article

Design of tangent vector fields

Authors:

Matthew Fisher,

Peter Schröder,

Mathieu Desbrun,

Hugues HoppeAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 26, Issue 3

Pages 56 - es

https://doi.org/10.1145/1276377.1276447

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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Cited By

Kovács ÁHermosilla PRaidou R(2024)Surface‐aware Mesh Texture Synthesis with Pre‐trained 2D CNNsComputer Graphics Forum10.1111/cgf.1501643:2Online publication date: 23-Apr-2024
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Index Terms

Design of tangent vector fields
1. Computing methodologies
  1. Computer graphics
    1. Image manipulation
      1. Texturing
    2. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 26, Issue 3

July 2007

976 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1276377

Issue’s Table of Contents

Copyright © 2007 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 29 July 2007

Published in TOG Volume 26, Issue 3

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Kovács ÁHermosilla PRaidou R(2024)Surface‐aware Mesh Texture Synthesis with Pre‐trained 2D CNNsComputer Graphics Forum10.1111/cgf.1501643:2Online publication date: 23-Apr-2024
https://doi.org/10.1111/cgf.15016
Zhang ZLi MZhao ZFang QFu X(2024)Practical Integer-Constrained Cone Construction for Conformal ParameterizationsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.328730330:8(5227-5239)Online publication date: Aug-2024
https://doi.org/10.1109/TVCG.2023.3287303
Bommes DZimmer HKobbelt L(2023)Mixed-Integer QuadrangulationSeminal Graphics Papers: Pushing the Boundaries, Volume 210.1145/3596711.3596740(249-258)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1145/3596711.3596740
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