Many papers, examples, and tutorials on interpolation with Radial Basis Functions (RBF) are understandably aimed at mathematicians, computer scientists, and mathematically inclined developers. Consequently, much of the literature can be overwhelming and difficult to fully comprehend for those without a strong mathematical background, including the author. However, in recent years, professionals such as geologists and geotechnical engineers—who may have little to no programming experience—have come to rely on RBF interpolation in their daily work through commercial implicit modeling software. To address this gap, the author has developed a more accessible explanation of the RBF interpolation process in the form of an Excel workbook.
This workbook features two interactive examples derived from familiar sources:
• A grade interpolation example from [4].
• A surface boundary example from [1].
The workbook provides guidance on how to use the example worksheets, along with the underlying theory explained step by step.
Also provided in this repository are companion Jupyter Notebooks, offering an alternative implementation for those who may prefer reading Python code to working with an Excel-based interface.
The workbook and Jupyter Notebooks are provided under the MIT license, allowing readers to freely reuse and distribute it, provided the license conditions are met. The author kindly requests acknowledgment of the original work and welcomes feedback from anyone who finds the workbook useful or intends to use it in their own projects.
References:
- https://geostatisticslessons.com/lessons/implicitrbf
- https://www.seequent.com/the-spheroidal-family-of-variograms-explained/
- Fasshauer, G., 2007. Meshfree Approximation Methods with Matlab. World Scientific Publishing Co.
- https://help.seequent.com/Geo/2024.1/en-GB/Content/concepts/interpolant-functions.htm
- J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans. 2001. Reconstruction and representation of 3D objects with radial basis functions. In Proceedings of the 28th annual conference on Computer graphics and interactive
techniques (SIGGRAPH '01). Association for Computing Machinery, New York, NY, USA, 67–76. https://doi.org/10.1145/383259.383266
- https://en.wikipedia.org/wiki/Monomial_basis
- Beatson, Richard K., William A. Light and Stephen D. Billings. “Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods.” SIAM J. Sci. Comput. 22 (2000): 1717-1740.
- Zhang, B., Du, L., Khan, U., Tong, Y., Wang, L., and Deng, H.: AdaHRBF v1.0: gradient-adaptive Hermite–Birkhoff radial basis function interpolants for three-dimensional stratigraphic implicit modeling, Geosci. Model Dev., 16, 3651–3674, https://doi.org/10.5194/gmd-16-3651-2023, 2023.