论文标题
为弯曲表面构建刚性折叠的通用Miura-Ori镶嵌物
Constructing rigid-foldable generalized Miura-ori tessellations for curved surfaces
论文作者
论文摘要
折纸表明，通过在平坦材料上设计的折痕图案折叠来折叠三维弯曲表面的潜力。 Miura-Ori Tessellation是工程中广泛使用的模式，当部分折叠时平面。基于受限的优化，本文介绍了通用的miura-ori模式的构建，这些模式可以近似于不同曲率的三维参数表面，同时保留了标准的miura-ori的固有特性，包括可开发性，扁平性可宽容性，扁平性和刚性性。初始配置是通过用三角形的miura样单元细胞铺平目标表面来构建的，并用作优化的初始猜测。为了近似单个目标表面，一侧的一部分顶点附着在目标表面上。为了拟合两个目标表面，另一侧的一部分顶点也附在第二个目标表面上。参数坐标被用作目标表面上顶点的未知变量，而笛卡尔坐标是其他顶点的未知数。构建的广义Miura-Ori镶嵌物可以用单个自由度将固定状态刚好折叠到目标状态。
Origami has shown the potential to approximate three-dimensional curved surfaces by folding through designed crease patterns on flat materials. The Miura-ori tessellation is a widely used pattern in engineering and tiles the plane when partially folded. Based on constrained optimization, this paper presents the construction of generalized Miura-ori patterns that can approximate three-dimensional parametric surfaces of varying curvatures while preserving the inherent properties of the standard Miura-ori, including developability, flat-foldability and rigid-foldability. An initial configuration is constructed by tiling the target surface with triangulated Miura-like unit cells and used as the initial guess for the optimization. For approximation of a single target surface, a portion of the vertexes on the one side is attached to the target surface; for fitting of two target surfaces, a portion of vertexes on the other side is also attached to the second target surface. The parametric coordinates are adopted as the unknown variables for the vertexes on the target surfaces whilst the Cartesian coordinates are the unknowns for the other vertexes. The constructed generalized Miura-ori tessellations can be rigidly folded from the flat state to the target state with a single degree of freedom.
