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Wang, Cheng 
ORCID: https://orcid.org/0000-0003-4711-4534, Jiang, Caigui, Tellier, Xavier, Wallner, Johannes and Pottmann, Helmut
(2022)
Planar panels and planar supporting beams in architectural structures.
ACM Transactions on Graphics, 42 (2).
ISSN 0730-0301
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Abstract
In this article, we investigate geometric properties and modeling capabilities of quad meshes with planar faces whose mesh polylines enjoy the additional property of being contained in a single plane. This planarity is a major benefit in architectural design and building construction: If a structural element is contained in a plane, it can be manufactured on the ground without scaffolding and put into place as a whole. Further, the plane it is contained in serves as part of a so-called support structure. We discuss design of meshes under the requirement that one half of mesh polylines are planar (“P meshes”), and we also investigate the geometry and design of meshes where all polylines enjoy this property (“PP meshes”). We work in the space of planes and with appropriate transformations of that space. We also incorporate further properties relevant for architectural design, such as near-rectangular panels and repetitive nodes. We provide geometric insights, give explicit constructions, and show an approach to geometric modeling of both P meshes and PP meshes, in particular, the case of nearly rectangular panels.
| Item Type: | Article |
|---|---|
| Additional Information: | Funding Information: This work was supported by the Austrian Science Fund via grants I2978 and F77 and by the Vienna Science and Technology Fund (grant ICT15-082). C. Jiang and C. Wang were supported by KAUST baseline funding. Copyright information: © 2022 Copyright held by the owner/author(s). Publication rights licensed to ACM. |
| Uncontrolled Keywords: | laguerre geometry,quad mesh,architectural geometry,discrete differential geometry,planar beams,support structure,computer graphics and computer-aided design ,/dk/atira/pure/subjectarea/asjc/1700/1704 |
| Faculty \ School: | Faculty of Science > School of Computing Sciences |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 23 Jan 2024 01:40 |
| Last Modified: | 04 Mar 2024 18:26 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/94227 |
| DOI: | 10.1145/3561050 |
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