research-article

General planar quadrilateral mesh design using conjugate direction field

Authors:

Guoping WangAuthors Info & Claims

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

Pages 1 - 10

https://doi.org/10.1145/2070781.2024174

Published: 12 December 2011 Publication History

Abstract

We present a novel method to approximate a freeform shape with a planar quadrilateral (PQ) mesh for modeling architectural glass structures. Our method is based on the study of conjugate direction fields (CDF) which allow the presence of ±κ/4(κ ε Z) singularities. Starting with a triangle discretization of a freeform shape, we first compute an as smooth as possible conjugate direction field satisfying the user's directional and angular constraints, then apply mixed-integer quadrangulation and planarization techniques to generate a PQ mesh which approximates the input shape faithfully. We demonstrate that our method is effective and robust on various 3D models.

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Index Terms

General planar quadrilateral mesh design using conjugate direction field
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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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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Liu SZhang ZLiu ZTan PZeng B(2025)Minimum Latency Deep Online Video Stabilization and Its ExtensionsIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2024.349317547:2(1238-1249)Online publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1109/TPAMI.2024.3493175
Dong FTang YZhang JQian K(2024)NRO-stylization: A novel algorithm for regular octahedral stylization aesthetic modeling of three-dimensional surface meshPLOS ONE10.1371/journal.pone.031024219:10(e0310242)Online publication date: 29-Oct-2024
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Miki MMitchell T(2024)Alignment conditions for NURBS-based design of mixed tension-compression grid shellsACM Transactions on Graphics10.1145/365814243:4(1-19)Online publication date: 19-Jul-2024
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Raffaele LBruno LLaccone FVenuti FTomei V(2024)Holistic performance assessment of gridshells: Methodological framework and applications to steel gridshellsJournal of Building Engineering10.1016/j.jobe.2024.10940690(109406)Online publication date: Aug-2024
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Laccone FPietroni NCignoni PMalomo L(2024)Bending-Reinforced Grid Shells for Free-form Architectural SurfacesComputer-Aided Design10.1016/j.cad.2023.103670168:COnline publication date: 1-Mar-2024
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Deng ZLiu YPan HJabi WZhang JDeng B(2023)Sketch2PQ: Freeform Planar Quadrilateral Mesh Design via a Single SketchIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.317085329:9(3826-3839)Online publication date: 1-Sep-2023
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Li CSong LChen SXie RZhang W(2023)Deep Online Video Stabilization Using IMU SensorsIEEE Transactions on Multimedia10.1109/TMM.2022.314242925(2047-2060)Online publication date: 1-Jan-2023
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Zhu TXu ZLiu LFu X(2023)Modeling with discrete equivalence classes of planar quadsComputers and Graphics10.1016/j.cag.2023.07.032115:C(404-411)Online publication date: 1-Oct-2023
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