research-article

Robust field-aligned global parametrization

Authors:

Denis ZorinAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 33, Issue 4

Article No.: 135, Pages 1 - 14

https://doi.org/10.1145/2601097.2601154

Published: 27 July 2014 Publication History

Abstract

We present a robust method for computing locally bijective global parametrizations aligned with a given cross-field. The singularities of the parametrization in general agree with singularities of the field, except in a small number of cases when several additional cones need to be added in a controlled way. Parametric lines can be constrained to follow an arbitrary set of feature lines on the surface. Our method is based on constructing an initial quad patch partition using robust cross-field integral line tracing. This process is followed by an algorithm modifying the quad layout structure to ensure that consistent parametric lengths can be assigned to the edges. For most meshes, the layout modification algorithm does not add new singularities; a small number of singularities may be added to resolve an explicitly described set of layouts. We demonstrate that our algorithm succeeds on a test data set of over a hundred meshes.

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Cited By

Yu YLi NGong G(2025)Robust motorcycle graph construction and simplification for semi-structured quad mesh generationComputers & Graphics10.1016/j.cag.2025.104173127(104173)Online publication date: Apr-2025
https://doi.org/10.1016/j.cag.2025.104173
Hinderink SBrückler HCampen M(2024)Bijective Volumetric Mapping via Star DecompositionACM Transactions on Graphics10.1145/368795043:6(1-11)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687950
Feng NCrane K(2024)A Heat Method for Generalized Signed DistanceACM Transactions on Graphics10.1145/365822043:4(1-19)Online publication date: 19-Jul-2024
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Index Terms

Robust field-aligned global parametrization
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 33, Issue 4

July 2014

1366 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2601097

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Copyright © 2014 ACM.

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Publication History

Published: 27 July 2014

Published in TOG Volume 33, Issue 4

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Cited By

Yu YLi NGong G(2025)Robust motorcycle graph construction and simplification for semi-structured quad mesh generationComputers & Graphics10.1016/j.cag.2025.104173127(104173)Online publication date: Apr-2025
https://doi.org/10.1016/j.cag.2025.104173
Hinderink SBrückler HCampen M(2024)Bijective Volumetric Mapping via Star DecompositionACM Transactions on Graphics10.1145/368795043:6(1-11)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687950
Feng NCrane K(2024)A Heat Method for Generalized Signed DistanceACM Transactions on Graphics10.1145/365822043:4(1-19)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658220
Capouellez RZorin D(2024)Seamless Parametrization in Penner CoordinatesACM Transactions on Graphics10.1145/365820243:4(1-13)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658202
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
Frühauf MRiemenschneider HGross MSchroers C(2024)QUADify: Extracting Meshes with Pixel-Level Details and Materials from Images2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52733.2024.00446(4661-4670)Online publication date: 16-Jun-2024
https://doi.org/10.1109/CVPR52733.2024.00446
Zheng WWu HXu GLing RGu R(2024)Feature-preserving quadrilateral mesh Boolean operation with cross-field guided layout blendingComputer Aided Geometric Design10.1016/j.cagd.2024.102324111(102324)Online publication date: Jun-2024
https://doi.org/10.1016/j.cagd.2024.102324
Lv YJia BYan YArmstrong CRobinson TSun L(2024)Enhanced block-structured quadrilateral mesh generation: integrating cross-field and distance field for optimal domain decompositionEngineering with Computers10.1007/s00366-024-02084-xOnline publication date: 28-Nov-2024
https://doi.org/10.1007/s00366-024-02084-x
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
https://dl.acm.org/doi/10.1007/s00366-024-02007-w
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
https://doi.org/10.1007/978-3-031-40594-5_16
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