Discrete Sibson interpolation

IEEE Transactions on Visualization and Computer Graphics
Sung W ParkBernd Hamann

Abstract

Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d-dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds.

References

Jan 1, 1992·Breast Cancer Research and Treatment·D Yee

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Citations

Sep 21, 2013·IEEE Transactions on Visualization and Computer Graphics·Samer S Barakat, Xavier Tricoche
Jun 8, 2013·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Xie XuAlireza Entezari
Nov 8, 2008·IEEE Transactions on Visualization and Computer Graphics·Paul Rosenthal, Lars Linsen
Nov 8, 2008·IEEE Transactions on Visualization and Computer Graphics·Christian LedergerberHanspeter Pfister
Jul 3, 2020·The Journal of the Acoustical Society of America·Jamie D J MacaulayPeter T Madsen

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