Curve-pleated structures
| Autor: | Klara Mundilova, Helmut Pottmann, Johannes Wallner, Caigui Jiang, Florian Rist |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Developable surface
Discretization Basis (linear algebra) Computer science Connection (vector bundle) 020207 software engineering 02 engineering and technology Conical surface Computer Science::Computational Geometry Topology Mathematics::Geometric Topology Computer Graphics and Computer-Aided Design 0202 electrical engineering electronic engineering information engineering Gravitational singularity Discrete differential geometry |
| Zdroj: | ACM Transactions on Graphics. 38:1-13 |
| ISSN: | 1557-7368 0730-0301 |
| DOI: | 10.1145/3355089.3356540 |
| Popis: | 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 flat-foldable. 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. |
| Databáze: | OpenAIRE |
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