research-article

Boundary aligned smooth 3D cross-frame field

Authors:

Hujun BaoAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 30, Issue 6

Pages 1 - 8

https://doi.org/10.1145/2070781.2024177

Published: 12 December 2011 Publication History

Abstract

In this paper, we present a method for constructing a 3D cross-frame field, a 3D extension of the 2D cross-frame field as applied to surfaces in applications such as quadrangulation and texture synthesis. In contrast to the surface cross-frame field (equivalent to a 4-Way Rotational-Symmetry vector field), symmetry for 3D cross-frame fields cannot be formulated by simple one-parameter 2D rotations in the tangent planes. To address this critical issue, we represent the 3D frames by spherical harmonics, in a manner invariant to combinations of rotations around any axis by multiples of π/2. With such a representation, we can formulate an efficient smoothness measure of the cross-frame field. Through minimization of this measure under certain boundary conditions, we can construct a smooth 3D cross-frame field that is aligned with the surface normal at the boundary. We visualize the resulting cross-frame field through restrictions to the boundary surface, streamline tracing in the volume, and singularities. We also demonstrate the application of the 3D cross-frame field to producing hexahedron-dominant meshes for given volumes, and discuss its potential in high-quality hexahedralization, much as its 2D counterpart has shown in quadrangulation.

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Cited By

Zhang CYu ZShi JLi YXu WGuo ZZhang HZhu ZQiang S(2024)A complex model decomposition algorithm based on 3D frame fields and featuresEngineering Computations10.1108/EC-01-2023-003741:1(237-258)Online publication date: 9-Feb-2024
https://doi.org/10.1108/EC-01-2023-0037
Duan JZheng XLei NLuo Z(2024)Singularity structure simplification for hex mesh via integer linear programComputer-Aided Design10.1016/j.cad.2023.103654168:COnline publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1016/j.cad.2023.103654
Liu HBommes D(2023)Locally Meshable Frame FieldsACM Transactions on Graphics10.1145/359245742:4(1-20)Online publication date: 26-Jul-2023
https://doi.org/10.1145/3592457
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Index Terms

Boundary aligned smooth 3D cross-frame field
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 30, Issue 6

December 2011

678 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2070781

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Copyright © 2011 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 December 2011

Published in TOG Volume 30, Issue 6

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Cited By

Zhang CYu ZShi JLi YXu WGuo ZZhang HZhu ZQiang S(2024)A complex model decomposition algorithm based on 3D frame fields and featuresEngineering Computations10.1108/EC-01-2023-003741:1(237-258)Online publication date: 9-Feb-2024
https://doi.org/10.1108/EC-01-2023-0037
Duan JZheng XLei NLuo Z(2024)Singularity structure simplification for hex mesh via integer linear programComputer-Aided Design10.1016/j.cad.2023.103654168:COnline publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1016/j.cad.2023.103654
Liu HBommes D(2023)Locally Meshable Frame FieldsACM Transactions on Graphics10.1145/359245742:4(1-20)Online publication date: 26-Jul-2023
https://doi.org/10.1145/3592457
Reberol MVerhetsel KHenrotte FBommes DRemacle J(2023)Robust Topological Construction of All-hexahedral Boundary Layer MeshesACM Transactions on Mathematical Software10.1145/357719649:1(1-32)Online publication date: 21-Mar-2023
https://dl.acm.org/doi/10.1145/3577196
Si LChen G(2023)A Visualization System for Hexahedral Mesh Quality Study2023 IEEE Visualization and Visual Analytics (VIS)10.1109/VIS54172.2023.00026(86-90)Online publication date: 21-Oct-2023
https://doi.org/10.1109/VIS54172.2023.00026
Fang XHuang JTong YBao H(2023)Metric-Driven 3D Frame Field GenerationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.313619929:4(1964-1976)Online publication date: 1-Apr-2023
https://doi.org/10.1109/TVCG.2021.3136199
Golovaty DKurzke MMontero JSpirn D(2023)Tetrahedral Frame Fields via Constrained Third-Order Symmetric TensorsJournal of Nonlinear Science10.1007/s00332-023-09898-x33:3Online publication date: 31-Mar-2023
https://doi.org/10.1007/s00332-023-09898-x
Pietroni NCampen MSheffer ACherchi GBommes DGao XScateni RLedoux FRemacle JLivesu M(2022)Hex-Mesh Generation and Processing: A SurveyACM Transactions on Graphics10.1145/355492042:2(1-44)Online publication date: 18-Oct-2022
https://dl.acm.org/doi/10.1145/3554920
Zhang TFang GHuang YDutta NLefebvre SKilic ZWang C(2022)S3-SlicerACM Transactions on Graphics10.1145/3550454.355551641:6(1-15)Online publication date: 30-Nov-2022
https://dl.acm.org/doi/10.1145/3550454.3555516
Yang YBarnes CAdams AFinkelstein A(2022)AδACM Transactions on Graphics10.1145/3528223.353012541:4(1-24)Online publication date: 22-Jul-2022
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