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Mixed-integer quadrangulation

Authors:

Leif KobbeltAuthors Info & Claims

SIGGRAPH '09: ACM SIGGRAPH 2009 papers

Article No.: 77, Pages 1 - 10

https://doi.org/10.1145/1576246.1531383

Published: 27 July 2009 Publication History

Abstract

We present a novel method for quadrangulating a given triangle mesh. After constructing an as smooth as possible symmetric cross field satisfying a sparse set of directional constraints (to capture the geometric structure of the surface), the mesh is cut open in order to enable a low distortion unfolding. Then a seamless globally smooth parametrization is computed whose iso-parameter lines follow the cross field directions. In contrast to previous methods, sparsely distributed directional constraints are sufficient to automatically determine the appropriate number, type and position of singularities in the quadrangulation. Both steps of the algorithm (cross field and parametrization) can be formulated as a mixed-integer problem which we solve very efficiently by an adaptive greedy solver. We show several complex examples where high quality quad meshes are generated in a fully automatic manner.

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Cited By

Gao JXiao ZXu CShen SXu G(2024)Quadrilateral surface mesh generation with improved quality by combination of trianglesInternational Journal for Numerical Methods in Engineering10.1002/nme.7539125:16Online publication date: 27-May-2024
https://doi.org/10.1002/nme.7539
MacLean KNadarajah S(2021)Unstructured Anisotropic Mesh Adaptation for Quads Based on a Local Error ModelAIAA Scitech 2021 Forum10.2514/6.2021-1840Online publication date: 4-Jan-2021
https://doi.org/10.2514/6.2021-1840
Jones BMei YZhao HGotfrid TMankoff JSchulz A(2021)Computational Design of Knit TemplatesACM Transactions on Graphics10.1145/348800641:2(1-16)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.1145/3488006
Show More Cited By

Index Terms

Mixed-integer quadrangulation
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

SIGGRAPH '09: ACM SIGGRAPH 2009 papers

July 2009

795 pages

ISBN:9781605587264

DOI:10.1145/1576246

Conference Chair:
Thomas Funkhouser,
Editor:
Hugues Hoppe
ACM Transactions on Graphics

Copyright © 2009 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 27 July 2009

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SIGGRAPH09: Special Interest Group on Computer Graphics and Interactive Techniques Conference

August 3 - 7, 2009

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SIGGRAPH '09 Paper Acceptance Rate 78 of 439 submissions, 18%;

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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Cited By

Gao JXiao ZXu CShen SXu G(2024)Quadrilateral surface mesh generation with improved quality by combination of trianglesInternational Journal for Numerical Methods in Engineering10.1002/nme.7539125:16Online publication date: 27-May-2024
https://doi.org/10.1002/nme.7539
MacLean KNadarajah S(2021)Unstructured Anisotropic Mesh Adaptation for Quads Based on a Local Error ModelAIAA Scitech 2021 Forum10.2514/6.2021-1840Online publication date: 4-Jan-2021
https://doi.org/10.2514/6.2021-1840
Jones BMei YZhao HGotfrid TMankoff JSchulz A(2021)Computational Design of Knit TemplatesACM Transactions on Graphics10.1145/348800641:2(1-16)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.1145/3488006
Li LZhang PSmirnov DAbulnaga SSolomon J(2021)Interactive all-hex meshing via cuboid decompositionACM Transactions on Graphics10.1145/3478513.348056840:6(1-17)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480568
Feng LTong YDesbrun M(2021)Q-zipACM Transactions on Graphics10.1145/3478513.348052340:6(1-13)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480523
Levi Z(2021)Direct Seamless ParametrizationACM Transactions on Graphics10.1145/343982840:1(1-14)Online publication date: 18-Jan-2021
https://dl.acm.org/doi/10.1145/3439828
Lyon MBommes DKobbelt L(2020)Cost Minimizing Local Anisotropic Quad Mesh RefinementComputer Graphics Forum10.1111/cgf.1407639:5(163-172)Online publication date: 12-Aug-2020
https://doi.org/10.1111/cgf.14076
Hefetz EChien EWeber O(2019)A Subspace Method for Fast Locally Injective Harmonic MappingComputer Graphics Forum10.1111/cgf.1362338:2(105-119)Online publication date: 7-Jun-2019
https://doi.org/10.1111/cgf.13623
Marinov MAmagliani MCharrot P(2019)Boundary conforming mesh to T-NURCC surface conversionComputers and Graphics10.1016/j.cag.2019.05.01282:C(95-105)Online publication date: 1-Aug-2019
https://dl.acm.org/doi/10.1016/j.cag.2019.05.012
Musto JLyon MTrautz MKobbelt L(2019)Beanspruchungsoptimierte Faltungen aus Stahl für selbsttragende RaumfaltwerkeBautechnik10.1002/bate.20190002496:12(902-911)Online publication date: 16-Sep-2019
https://doi.org/10.1002/bate.201900024
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