research-article

Form-finding with polyhedral meshes made simple

Authors:

Chengcheng Tang,

Alexandra Gomes,

Johannes Wallner,

Helmut PottmannAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 33, Issue 4

Article No.: 70, Pages 1 - 9

https://doi.org/10.1145/2601097.2601213

Published: 27 July 2014 Publication History

Abstract

We solve the form-finding problem for polyhedral meshes in a way which combines form, function and fabrication; taking care of user-specified constraints like boundary interpolation, planarity of faces, statics, panel size and shape, enclosed volume, and last, but not least, cost. Our main application is the interactive modeling of meshes for architectural and industrial design. Our approach can be described as guided exploration of the constraint space whose algebraic structure is simplified by introducing auxiliary variables and ensuring that constraints are at most quadratic. Computationally, we perform a projection onto the constraint space which is biased towards low values of an energy which expresses desirable "soft" properties like fairness. We have created a tool which elegantly handles difficult tasks, such as taking boundary-alignment of polyhedral meshes into account, planarization, fairing under planarity side conditions, handling hybrid meshes, and extending the treatment of static equilibrium to shapes which possess overhanging parts.

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Cited By

Cisneros Ramos AKilian MAikyn APottmann HMüller C(2024)Approximation by Meshes with Spherical FacesACM Transactions on Graphics10.1145/368794243:6(1-18)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687942
Ceballos Inza VFykouras PRist FHäseker DHojjat MMüller CPottmann H(2024)Designing triangle meshes with controlled roughnessACM Transactions on Graphics10.1145/368794043:6(1-20)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687940
Jiang CLyakhov DRist FPottmann HWallner J(2024)Quad mesh mechanismsACM Transactions on Graphics10.1145/368793943:6(1-17)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687939
Show More Cited By

Index Terms

Form-finding with polyhedral meshes made simple
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 33, Issue 4

July 2014

1366 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2601097

Issue’s Table of Contents

Copyright © 2014 ACM.

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Publication History

Published: 27 July 2014

Published in TOG Volume 33, Issue 4

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Cited By

Cisneros Ramos AKilian MAikyn APottmann HMüller C(2024)Approximation by Meshes with Spherical FacesACM Transactions on Graphics10.1145/368794243:6(1-18)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687942
Ceballos Inza VFykouras PRist FHäseker DHojjat MMüller CPottmann H(2024)Designing triangle meshes with controlled roughnessACM Transactions on Graphics10.1145/368794043:6(1-20)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687940
Jiang CLyakhov DRist FPottmann HWallner J(2024)Quad mesh mechanismsACM Transactions on Graphics10.1145/368793943:6(1-17)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687939
Pellis D(2024)Alignable Lamella GridshellsACM Transactions on Graphics10.1145/368789843:6(1-21)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687898
Zhang HCheng SAmm CKim J(2024)Efficient Pooling Operator for 3D Morphable ModelsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.325582030:7(4225-4233)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3255820
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
https://doi.org/10.1016/j.jobe.2024.109406
Pellis DPottmann H(2024)The geometry of principal symmetric structuresStructures10.1016/j.istruc.2024.10597260(105972)Online publication date: Feb-2024
https://doi.org/10.1016/j.istruc.2024.105972
Kilian MNawratil GRaffaelli MRasoulzadeh ASharifmoghaddam K(2024)Interactive design of discrete Voss nets and simulation of their rigid foldingsComputer Aided Geometric Design10.1016/j.cagd.2024.102346111(102346)Online publication date: Jun-2024
https://doi.org/10.1016/j.cagd.2024.102346
Wang BWang HSchling EPottmann H(2023)Rectifying Strip PatternsACM Transactions on Graphics10.1145/361837842:6(1-18)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618378
Kilian MCisneros AMüller CPottmann H(2023)Meshes with Spherical FacesACM Transactions on Graphics10.1145/361834542:6(1-19)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618345
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