Deployable strip structures

Daoming Liu

doi:10.1145/3592393

Deployable strip structures

2023-07-26

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DOI：10.1145/3592393

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Abstract

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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.

Keywords:

discrete differential geometry

digital fabrication

architectural geometry

computational design

inverse design

deployable structure

spherical paneling

Deployable strip structures

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