Incremental algorithms are among the most popular approaches for Delaunay triangulation, and the point insertion sequence has a substantial impact on the amount of work needed to construct Delaunay triangulations in incremental algorithm triangulation. In this paper, 2D adaptive Hilbert curve insertion, including the method of dividing 3D multi-grids and adjusting the 3D adaptive Hilbert curve to avoid the “jump” phenomenon, is extended to 3D Delaunay triangulation. In addition, on the basis of adaptive Hilbert curve insertion, we continue to optimize the addition of control points by selecting control points in every order and every grid level. As a result, the number of conflicting elongated tetrahedra that have to be created and deleted multiple times and the number of search steps for positioning inserted points can both be reduced. Lastly, a new comparison method is used in the point location process to solve the precision problem in 3D Delaunay triangulation. As shown by detailed experiments and analysis, compared with previous adaptive Hilbert curve insertion, CGAL, regular grid insertion, multi-grid insertion and random insertion, the proposed 3D Delaunay triangulation is the most efficient for both artificial and real surface sampling point sets.

中文翻译：

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随机分布点云数据的自适应快速 3D Delaunay 三角剖分

增量算法是最流行的 Delaunay 三角剖分方法之一，点插入序列对增量算法三角剖分中构建 Delaunay 三角剖分所需的工作量有很大影响。本文将2D自适应希尔伯特曲线插入，包括划分3D多重网格和调整3D自适应希尔伯特曲线以避免“跳跃”现象的方法，扩展到3D Delaunay三角剖分。此外，在自适应希尔伯特曲线插入的基础上，我们通过选择每个顺序和每个网格级别的控制点来继续优化控制点的添加。结果，必须多次创建和删除的冲突细长四面体的数量以及用于定位插入点的搜索步骤的数量都可以减少。最后，在点定位过程中使用了一种新的比较方法来解决3D Delaunay三角剖分中的精度问题。详细的实验和分析表明，与之前的自适应希尔伯特曲线插入、CGAL、规则网格插入、多重网格插入和随机插入相比，所提出的 3D Delaunay 三角剖分对于人工和真实表面采样点集都是最有效的。