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Design of tangent vector fields

Fisher, Matthew and Schröder, Peter and Desbrun, Mathieu and Hoppe, Hugues (2007) Design of tangent vector fields. ACM Transactions on Graphics, 26 (3). Article 56. ISSN 0730-0301. doi:10.1145/1239451.1239507.

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Tangent vector fields are an essential ingredient in controlling surface appearance for applications ranging from anisotropic shading to texture synthesis and non-photorealistic rendering. To achieve a desired effect one is typically interested in smoothly varying fields that satisfy a sparse set of user-provided constraints. Using tools from Discrete Exterior Calculus, we present a simple and efficient algorithm for designing such fields over arbitrary triangle meshes. By representing the field as scalars over mesh edges (i.e., discrete 1-forms), we obtain an intrinsic, coordinate-free formulation in which field smoothness is enforced through discrete Laplace operators. Unlike previous methods, such a formulation leads to a linear system whose sparsity permits efficient pre-factorization. Constraints are incorporated through weighted least squares and can be updated rapidly enough to enable interactive design, as we demonstrate in the context of anisotropic texture synthesis.

Item Type:Article
Related URLs:
URLURL TypeDescription
Fisher, Matthew0000-0002-8908-3417
Schröder, Peter0000-0002-0323-7674
Desbrun, Mathieu0000-0003-3424-6079
Hoppe, Hugues0000-0002-9699-2539
Additional Information:© 2007 ACM. This work was supported in part by NSF (CCF-0528101, CCR-0503786 and ITR DMS-0453145), DOE (W-7405- ENG-48/B341492 and DE-FG02-04ER25657), the Caltech Center for Mathematics of Information, the Alexander von Humboldt Stiftung, SUN Microsystems, Pixar, nVidia, and Autodesk. Some models courtesy Stanford University, Cyberware, and Leif Kobbelt. Special thanks to Ke Wang, Cici Koenig, Max Wardetzky, Yiying Tong, and the anonymous reviewers.
Funding AgencyGrant Number
NSFITR DMS-0453145
Department of Energy (DOE)W-7405-ENG-48/B341492
Department of Energy (DOE)DE-FG02-04ER25657
Caltech Center for Mathematics of InformationUNSPECIFIED
Alexander von Humboldt StiftungUNSPECIFIED
Subject Keywords:Discrete exterior calculus, discrete differential 1- forms, constrained Laplace and Poisson problems for 1-forms, texture synthesis
Issue or Number:3
Record Number:CaltechAUTHORS:20100507-094443477
Persistent URL:
Official Citation:Fisher, M., Schröder, P., Desbrun, M., Hoppe, H. 2007. Design of Tangent Vector Fields. ACM Trans. Graph. 26, 3, Article 56 (July 2007), 9 pages. DOI = 10.1145/1239451.1239507 51.1239507.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18186
Deposited On:07 May 2010 18:30
Last Modified:08 Nov 2021 23:42

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