用刻划弯曲坐标建立可展带模型
Modelling Developable Ribbons Using Ruling Bending Coordinates
摘要：
本文提出了一种新的方法来模拟可展带的动态行为，可展带是一种宽度远小于长度的二维带。而不是近似这样的表面与一个一般的三角形网格，我们的特点是它的折痕和弯曲角度在他们的集合。这种表示允许可展性在任何地方都得到满足，同时仍然留下足够的自由度来表示显着的全局变形。我们展示了如何在这个配置空间和时间集成在一个完全隐式的方式，可以适当地离散的势能和动能。其结果是一个动态模拟器具有几个理想的功能：我们可以使用比传统的有限元方法少得多的元素来模拟非平凡的变形。它在极端变形、外力或大时间步长下是稳定的。我们可以很容易地处理欧几里得空间中的各种用户约束。
英文摘要：
This paper presents a new method for modelling the dynamic behaviour of developable ribbons, two dimensional strips with much smaller width than length. Instead of approximating such surface with a general triangle mesh, we characterize it by a set of creases and bending angles across them. This representation allows the developability to be satisfied everywhere while still leaves enough degree of freedom to represent salient global deformation. We show how the potential and kinetic energies can be properly discretized in this configuration space and time integrated in a fully implicit manner. The result is a dynamic simulator with several desirable features: We can model non-trivial deformation using much fewer elements than conventional FEM method. It is stable under extreme deformation, external force or large timestep size. And we can readily handle various user constraints in Euclidean space.
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