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Subdivision surface fitting to a dense mesh using ridges and umbilics

Subdivision surface fitting to a dense mesh using ridges and umbilics

Ma, Xinhui, Keates, Simeon ORCID: 0000-0002-2826-672X, Jiang, Yong and Kosinka, Jiří (2015) Subdivision surface fitting to a dense mesh using ridges and umbilics. Computer Aided Geometric Design, 32. pp. 5-21. ISSN 0167-8396 (Print), 1879-2332 (Online) (doi:https://doi.org/10.1016/j.cagd.2014.10.001)

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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. Further more, 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.

Item Type: Article
Additional Information: © 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords: Subdivision surface fitting, Dense mesh, Feature alignment, Ridges, Umbilics, Hausdorff distance, Principal curvature vector
Faculty / Department / Research Group: Faculty of Engineering & Science
Faculty of Engineering & Science > Future Technology and the Internet of Things
Last Modified: 27 Apr 2017 14:46
Selected for GREAT 2016: None
Selected for GREAT 2017: GREAT a
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/14421

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