Curve-pleated structures

Caigui Jiang, Klara Mundilova, Florian Rist, Johannes Wallner, Helmut Pottmann

Research output: Contribution to journalArticle

Abstract

In this paper we study pleated structures generated by folding paper along curved creases. We discuss their properties and the special case of principal pleated structures. A discrete version of pleated structures is particularly interesting because of the rich geometric properties of the principal case, where we are able to establish a series of analogies between the smooth and discrete situations, as well as several equivalent characterizations of the principal property. These include being a conical mesh, and being fatfoldable. This structure-preserving discretization is the basis of computation and design. We propose a new method for designing pleated structures and reconstructing reference shapes as pleated structures: we first gain an overview of possible crease patterns by establishing a connection to pseudogeodesics, and then initialize and optimize a quad mesh so as to become a discrete pleated structure. We conclude by showing applications in design and reconstruction, including cases with combinatorial singularities. Our work is relevant to fabrication in so far as the offset properties of principal pleated structures allow us to construct curved sculptures of finite thickness.

Original languageEnglish
Article number169
Number of pages13
JournalACM Transactions on Graphics
Volume38
Issue number6
DOIs
Publication statusPublished - Nov 2019

Keywords

  • Computational fabrication
  • Computational origami
  • Conical mesh
  • Curved crease
  • Developable surface
  • Discrete differential geometry
  • Pleated surface
  • Pseudo-geodesic

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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