Approximating 3D surfaces using generalized waterbomb tessellations. Issue 4 (9th January 2018)

• Record Type: Journal Article
• Authors: Zhao, Yan; Endo, Yuki; Kanamori, Yoshihiro; Mitani, Jun
• Is Part Of: Journal of computational design and engineering. Volume 5:Issue 4(2018)
• Page Start: 442
• Page End: 448
• Publication Date: 2018-01-09
• Subjects: 00-01 -- 99-00; Computational origami -- Approximation -- Developable constraint -- Computer aided design; Engineering -- Data processing -- Periodicals; Computer-aided design -- Periodicals; Computer-aided design; Engineering -- Data processing; Electronic journals; Electronic journals; Periodicals; 620.0042
• DOI: 10.1016/j.jcde.2018.01.002
• Languages: English
• ISSNs: 2288-4300

Abstract

Graphical Abstract: Abstract: Origami has received much attention in geometry, mathematics, and engineering due to its potential to construct 3D developable shapes from designed crease patterns on a flat sheet. Waterbomb tessellation, which is one type of traditional origami consisting of a set of waterbomb bases, has been used to create geometrically appealing 3D shapes and been widely studied. In this paper, we propose a method for approximating target surfaces, which are parametric surfaces of varying or constant curvatures, using generalized waterbomb tessellations. First, we generate a base mesh by tiling the target surface using waterbomb bases. Then, by applying a simple numerical optimization algorithm to the base mesh, we achieve a developable waterbomb tessellation, which can be developed onto a plane without stretching. We provide a prototype system using which the user can adjust the resolution of the tessellation and modify waterbomb bases. Our work could expand the exploration of building developable 3D structures using origami.