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Open AccessArticle

Fast Implicit Surface Reconstruction for the Radial Basis Functions Interpolant

by Deyun Zhong 1,2,*, Ju Zhang 1,2 and Liguan Wang 1,2
1
School of Resources and Safety Engineering, Central South University, Changsha 410083, China
2
Research Center of Digital Mine, Central South University, Changsha 410083, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(24), 5335; https://doi.org/10.3390/app9245335
Received: 14 November 2019 / Revised: 29 November 2019 / Accepted: 3 December 2019 / Published: 6 December 2019
In this paper we improve an efficient implicit surface reconstruction method based on the surface following method for the radial basis functions interpolant. The method balances the reconstruction efficiency and the evaluation efficiency in the process of surface following. The growing strategy of the surface following method combines both the evaluation and reconstruction processes. Based on the analysis of the black-box fast multipole method (FMM) operations, we improve the FMM procedures for single point evaluation. The goal is to ensure that one point evaluation of the method obtains an optimum efficiency, so that it can be efficiently applied to the voxel growing method. Combined with the single point FMM, we improve the voxel growing method without manually specifying the seed points, and the leaf growing method is developed to avoid a mass of redundant computation. It ensures a smaller number of evaluation points and a higher evaluation efficiency in surface following. The numerical results of several data sets showed the reliability and performance of the efficient implicit surface reconstruction method. Compared with the existing methods, the improved method performs a better time and space efficiency. View Full-Text
Keywords: surface reconstruction; radial basis functions; fast multipole method; implicit modeling; marching cubes surface reconstruction; radial basis functions; fast multipole method; implicit modeling; marching cubes
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Zhong, D.; Zhang, J.; Wang, L. Fast Implicit Surface Reconstruction for the Radial Basis Functions Interpolant. Appl. Sci. 2019, 9, 5335.

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