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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. In: SIGGRAPH '07 ACM SIGGRAPH 2007 papers. ACM , New York, NY, Art. No. 56.

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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:Book Section
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
Department of Energy (DOE)W-7405-ENG-48/B341492
Department of Energy (DOE)DE-FG02-04ER25657
Center for the Mathematics of Information, CaltechUNSPECIFIED
Alexander von Humboldt StiftungUNSPECIFIED
Sun MicrosystemsUNSPECIFIED
Subject Keywords:Discrete exterior calculus, discrete differential 1-forms, constrained Laplace and Poisson problems for 1-forms, texture synthesis
Record Number:CaltechAUTHORS:20161019-155301872
Persistent URL:
Official Citation:Matthew Fisher, Peter Schröder, Mathieu Desbrun, and Hugues Hoppe. 2007. Design of tangent vector fields. In ACM SIGGRAPH 2007 papers (SIGGRAPH '07). ACM, New York, NY, USA, , Article 56 . DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71302
Deposited On:20 Oct 2016 01:36
Last Modified:11 Nov 2021 04:43

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