Structuring finite sets of points is at the heart of computational geometry. Such point sets arise naturally in many applications. Examples in R3 are point sets sampled from the surface of a solid or the locations of atoms in a molecule. A first step in processing these point sets is to organize them in some data structure. Structuring a point set into a simplicial complex like the Delaunay triangulation has turned out to be appropriate for many modeling tasks. Here we introduce the flow complex which is another simplicial complex that can be computed efficiently from a finite set of points. The flow complex turned out to be well suited for surface reconstruction from a finite sample and for some tasks in structural biology. Here we study mathematical and algorithmic properties of the flow complex and show how to exploit it in applications.
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机译：构建有限的点集是计算几何的核心。这样的点集在许多应用中自然而然地出现。 R 3 中的示例是从固体表面或分子中原子的位置采样的点集。处理这些点集的第一步是将它们组织成某种数据结构。事实证明，将点集构造为简单的复杂体（例如Delaunay三角剖分）非常适合许多建模任务。在这里，我们介绍了流量复合体，它是可以从一组有限的点有效地计算出的另一种简单复合体。事实证明，这种流动复合物非常适合从有限的样本进行表面重建以及结构生物学中的某些任务。在这里，我们研究流动复合体的数学和算法属性，并展示如何在应用程序中加以利用。
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