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Approximating 3D surfaces using generalized waterbomb tessellations
Yan Zhao,Yuki Endo,Yoshihiro Kanamori,Jun Mitani 한국CDE학회 2018 Journal of computational design and engineering Vol.5 No.4
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.
AR based ornament design system for 3D printing
Aoki, Hiroshi,Mitanin, Jun,Kanamori, Yoshihiro,Fukui, Yukio Society for Computational Design and Engineering 2015 Journal of computational design and engineering Vol.2 No.1
In recent years, 3D printers have become popular as a means of outputting geometries designed on CAD or 3D graphics systems. However, the complex user interfaces of standard 3D software can make it difficult for ordinary consumers to design their own objects. Furthermore, models designed on 3D graphics software often have geometrical problems that make them impossible to output on a 3D printer. We propose a novel AR (augmented reality) 3D modeling system with an air-spray like interface. We also propose a new data structure (octet voxel) for representing designed models in such a way that the model is guaranteed to be a complete solid. The target shape is based on a regular polyhedron, and the octet voxel representation is suitable for designing geometrical objects having the same symmetries as the base regular polyhedron. Finally, we conducted a user test and confirmed that users can intuitively design their own ornaments in a short time with a simple user interface.