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Deployable strip structures

Published: 26 July 2023 Publication History

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.

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    cover image ACM Transactions on Graphics
    ACM Transactions on Graphics  Volume 42, Issue 4
    August 2023
    1912 pages
    ISSN:0730-0301
    EISSN:1557-7368
    DOI:10.1145/3609020
    Issue’s Table of Contents
    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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    Publication History

    Published: 26 July 2023
    Published in TOG Volume 42, Issue 4

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    Author Tags

    1. discrete differential geometry
    2. digital fabrication
    3. architectural geometry
    4. computational design
    5. inverse design
    6. deployable structure
    7. spherical paneling

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