论文标题
用拉格朗日乘法器方法对刚性折纸的折叠模拟
Folding Simulation of Rigid Origami with Lagrange Multiplier Method
论文作者
论文摘要
折纸折痕图案是折叠路径，将扁平板转化为空间对象。具有单个自由度（DOF）的折纸图案具有同时折叠的折痕。通常，需要几种取代才能依次折叠多个DOF的折纸，在每个取代，有些折痕折叠，其余的则保持固定。在这项研究中，我们通过控制连续取代过程中不同折痕的旋转来结合环闭合约束方法，以解释多个DOF的刚性折纸的顺序折叠。该策略还适用于模型折纸风格的设备，其中折痕可能配备旋转弹簧，折叠过程涉及弹性能。提供了几个示例，以验证追踪顺序折叠过程中所提出的算法以及搜索折纸的平衡构型，并使用旋转弹簧进行折纸。
Origami crease patterns are folding paths that transform flat sheets into spatial objects. Origami patterns with a single degree of freedom (DOF) have creases that fold simultaneously. More often, several substeps are required to sequentially fold origami of multiple DOFs, and at each substep some creases fold and the rest remain fixed. In this study, we combine the loop closure constraint with Lagrange multiplier method to account for the sequential folding of rigid origami of multiple DOFs, by controlling the rotation of different sets of creases during successive substeps. This strategy is also applicable to model origami-inspired devices, where creases may be equipped with rotational springs and the folding process involves elastic energy. Several examples are presented to verify the proposed algorithms in tracing the sequential folding process as well as searching the equilibrium configurations of origami with rotational springs.
