Subdivision surface fitting to a dense mesh using ridges and umbilics

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

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

Ma, X., Keates, S., Jiang, Y., & 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
• 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
• Additional Information: Author's accepted manuscript of article published in: Computer aided geometric design, 2015, v.32, January.
• Contract Date: Nov 23, 2017