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An adaptive and rapid 3D Delaunay triangulation for randomly distributed point cloud data

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Abstract

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.

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Funding

This study was funded by the National Key Research and Development Project (Grant Number 2016YFA0602200) and the National Natural Science Foundation of China (Grant Number U1806205).

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Authors and Affiliations

  1. Marine Data and Information Center, The First Institute of Oceanography, MNR, Qingdao, China

    Tianyun Su, Wen Wang, Haixing Liu, Zhendong Liu, Xinfang Li, Zhen Jia, Lin Zhou, Zhuanling Song, Ming Ding & Aiju Cui

  2. Laboratory for Regional Oceanography and Numerical Modeling, Pilot National Laboratory for Marine Science and Technology, Qingdao, China

    Tianyun Su, Haixing Liu & Xinfang Li

  3. National Engineering Laboratory for Integrated Aero-Space-Ground-Ocean Big Data Application Technology, Xi’an, China

    Tianyun Su & Zhendong Liu

  4. Key Laboratory of Marine Science and Numerical Modeling, Ministry of Natural Resources, Qingdao, China

    Haixing Liu

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  1. Tianyun Su
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  2. Wen Wang
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Correspondence to Wen Wang.

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Su, T., Wang, W., Liu, H. et al. An adaptive and rapid 3D Delaunay triangulation for randomly distributed point cloud data. Vis Comput 38, 197–221 (2022). https://doi.org/10.1007/s00371-020-02011-3

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