research-article

Exploring quadrangulations

Authors:

Michael Barton,

Peter WonkaAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 33, Issue 1

Article No.: 12, Pages 1 - 13

https://doi.org/10.1145/2541533

Published: 07 February 2014 Publication History

Abstract

We present a framework for exploring topologically unique quadrangulations of an input shape. First, the input shape is segmented into surface patches. Second, different topologies are enumerated and explored in each patch. This is realized by an efficient subdivision-based quadrangulation algorithm that can exhaustively enumerate all mesh topologies within a patch. To help users navigate the potentially huge collection of variations, we propose tools to preview and arrange the results. Furthermore, the requirement that all patches need to be jointly quadrangulatable is formulated as a linear integer program. Finally, we apply the framework to shape-space exploration, remeshing, and design to underline the importance of topology exploration.

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Cited By

Karčiauskas KLo KGunpinar EPeters J(2024)Bicubic Splines for Fast-Contracting Control NetsAxioms10.3390/axioms1306039013:6(390)Online publication date: 9-Jun-2024
https://doi.org/10.3390/axioms13060390
Heistermann MWarnett JBommes D(2023)Min-Deviation-Flow in Bi-directed Graphs for T-Mesh QuantizationACM Transactions on Graphics10.1145/359243742:4(1-25)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592437
Tong HQian KHalilaj EZhang Y(2023)SRL-assisted AFM: Generating planar unstructured quadrilateral meshes with supervised and reinforcement learning-assisted advancing front methodJournal of Computational Science10.1016/j.jocs.2023.10210972(102109)Online publication date: Sep-2023
https://doi.org/10.1016/j.jocs.2023.102109
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Index Terms

Exploring quadrangulations
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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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 33, Issue 1

January 2014

179 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2577382

Issue’s Table of Contents

Copyright © 2014 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 the author(s) 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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 07 February 2014

Accepted: 01 November 2013

Revised: 01 July 2013

Received: 01 November 2012

Published in TOG Volume 33, Issue 1

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Cited By

Karčiauskas KLo KGunpinar EPeters J(2024)Bicubic Splines for Fast-Contracting Control NetsAxioms10.3390/axioms1306039013:6(390)Online publication date: 9-Jun-2024
https://doi.org/10.3390/axioms13060390
Heistermann MWarnett JBommes D(2023)Min-Deviation-Flow in Bi-directed Graphs for T-Mesh QuantizationACM Transactions on Graphics10.1145/359243742:4(1-25)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592437
Tong HQian KHalilaj EZhang Y(2023)SRL-assisted AFM: Generating planar unstructured quadrilateral meshes with supervised and reinforcement learning-assisted advancing front methodJournal of Computational Science10.1016/j.jocs.2023.10210972(102109)Online publication date: Sep-2023
https://doi.org/10.1016/j.jocs.2023.102109
Pandey KBærentzen JSingh K(2022)Face Extrusion Quad MeshesACM SIGGRAPH 2022 Conference Proceedings10.1145/3528233.3530754(1-9)Online publication date: 27-Jul-2022
https://dl.acm.org/doi/10.1145/3528233.3530754
Akram MXu KChen G(2022)Structure simplification of planar quadrilateral meshesComputers and Graphics10.1016/j.cag.2022.10.001109:C(1-14)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1016/j.cag.2022.10.001
Tarini M(2022)Closed-form quadrangulation of n-sided patchesComputers and Graphics10.1016/j.cag.2022.06.015107:C(60-65)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1016/j.cag.2022.06.015
Chen LBu NJin YXu GLi B(2022)Construction of IGA-suitable Volume Parametric Models by the Segmentation–Mapping–Merging Mechanism of Design FeaturesComputer-Aided Design10.1016/j.cad.2022.103228146:COnline publication date: 1-May-2022
https://dl.acm.org/doi/10.1016/j.cad.2022.103228
Dielen ALim ILyon MKobbelt L(2021)Learning Direction Fields for Quad Mesh GenerationComputer Graphics Forum10.1111/cgf.1436640:5(181-191)Online publication date: 23-Aug-2021
https://doi.org/10.1111/cgf.14366
Zhang CChai SLiu LFu X(2021)Quad Meshing with Coarse Layouts for Planar DomainsComputer-Aided Design10.1016/j.cad.2021.103084140:COnline publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1016/j.cad.2021.103084
Zhou JTu CZorin DCampen M(2020)Combinatorial Construction of Seamless Parameter DomainsComputer Graphics Forum10.1111/cgf.1392239:2(179-190)Online publication date: 13-Jul-2020
https://doi.org/10.1111/cgf.13922
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