论文标题
弯曲折叠的传播：存在多个折痕的折叠环
Propagation of curved folding: The folded annulus with multiple creases exists
论文作者
论文摘要
在本文中，我们考虑了可开发的表面，这些表面是平面域等等距，它们是分段可区分的，沿曲线呈折叠。该论文围绕着长期存在的折叠环的存在问题，并有多个折痕，我们通过更深入地了解弯曲折叠如何传播到其他规定的折叠线来部分地解决。在回忆了开发物的一些关键特性之后，我们描述了采用正常曲率和相对扭转作为参数的弯曲折叠的局部行为，然后在连续折叠处计算此类几何描述符之间的非常笼统的关系，获得了新的公式，获得了享受很好的对称程度的新公式。我们利用这些公式来证明任何适当的折叠都可以传播到任意有限数量的第一个折叠线的重新定制副本，并给出了为什么涉及无限多个折叠线的问题更难解决。
In this paper we consider developable surfaces which are isometric to planar domains and which are piecewise differentiable, exhibiting folds along curves. The paper revolves around the longstanding problem of existence of the so-called folded annulus with multiple creases, which we partially settle by building upon a deeper understanding of how a curved fold propagates to additional prescribed foldlines. After recalling some crucial properties of developables, we describe the local behaviour of curved folding employing normal curvature and relative torsion as parameters and then compute the very general relation between such geometric descriptors at consecutive folds, obtaining novel formulae enjoying a nice degree of symmetry. We make use of these formulae to prove that any proper fold can be propagated to an arbitrary finite number of rescaled copies of the first foldline and to give reasons why problems involving infinitely many foldlines are harder to solve.
