We introduce a novel algorithm to transform any generic set of triangles in 3D space into a well-formed simplicial complex. Intersecting elements in the input are correctly identified, subdivided, and connected to arrange a valid configuration, leading to a topologically sound partition of the space into piece-wise linear cells. Our approach does not require the exact coordinates of intersection points to calculate the resulting complex. We represent any intersection point as an unevaluated combination of input vertices. We then extend the recently introduced concept of indirect predicates [Attene 2020] to define all the necessary geometric tests that, by construction, are both exact and efficient since they fully exploit the floating-point hardware. This design makes our method robust and guaranteed correct, while being virtually as fast as non-robust floating-point based implementations. Compared with existing robust methods, our algorithm offers a number of advantages: it is much faster, has a better memory layout, scales well on extremely challenging models, and allows fully exploiting modern multi-core hardware with a parallel implementation. We thoroughly tested our method on thousands of meshes, concluding that it consistently outperforms prior art. We also demonstrate its usefulness in various applications, such as computing efficient mesh booleans, Minkowski sums, and volume meshes.

中文翻译：

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使用浮点算法进行快速和稳健的网格排列

我们引入了一种新颖的算法，将 3D 空间中的任何通用三角形集合转换为格式良好的单纯复形。输入中的相交元素被正确识别、细分和连接以安排有效配置，从而将空间拓扑合理地划分为分段线性单元。我们的方法不需要交点的精确坐标来计算得到的复合体。我们将任何交点表示为输入顶点的未评估组合。然后我们扩展最近引入的概念间接谓词[Atten 2020] 定义所有必要的几何测试，这些测试通过构建既准确又高效，因为它们充分利用了浮点硬件。这种设计使我们的方法稳健并保证正确，同时几乎与基于非稳健浮点的实现一样快。与现有的鲁棒方法相比，我们的算法具有许多优势：速度更快、内存布局更好、在极具挑战性的模型上可以很好地扩展，并允许通过并行实现充分利用现代多核硬件。我们在数千个网格上彻底测试了我们的方法，得出的结论是它始终优于现有技术。我们还展示了它在各种应用中的有用性，例如计算高效的网格布尔值、Minkowski 和和体积网格。