement and ease of implementation. For comparative purposes, three alternative interpolation methods were simultaneously carried out, i.e. TBB, IDW and Radial Basis Function-Based (RBF) method. The investigation clearly revealed promising aspects of the proposed scheme where a good quality of results was anticipated, and CPU-time and storage were seen to have been significantly reduced. The research strongly indicates the benefits of the proposed method for larger sized datasets for real practical scientific and engineering uses in the future.
Keywords: interpolation; scattered datasets; distance-weighted; triangle-based blending; radial basis function
*Corresponding author: (+66) 44224747 Fax: (+66)44224649
E-mail: sayan_kk@g.sut.ac.th
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright Transfer Statement
The copyright of this article is transferred to Current Applied Science and Technology journal with effect if and when the article is accepted for publication. The copyright transfer covers the exclusive right to reproduce and distribute the article, including reprints, translations, photographic reproductions, electronic form (offline, online) or any other reproductions of similar nature.
The author warrants that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors.
Here is the link for download: Copyright transfer form.pdf
References
Malvić, T., Ivšinović, J., Velić, J. and Rajić, R., 2019. Interpolation of small datasets in the sandstone hydrocarbon reservoirs, case study of the Sava Depression, Croatia. Geosciences, 9(5), 201.
Bronowicka-Mielniczuk, U., Mielniczuk, J., Obroślak, R. and Przystupa, W., 2019. A comparison of some interpolation techniques for determining spatial distribution of nitrogen compounds in groundwater. International Journal of Environmental Research, 13, 679-687.
Smolik, M. and Skala, V., 2017. Large scattered data interpolation with radial basis functions and space subdivision. Integrated Computer-Aided Engineering, IOS Press, 25(1), 49-62, https://doi.org/10.3233/ICA-170556.
Malvić, T., Ivšinović, J., Velić, J., Sremac, J. and Barudžija, U., 2020. Application of the Modified Shepard’s Method (MSM): A case study with the Interpolation of Neogene Reservoir Variables in Northern Croatia. Stats, 3(1), 68-83.
Shepard, D., 1968. A two-dimensional interpolation function for irregularly spaced data. ACM '68: Proceedings of the 23rd ACM National Conference, New York, United States, August 27-29, 1968, pp. 517-524.
Barnhill, R.E., 1977. Representation and approximation of surfaces. In: John R. Rice, ed. Mathematical Software III. New York: Academic Press, pp. 69-120.
Franke, R., 1982. Scattered data interpolation: tests of some methods, Mathematics of Computation, 38(157), 181-200.
McLain, D.H., 1976. Two dimensional interpolation from random data. The Computer Journal, 19(2), 178-181.
Amidror, I., 2002. Scattered data interpolation methods for electronic imaging systems: a survey. Journal of Electronic Imaging, 11(2), 157-176.
Franke, C. and Schaback, R., 1998. Convergence order estimates of meshless collocation methods using radial basis functions. Advances in Computational Mathematics, 8(4), 381-399.
Tavaen, S., Viriyapong, R. and Kaennakham, S., 2020. Performances of non-parameterised radial basis functions in pattern recognition applications. Journal of Physics: Conference Series, 1706, 012165, https://doi.org/10.1088/1742-6596/1706/1/012165.
Lazzaro, D. and Montefusco, L.B., 2002. Radial basis functions for the multivariate interpolationof large scattered data sets. Journal of Computational and Applied Mathematics, 140(1-2), 521-536.
Carlson, R.E. and Foley, T.A., 1991. The parameter R2 in multiquadric interpolation. Computers and Mathematics with Applications, 21(9), 29-42.
Tavaen, S. and Kaennakham, S., 2021. A comparison study on shape parameter selection in pattern recognition by Radial Basis Function neural networks. Journal of Physics: Conference Series, 1921, 012124, https://doi.org/10.1088/1742-6596/1921/1/012124.
Franke, R. and Nielson, G., 1979. Smooth Interpolation of Large Sets of Scattered Data. Technical Report, Naval Postgraduate School, Monterey, California.