双线刚性折纸
Double-line rigid origami
摘要：
在本文中，我们将展示的方法来解释一些刚性折纸与更高的程度顶点的极限情况下的结构与度-4补角顶点。解释是基于将每个折痕分成两个平行折痕，或\emph{double lines}，由顶点处的附加结构连接。我们发现，双线版本的度-4平坦的可折叠的顶点具有刚性的折叠运动，因为这样的对称度-$2n$顶点。后者给了我们一个象征性的分析，原来的顶点，表明四分之一折叠角的切线是成比例的。双线法也是一个潜在的有用的厚度给刚性折纸机制。通过将单个折痕制成两个折痕，可以分布折叠角度以避免当面板容易彼此碰撞时发生$180^\circ$折叠。这可以被理解为厚刚性折纸的折痕偏移方法的扩展，具有刚性可折叠性的额外保证。
英文摘要：
In this paper, we will show methods to interpret some rigid origami with higher degree vertices as the limit case of structures with degree-4 supplementary angle vertices. The interpretation is based on separating each crease into two parallel creases, or \emph{double lines}, connected by additional structures at the vertex. We show that double-lined versions of degree-4 flat-foldable vertices possess a rigid folding motion, as do symmetric degree-$2n$ vertices. The latter gives us a symbolic analysis of the original vertex, showing that the tangent of the quarter fold angles are proportional to each other. The double line method is also a potentially useful in giving thickness to rigid origami mechanisms. By making single crease into two creases, the fold angles can be distributed to avoid $180^\circ$ folds, when panels can easily collide with each other. This can be understood as an extension of the crease offset method of thick rigid origami with an additional guarantee of rigid-foldability.
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