Discrete elastic rods
Discrete elastic rods
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DOI：
10.1145/1399504.1360662
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发表时间：
2008-08
期刊：
影响因子：
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通讯作者：
M. Bergou;M. Wardetzky;Stephen Robinson;B. Audoly;E. Grinspun
中科院分区：
文献类型：
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作者：
M. Bergou;M. Wardetzky;Stephen Robinson;B. Audoly;E. Grinspun
我们提出了一个离散处理的适应框架曲线，平行运输，holonomy，从而建立了一个离散的几何模型的语言薄的柔性杆具有任意横截面和未变形的配置。我们的方法不同于现有的模拟技术，在图形和力学文献中的运动学描述-我们表示的材料框架的角度偏离自然主教框架-以及在动态处理-我们把中心线作为动态和准静态的材料框架。此外，我们描述了一个流形投影耦合杆的刚体，同时强制杆不可扩展性的方法。准静态和约束的使用提供了一个有效的治疗刚性扭曲和拉伸模式，在同一时间，我们保留了动态弯曲的中心线，并准确地再现弯曲和扭曲模式之间的耦合。我们通过定量屈曲，稳定性和耦合模式实验，并通过定性打结比较，验证离散杆模型。
We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for a discrete geometric model of thin flexible rods with arbitrary cross section and undeformed configuration. Our approach differs from existing simulation techniques in the graphics and mechanics literature both in the kinematic description---we represent the material frame by its angular deviation from the natural Bishop frame---as well as in the dynamical treatment---we treat the centerline as dynamic and the material frame as quasistatic. Additionally, we describe a manifold projection method for coupling rods to rigid-bodies and simultaneously enforcing rod inextensibility. The use of quasistatics and constraints provides an efficient treatment for stiff twisting and stretching modes; at the same time, we retain the dynamic bending of the centerline and accurately reproduce the coupling between bending and twisting modes. We validate the discrete rod model via quantitative buckling, stability, and coupled-mode experiments, and via qualitative knot-tying comparisons.