论文标题
刚性和平坦的四边形网眼折纸的设计和变形
The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami
论文作者
论文摘要
僵硬且平坦的四边形网眼折纸是具有一个基本特性的四边形网状折痕图案：可以通过连续的一部分分段仿射变形型家族将图案从平坦到完全折叠的平坦折叠，这些仿射变形不会伸展或弯曲网状锅。在这项工作中，我们明确表征了所有可能的刚性折叠四边形网眼折纸的设计和变形。我们的关键想法是一个刚性定理（定理3.1），该定理表征了单个面板周围的兼容折痕图案，并使我们能够从面板到面板向前行进，以明确计算模式及其相应的变形。行进过程在计算上是有效的。因此，我们使用它来制定反问题：设计折痕图案以沿其刚性和扁平折叠运动的路径实现目标形状。逆问题的初始结果是有希望的，并提出了一种具有折纸形状形状的广泛有用的工程设计策略。
Rigidly and flat-foldable quadrilateral mesh origami is the class of quadrilateral mesh crease patterns with one fundamental property: the patterns can be folded from flat to fully-folded flat by a continuous one-parameter family of piecewise affine deformations that do not stretch or bend the mesh-panels. In this work, we explicitly characterize the designs and deformations of all possible rigidly and flat-foldable quadrilateral mesh origami. Our key idea is a rigidity theorem (Theorem 3.1) that characterizes compatible crease patterns surrounding a single panel and enables us to march from panel to panel to compute the pattern and its corresponding deformations explicitly. The marching procedure is computationally efficient. So we use it to formulate the inverse problem: to design a crease pattern to achieve a targeted shape along the path of its rigidly and flat-foldable motion. The initial results on the inverse problem are promising and suggest a broadly useful engineering design strategy for shape-morphing with origami.
