Curve-pleated Structures

摘要

In this paper we study pleated structures generated by folding paper alongcurved creases. We discuss their properties and the special case of principalpleated structures. A discrete version of pleated structures is particularlyinteresting 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 flatfoldable.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 anoverview of possible crease patterns by establishing a connection to pseudogeodesics,and then initialize and optimize a quad mesh so as to become adiscrete pleated structure. We conclude by showing applications in designand reconstruction, including cases with combinatorial singularities. Ourwork is relevant to fabrication in so far as the offset properties of principalpleated structures allow us to construct curved sculptures of finite thickness.