We describe a method for simulating biomembranes of arbitrary shape. In contrast to other dynamically triangulated surface (DTS) algorithms, our method provides a rich, -tangent-continuous, yet local description of the surface. We use curved Nagata triangles, which we generalize to cubic order to achieve the requisite flexibility. The resulting interpolation can be constructed locally without iterations, at the cost of having only approximate tangent continuity away from the vertices. This allows us to provide a parallelized and fine-tuned Monte Carlo implementation. As a first example of the potential benefits of the enhanced description, our method supports inhomogeneous lipid distributions as well as lipid mixing. It also supports restraints and constraints of various types and is constructed to be as easily extensible as possible. We validate the approach by testing its numerical accuracy, followed by reproducing the known Helfrich solutions for shapes with rotational symmetry. Finally, we present some example applications, including curvature-driven demixing and stylized effects of proteins. Input files for these examples, as well as the implementation itself, are freely available for researchers under the name OrganL ().

中文翻译：

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OrganL：使用弯曲元件对生物膜进行动态三角测量


我们描述了一种模拟任意形状的生物膜的方法。与其他动态三角表面（DTS）算法相比，我们的方法提供了丰富的、切线连续的、局部的表面描述。我们使用弯曲的 Nagata 三角形，并将其推广到立方阶以实现必要的灵活性。所得到的插值可以在本地构建而无需迭代，但代价是仅具有远离顶点的近似切线连续性。这使我们能够提供并行且微调的蒙特卡罗实现。作为增强描述的潜在好处的第一个例子，我们的方法支持不均匀的脂质分布以及脂质混合。它还支持各种类型的限制和约束，并且被构造为尽可能容易扩展。我们通过测试其数值准确性来验证该方法，然后重现具有旋转对称形状的已知 Helfrich 解。最后，我们展示了一些示例应用，包括曲率驱动的分层和蛋白质的程式化效果。这些示例的输入文件以及实现本身可以免费提供给研究人员，名称为 OrganL ()。