Deployable strip structures

Daoming Liu; Davide Pellis; Yu-Chou Chiang; Florian Rist; Johannes Wallner; Helmut Pottmann

doi:10.1145/3592393

Deployable strip structures

Daoming Liu, Davide Pellis, Yu-Chou Chiang, Florian Rist, Johannes Wallner, Helmut Pottmann

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We introduce the new concept of C-mesh to capture kinetic structures that can be deployed from a collapsed state. Quadrilateral C-meshes enjoy rich geometry and surprising relations with differential geometry: A structure that collapses onto a flat and straight strip corresponds to a Chebyshev net of curves on a surface of constant Gaussian curvature, while structures collapsing onto a circular strip follow surfaces which enjoy the linear-Weingarten property. Interestingly, allowing more general collapses actually leads to a smaller class of shapes. Hexagonal C-meshes have more degrees of freedom, but a local analysis suggests that there is no such direct relation to smooth surfaces. Besides theory, this paper provides tools for exploring the shape space of C-meshes and for their design. We also present an application for freeform architectural skins, namely paneling with spherical panels of constant radius, which is an important fabrication-related constraint.

Original language	English (US)
Pages (from-to)	1-16
Number of pages	16
Journal	ACM transactions on graphics
Volume	42
Issue number	4
DOIs	https://doi.org/10.1145/3592393
State	Published - Jul 26 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-07-31
Acknowledged KAUST grant number(s): BAS/1/1679-01-01
Acknowledgements: The authors wish to thank the anonymous reviewers for their helpful comments. D. Liu, Y.-C. Chiang, and F. Rist have been supported by KAUST baseline funding (grant BAS/1/1679-01-01).

ASJC Scopus subject areas

Computer Graphics and Computer-Aided Design

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10.1145/3592393

Cite this

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title = "Deployable strip structures",

abstract = "We introduce the new concept of C-mesh to capture kinetic structures that can be deployed from a collapsed state. Quadrilateral C-meshes enjoy rich geometry and surprising relations with differential geometry: A structure that collapses onto a flat and straight strip corresponds to a Chebyshev net of curves on a surface of constant Gaussian curvature, while structures collapsing onto a circular strip follow surfaces which enjoy the linear-Weingarten property. Interestingly, allowing more general collapses actually leads to a smaller class of shapes. Hexagonal C-meshes have more degrees of freedom, but a local analysis suggests that there is no such direct relation to smooth surfaces. Besides theory, this paper provides tools for exploring the shape space of C-meshes and for their design. We also present an application for freeform architectural skins, namely paneling with spherical panels of constant radius, which is an important fabrication-related constraint.",

author = "Daoming Liu and Davide Pellis and Yu-Chou Chiang and Florian Rist and Johannes Wallner and Helmut Pottmann",

note = "KAUST Repository Item: Exported on 2023-07-31 Acknowledged KAUST grant number(s): BAS/1/1679-01-01 Acknowledgements: The authors wish to thank the anonymous reviewers for their helpful comments. D. Liu, Y.-C. Chiang, and F. Rist have been supported by KAUST baseline funding (grant BAS/1/1679-01-01).",

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AU - Liu, Daoming

AU - Pellis, Davide

AU - Chiang, Yu-Chou

AU - Rist, Florian

AU - Wallner, Johannes

AU - Pottmann, Helmut

N1 - KAUST Repository Item: Exported on 2023-07-31 Acknowledged KAUST grant number(s): BAS/1/1679-01-01 Acknowledgements: The authors wish to thank the anonymous reviewers for their helpful comments. D. Liu, Y.-C. Chiang, and F. Rist have been supported by KAUST baseline funding (grant BAS/1/1679-01-01).

PY - 2023/7/26

Y1 - 2023/7/26

N2 - We introduce the new concept of C-mesh to capture kinetic structures that can be deployed from a collapsed state. Quadrilateral C-meshes enjoy rich geometry and surprising relations with differential geometry: A structure that collapses onto a flat and straight strip corresponds to a Chebyshev net of curves on a surface of constant Gaussian curvature, while structures collapsing onto a circular strip follow surfaces which enjoy the linear-Weingarten property. Interestingly, allowing more general collapses actually leads to a smaller class of shapes. Hexagonal C-meshes have more degrees of freedom, but a local analysis suggests that there is no such direct relation to smooth surfaces. Besides theory, this paper provides tools for exploring the shape space of C-meshes and for their design. We also present an application for freeform architectural skins, namely paneling with spherical panels of constant radius, which is an important fabrication-related constraint.

AB - We introduce the new concept of C-mesh to capture kinetic structures that can be deployed from a collapsed state. Quadrilateral C-meshes enjoy rich geometry and surprising relations with differential geometry: A structure that collapses onto a flat and straight strip corresponds to a Chebyshev net of curves on a surface of constant Gaussian curvature, while structures collapsing onto a circular strip follow surfaces which enjoy the linear-Weingarten property. Interestingly, allowing more general collapses actually leads to a smaller class of shapes. Hexagonal C-meshes have more degrees of freedom, but a local analysis suggests that there is no such direct relation to smooth surfaces. Besides theory, this paper provides tools for exploring the shape space of C-meshes and for their design. We also present an application for freeform architectural skins, namely paneling with spherical panels of constant radius, which is an important fabrication-related constraint.

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SP - 1

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JO - ACM transactions on graphics

JF - ACM transactions on graphics

IS - 4

ER -

Deployable strip structures

Abstract

Bibliographical note

ASJC Scopus subject areas

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