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Volume 26, Issue 2
Surface Reconstruction of 3D Scattered Data with Radial Basis Functions

Xinwei Du, Xiaoying Yang & Xuezhang Liang

Commun. Math. Res., 26 (2010), pp. 183-192.

Published online: 2021-05

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  • Abstract

We use Radial Basis Functions (RBFs) to reconstruct smooth surfaces from 3D scattered data. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.

  • Keywords

radial basis function, scattered data, implicit surface, surface reconstruction.

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COPYRIGHT: © Global Science Press

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@Article{CMR-26-183, author = {Xinwei and Du and and 18240 and and Xinwei Du and Xiaoying and Yang and and 18241 and and Xiaoying Yang and Xuezhang and Liang and and 18242 and and Xuezhang Liang}, title = {Surface Reconstruction of 3D Scattered Data with Radial Basis Functions}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {26}, number = {2}, pages = {183--192}, abstract = {

We use Radial Basis Functions (RBFs) to reconstruct smooth surfaces from 3D scattered data. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19170.html} }
TY - JOUR T1 - Surface Reconstruction of 3D Scattered Data with Radial Basis Functions AU - Du , Xinwei AU - Yang , Xiaoying AU - Liang , Xuezhang JO - Communications in Mathematical Research VL - 2 SP - 183 EP - 192 PY - 2021 DA - 2021/05 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19170.html KW - radial basis function, scattered data, implicit surface, surface reconstruction. AB -

We use Radial Basis Functions (RBFs) to reconstruct smooth surfaces from 3D scattered data. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.

XinweiDu, XiaoyingYang & XuezhangLiang. (2021). Surface Reconstruction of 3D Scattered Data with Radial Basis Functions. Communications in Mathematical Research . 26 (2). 183-192. doi:
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