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Subdivision surface fitting to a dense mesh using ridges and umbilics

Ma, Xinhui; Keates, Simeon; Jiang, Yong; Kosinka, Jiří

Authors

Simeon Keates

Yong Jiang

Jiří Kosinka



Abstract

Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach.

Citation

Kosinka, J., Ma, X., Jiang, Y., Keates, S., & Kosinka, J. (2015). Subdivision surface fitting to a dense mesh using ridges and umbilics. Computer aided geometric design, 32(January), 5-21. https://doi.org/10.1016/j.cagd.2014.10.001

Acceptance Date Oct 31, 2014
Online Publication Date Nov 20, 2014
Publication Date Jan 1, 2015
Deposit Date Nov 4, 2015
Publicly Available Date Nov 23, 2017
Journal Computer aided geometric design
Print ISSN 0167-8396
Electronic ISSN 1879-2332
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 32
Issue January
Pages 5-21
DOI https://doi.org/10.1016/j.cagd.2014.10.001
Keywords Subdivision surface fitting; Feature alignment; Ridges; Umbilics; Hausdorff distance; Principal curvature vector
Public URL https://hull-repository.worktribe.com/output/380868
Publisher URL http://www.sciencedirect.com/science/article/pii/S0167839614001009
Copyright Statement © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Additional Information Author's accepted manuscript of article published in: Computer aided geometric design, 2015, v.32, January.

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Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Statement
© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/





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