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Design of tangent vector fields

Published: 29 July 2007 Publication History

Abstract

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.

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cover image ACM Conferences
SIGGRAPH '07: ACM SIGGRAPH 2007 papers
August 2007
1019 pages
ISBN:9781450378369
DOI:10.1145/1275808
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 29 July 2007

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Author Tags

  1. constrained Laplace and Poisson problems for 1-forms
  2. discrete differential 1-forms
  3. discrete exterior calculus
  4. texture synthesis

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SIGGRAPH '07 Paper Acceptance Rate 108 of 455 submissions, 24%;
Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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  • (2014)Optimizing BRDF orientations for the manipulation of anisotropic highlightsComputer Graphics Forum10.1111/cgf.1230033:2(313-321)Online publication date: 1-May-2014
  • (2013)On the equilibrium of simplicial masonry structuresACM Transactions on Graphics10.1145/2461912.246193232:4(1-10)Online publication date: 21-Jul-2013
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