刚性可折叠四边形网格折纸的设计与变形
The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami
摘要：
刚性可折叠四边形网格折纸是一类四边形网格折痕模式，具有一个基本属性：通过连续的单参数分段仿射变形族，可以将图案从平面折叠到完全折叠平面，该变形不会拉伸或弯曲网格面板。在这项工作中，我们明确地描述了所有可能的刚性和平面折叠四边形网格折纸的设计和变形。我们的关键思想是刚性定理（定理3.1），它描述了单个面板周围的兼容折痕图案，使我们能够从一个面板到另一个面板，显式地计算图案及其相应的变形。行进过程在计算上是有效的。因此，我们用它来制定逆问题：设计一个折痕图案，以实现沿着其刚性和平折运动的路径的目标形状。反问题的初步结果是有前途的，并建议一个广泛有用的工程设计策略的形状变形折纸。
英文摘要：
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.
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