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Globally Optimal Direction Fields

Knöppel, Felix and Crane, Keenan and Pinkall, Ulrich and Schröder, Peter (2013) Globally Optimal Direction Fields. ACM Transactions on Graphics, 32 (4). Art. No. 59. ISSN 0730-0301. doi:10.1145/2461912.2462005.

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We present a method for constructing smooth n-direction fields (line fields, cross fields, etc.) on surfaces that is an order of magnitude faster than state-of-the-art methods, while still producing fields of equal or better quality. Fields produced by the method are globally optimal in the sense that they minimize a simple, well-defined quadratic smoothness energy over all possible configurations of singularities (number, location, and index). The method is fully automatic and can optionally produce fields aligned with a given guidance field such as principal curvature directions. Computationally the smoothest field is found via a sparse eigenvalue problem involving a matrix similar to the cotan-Laplacian. When a guidance field is present, finding the optimal field amounts to solving a single linear system.

Item Type:Article
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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:discrete differential geometry, digital geometry processing, direction fields, curvature lines, singularities
Issue or Number:4
Record Number:CaltechAUTHORS:20130829-154018080
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Official Citation:Knöppel, F., Crane, K., Pinkall, U., Schröder, P. 2013. Globally Optimal Direction Fields. ACM Trans. Graph. 32, 4, Article 59 (July 2013), 10 pages. DOI = 10.1145/2461912.2462005
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41016
Deposited By: Tony Diaz
Deposited On:29 Aug 2013 23:01
Last Modified:10 Nov 2021 04:25

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