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Globally smooth parameterizations with low distortion

Authors:

Andrei Khodakovsky,

Peter SchröderAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 22, Issue 3

Pages 350 - 357

https://doi.org/10.1145/882262.882275

Published: 01 July 2003 Publication History

Abstract

Good parameterizations are of central importance in many digital geometry processing tasks. Typically the behavior of such processing algorithms is related to the smoothness of the parameterization and how much distortion it contains. Since a parameterization maps a bounded region of the plane to the surface, a parameterization for a surface which is not homeomorphic to a disc must be made up of multiple pieces. We present a novel parameterization algorithm for arbitrary topology surface meshes which computes a globally smooth parameterization with low distortion. We optimize the patch layout subject to criteria such as shape quality and metric distortion, which are used to steer a mesh simplification approach for base complex construction. Global smoothness is achieved through simultaneous relaxation over all patches, with suitable transition functions between patches incorporated into the relaxation procedure. We demonstrate the quality of our parameterizations through numerical evaluation of distortion measures and the excellent rate distortion performance of semi-regular remeshes produced with these parameterizations. The numerical algorithms required to compute the parameterizations are robust and run on the order of minutes even for large meshes.

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Cited By

Ju TSchaefer SWarren J(2023)Mean Value Coordinates for Closed Triangular MeshesSeminal Graphics Papers: Pushing the Boundaries, Volume 210.1145/3596711.3596737(223-228)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1145/3596711.3596737
Liu HGillespie MChislett BSharp NJacobson ACrane K(2023)Surface Simplification using Intrinsic Error MetricsACM Transactions on Graphics10.1145/359240342:4(1-17)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592403
Cherchi GLivesu M(2023)VOLMAP: a Large Scale Benchmark for Volume Mappings to Simple Base DomainsComputer Graphics Forum10.1111/cgf.1491542:5Online publication date: 10-Aug-2023
https://doi.org/10.1111/cgf.14915
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Index Terms

Globally smooth parameterizations with low distortion
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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Information

Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 22, Issue 3

July 2003

683 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/882262

Issue’s Table of Contents

Copyright © 2003 ACM.

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Association for Computing Machinery

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Publication History

Published: 01 July 2003

Published in TOG Volume 22, Issue 3

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Cited By

Ju TSchaefer SWarren J(2023)Mean Value Coordinates for Closed Triangular MeshesSeminal Graphics Papers: Pushing the Boundaries, Volume 210.1145/3596711.3596737(223-228)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1145/3596711.3596737
Liu HGillespie MChislett BSharp NJacobson ACrane K(2023)Surface Simplification using Intrinsic Error MetricsACM Transactions on Graphics10.1145/359240342:4(1-17)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592403
Cherchi GLivesu M(2023)VOLMAP: a Large Scale Benchmark for Volume Mappings to Simple Base DomainsComputer Graphics Forum10.1111/cgf.1491542:5Online publication date: 10-Aug-2023
https://doi.org/10.1111/cgf.14915
Shi HJiang LZheng JZeng J(2023)Self-Parameterization Based Multi-Resolution Mesh Convolution NetworksComputer-Aided Design10.1016/j.cad.2023.103550162:COnline publication date: 13-Jul-2023
https://dl.acm.org/doi/10.1016/j.cad.2023.103550
Hu SLiu ZGuo MCai JHuang JMu TMartin R(2022)Subdivision-based Mesh Convolution NetworksACM Transactions on Graphics10.1145/350669441:3(1-16)Online publication date: 7-Mar-2022
https://dl.acm.org/doi/10.1145/3506694
Liu HZhang JBen-Chen MJacobson A(2021)Surface multigrid via intrinsic prolongationACM Transactions on Graphics10.1145/3476576.347663640:4(1-13)Online publication date: Aug-2021
https://doi.org/10.1145/3476576.3476636
Liu HZhang JBen-Chen MJacobson A(2021)Surface multigrid via intrinsic prolongationACM Transactions on Graphics10.1145/3450626.345976840:4(1-13)Online publication date: 19-Jul-2021
https://dl.acm.org/doi/10.1145/3450626.3459768
Liu HKim VChaudhuri SAigerman NJacobson A(2020)Neural subdivisionACM Transactions on Graphics10.1145/3386569.339241839:4(124:1-124:16)Online publication date: 12-Aug-2020
https://dl.acm.org/doi/10.1145/3386569.3392418
Dolonius DSintorn EAssarsson U(2020)UV‐free Texturing using Sparse Voxel DAGsComputer Graphics Forum10.1111/cgf.1391739:2(121-132)Online publication date: 13-Jul-2020
https://doi.org/10.1111/cgf.13917
Zhang DFang ZLu XQin HRobles-Kelly AZhang CHe Y(2020)Deep Patch-Based Human SegmentationNeural Information Processing10.1007/978-3-030-63830-6_20(229-240)Online publication date: 18-Nov-2020
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