research-article

Which cross fields can be quadrangulated?: global parameterization from prescribed holonomy signatures

Authors:

Ryan Capouellez,

Daniele Panozzo,

Denis ZorinAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 41, Issue 4

Article No.: 59, Pages 1 - 12

https://doi.org/10.1145/3528223.3530187

Published: 22 July 2022 Publication History

Abstract

We describe a method for the generation of seamless surface parametrizations with guaranteed local injectivity and full control over holonomy. Previous methods guarantee only one of the two. Local injectivity is required to enable these parametrizations' use in applications such as surface quadrangulation and spline construction. Holonomy control is crucial to enable guidance or prescription of the parametrization's isocurves based on directional information, in particular from cross-fields or feature curves, and more generally to constrain the parametrization topologically. To this end we investigate the relation between cross-field topology and seamless parametrization topology. Leveraging previous results on locally injective parametrization and combining them with insights on this relation in terms of holonomy, we propose an algorithm that meets these requirements. A key component relies on the insight that arbitrary surface cut graphs, as required for global parametrization, can be homeomorphically modified to assume almost any set of turning numbers with respect to a given target cross-field.

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Index Terms

Which cross fields can be quadrangulated?: global parameterization from prescribed holonomy signatures
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Mesh models

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 41, Issue 4

July 2022

1978 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3528223

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Copyright © 2022 ACM.

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Publication History

Published: 22 July 2022

Published in TOG Volume 41, Issue 4

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Cited By

Wang XZhang XCui WXiong RFan XZhao DCai JKankanhalli MPrabhakaran BBoll SSubramanian RZheng LSingh VCesar PXie LXu D(2024)Mesh Denoising Using Filtering Coefficients Jointly Aware of Noise and GeometryProceedings of the 32nd ACM International Conference on Multimedia10.1145/3664647.3681143(1791-1799)Online publication date: 28-Oct-2024
https://dl.acm.org/doi/10.1145/3664647.3681143
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
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
Sarmah MNeelima A(2024)Enhanced 3D reconstruction with all-neighbor-first philosophy and Ricci flow-based mesh smoothing approachMultimedia Systems10.1007/s00530-023-01210-x30:1Online publication date: 19-Jan-2024
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Bhatti UTang HWu GMarjan SHussain A(2023)Deep Learning with Graph Convolutional NetworksInternational Journal of Intelligent Systems10.1155/2023/83421042023Online publication date: 1-Jan-2023
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Chen HLi ZWei MWang J(2023)Geometric and Learning-Based Mesh Denoising: A Comprehensive SurveyACM Transactions on Multimedia Computing, Communications, and Applications10.1145/362509820:3(1-28)Online publication date: 10-Nov-2023
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Levi Z(2023)Seamless Parametrization with Cone and Partial Loop ControlACM Transactions on Graphics10.1145/360008742:5(1-22)Online publication date: 30-Aug-2023
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