Approximating 3D surfaces using generalized waterbomb tessellations
Approximating 3D surfaces using generalized waterbomb tessellations
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DOI：
10.1016/j.jcde.2018.01.002
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发表时间：
2018-10
期刊：
影响因子：
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通讯作者：
Yan Zhao;Yuki Endo;Yoshihiro Kanamori;J. Mitani
中科院分区：
文献类型：
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作者：
Yan Zhao;Yuki Endo;Yoshihiro Kanamori;J. Mitani
折纸在几何、数学和工程领域受到了广泛的关注，因为它具有从平面上设计的折痕图案构建3D可展开形状的潜力。水弹镶嵌是一种由一组水弹底座组成的传统折纸，已被用于创造几何上吸引人的3D形状，并被广泛研究。本文提出了一种用广义水弹镶嵌法逼近变曲率或常曲率参数曲面的方法。首先，我们通过使用水弹基地平铺目标表面来生成一个基本网格。然后，通过对基网格应用简单的数值优化算法，我们实现了可展开的水弹镶嵌，可以在不拉伸的情况下在平面上展开。我们提供了一个原型系统，用户可以使用它来调整镶嵌的分辨率和修改水弹基座。我们的工作可以扩展使用折纸构建可开发的3D结构的探索。高光概括水弹镶嵌，以适应目标3D参数表面。用简单的数值优化算法实现可展开镶嵌。证明了非轴对称或不可定向的近似结果。
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.HighlightsGeneralizing waterbomb tessellations to fit target 3D parametric surfaces.Achieving developable tessellations by a simple numerical optimization algorithm.Non-axisymmetric or non-orientable resulting approximations are demonstrated.