Implicit surfaces from polygon soup with compactly supported radial basis functions

Implicit surfaces from polygon soup with compactly supported radial basis functions This paper presents a method for generating implicit surfaces from polygon soups based on compactly supported radial basis functions (CSRBFs). The surface is represented as the zero level set of an implicit function which interpolates the polygonal data with their outward normal constraints. By specifying two parameters, the support size and the shape parameter, users can flexibly control the accuracy of the reconstructed surfaces. For determining coefficients of RBFs, our method uses a quasi-interpolation framework to avoid solving a large linear system, which allows processing large meshes efficiently and robustly. Moreover, a relationship between the shape parameter and the support radius is provided for the quasi-solution validity, and an error bound of the reconstructed surfaces approximating the original models is deduced through the rigorous theoretical analysis. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Visual Computer Springer Journals

Implicit surfaces from polygon soup with compactly supported radial basis functions

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Computer Science; Computer Graphics; Computer Science, general; Artificial Intelligence (incl. Robotics); Image Processing and Computer Vision
ISSN
0178-2789
eISSN
1432-2315
D.O.I.
10.1007/s00371-018-1529-3
Publisher site
See Article on Publisher Site

Abstract

This paper presents a method for generating implicit surfaces from polygon soups based on compactly supported radial basis functions (CSRBFs). The surface is represented as the zero level set of an implicit function which interpolates the polygonal data with their outward normal constraints. By specifying two parameters, the support size and the shape parameter, users can flexibly control the accuracy of the reconstructed surfaces. For determining coefficients of RBFs, our method uses a quasi-interpolation framework to avoid solving a large linear system, which allows processing large meshes efficiently and robustly. Moreover, a relationship between the shape parameter and the support radius is provided for the quasi-solution validity, and an error bound of the reconstructed surfaces approximating the original models is deduced through the rigorous theoretical analysis.

Journal

The Visual ComputerSpringer Journals

Published: May 2, 2018

References

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