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Robust Fairing via Conformal Curvature Flow

Crane, Keenan and Pinkall, Ulrich and Schröder, Peter (2013) Robust Fairing via Conformal Curvature Flow. ACM Transactions on Graphics, 32 (4). Art. No. 61. ISSN 0730-0301. doi:10.1145/2461912.2461986.

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We present a formulation of Willmore flow for triangulated surfaces that permits extraordinarily large time steps and naturally preserves the quality of the input mesh. The main insight is that Willmore flow becomes remarkably stable when expressed in curvature space – we develop the precise conditions under which curvature is allowed to evolve. The practical outcome is a highly efficient algorithm that naturally preserves texture and does not require remeshing during the flow. We apply this algorithm to surface fairing, geometric modeling, and construction of constant mean curvature (CMC) surfaces. We also present a new algorithm for length-preserving flow on planar curves, which provides a valuable analogy for the surface case.

Item Type:Article
Related URLs:
URLURL TypeDescription DOIArticle
Schröder, Peter0000-0002-0323-7674
Additional Information:© 2013 ACM. This research was supported by a Google PhD Fellowship, the Hausdorff Research Institute for Mathematics, BMBF Research Project GEOMEC, SFB / Transregio 109 “Discretization in Geometry and Dynamics,” and the TU München Institute for Advanced Study, funded by the German Excellence Initiative. Meshes provided by the Stanford Computer Graphics Laboratory and the AIM@SHAPE Shape Repository.
Funding AgencyGrant Number
Google PhD FellowshipUNSPECIFIED
Hausdorff Research Institute for MathematicsUNSPECIFIED
SFB/Transregio 109 “Discretization in Geometry and Dynamics"UNSPECIFIED
TU München Institute for Advanced StudyUNSPECIFIED
German Excellence InitiativeUNSPECIFIED
Subject Keywords:digital geometry processing, discrete differential geometry, geometric modeling, surface fairing, shape spaces, conformal geometry, quaternions, spin geometry
Issue or Number:4
Record Number:CaltechAUTHORS:20130829-152759082
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Official Citation:Crane, K., Pinkall, U., Schröder, P. 2013. Robust Fairing via Conformal Curvature Flow. ACM Trans. Graph. 32, 4, Article 61 (July 2013), 10 pages. DOI = 10.1145/2461912.2461986
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41014
Deposited By: Tony Diaz
Deposited On:29 Aug 2013 23:05
Last Modified:10 Nov 2021 04:25

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