research-article

Globally optimal direction fields

Authors:

Felix Knöppel,

Ulrich Pinkall,

Peter SchröderAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 32, Issue 4

Article No.: 59, Pages 1 - 10

https://doi.org/10.1145/2461912.2462005

Published: 21 July 2013 Publication History

Abstract

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.

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Cited By

Gao AChu MKapadia MLin MLiu HSalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)An intrinsic vector heat networkProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692654(14638-14650)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3692654
Liu SJi YGuo JLiu LFu X(2024)Smooth Bijective Projection in a High-order ShellACM Transactions on Graphics10.1145/365820743:4(1-13)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658207
Palmer DChern ASolomon J(2024)Lifting Directional Fields to Minimal SectionsACM Transactions on Graphics10.1145/365819843:4(1-20)Online publication date: 19-Jul-2024
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Index Terms

Globally optimal direction fields
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 32, Issue 4

July 2013

1215 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2461912

Issue’s Table of Contents

Copyright © 2013 ACM.

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Publication History

Published: 21 July 2013

Published in TOG Volume 32, Issue 4

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Hausdorff Research Institute for Mathematics
Bundesministerium für Bildung und Forschung
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TU München Institute for Advanced Study

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Cited By

Gao AChu MKapadia MLin MLiu HSalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)An intrinsic vector heat networkProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692654(14638-14650)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3692654
Liu SJi YGuo JLiu LFu X(2024)Smooth Bijective Projection in a High-order ShellACM Transactions on Graphics10.1145/365820743:4(1-13)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658207
Palmer DChern ASolomon J(2024)Lifting Directional Fields to Minimal SectionsACM Transactions on Graphics10.1145/365819843:4(1-20)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658198
Corman E(2024)Curvature-Driven Conformal DeformationsACM Transactions on Graphics10.1145/365814543:4(1-16)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658145
Simons LAmenta N(2024)Anisotropy and Cross FieldsComputer Graphics Forum10.1111/cgf.1513243:5Online publication date: 5-Aug-2024
https://doi.org/10.1111/cgf.15132
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
Wu LZang XYin WZhang XLi CZhu YZhao J(2024)Pose and Path Planning for Industrial Robot Surface Machining Based on Direction FieldsIEEE Robotics and Automation Letters10.1109/LRA.2024.34745219:11(10455-10462)Online publication date: Nov-2024
https://doi.org/10.1109/LRA.2024.3474521
Mitchel TEsteves CMakadia A(2024)Single Mesh Diffusion Models with Field Latents for Texture Generation2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52733.2024.00760(7953-7963)Online publication date: 16-Jun-2024
https://doi.org/10.1109/CVPR52733.2024.00760
Shepherd KHiemstra RGu XHughes T(2024)Extraction of surface quad layouts from quad layout immersions: application to an isogeometric model of car crashEngineering with Computers10.1007/s00366-024-02007-w40:6(3683-3716)Online publication date: 1-Dec-2024
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Jezdimirović JChemin ARemacle J(2024)Integrable Cross-Field Generation Based on Imposed Singularity Configuration—The 2D Manifold CaseSIAM International Meshing Roundtable 202310.1007/978-3-031-40594-5_16(343-369)Online publication date: 21-Mar-2024
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