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Mathematical Problems in Engineering
Volume 2015, Article ID 582870, 11 pages
Research Article

Spherical Harmonics for Surface Parametrisation and Remeshing

School of Computer Science, The University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK

Received 5 August 2015; Revised 2 November 2015; Accepted 9 November 2015

Academic Editor: Masoud Hajarian

Copyright © 2015 Caitlin R. Nortje et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a novel method for parametrisation and remeshing incomplete and irregular polygonal meshes. Spherical harmonics basis functions are used for parametrisation. This involves least squares fitting of spherical harmonics basis functions to the surface mesh. Tikhonov regularisation is then used to improve the parametrisation before remeshing the surface. Experiments show that the proposed techniques are effective for parametrising and remeshing polygonal meshes.