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C. Jiang, K. Mundilova, F. Rist, J. Wallner, H. Pottmann:
"Curve-pleated structures";
ACM Transactions on Graphics, 38/6 (2019), 169; 1 - 13.

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 smoothand discrete situations, as well as several equivalent characterizations ofthe principal property. These include being a conical mesh, and being flat-foldable. This structure-preserving discretization is the basis of computationand design. We propose a new method for designing pleated structuresand reconstructing reference shapes as pleated structures: we first gain an overview of possible crease patterns by establishing a connection to pseudo-geodesics, 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.

CCS Concepts; Computing methodologies; Computer graphics; Shape modeling; Mesh geometry models.

http://dx.doi.org/10.1145/3355089.3356540

https://dmg.tuwien.ac.at/geom/ig/publications/folding/folding.pdf