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一种基于边指针搜索及区域划分的三角剖分算法

张俊 田慧敏

张俊, 田慧敏.一种基于边指针搜索及区域划分的三角剖分算法.自动化学报, 2021, 47(1): 100-107 doi: 10.16383/j.aas.c190155
引用本文: 张俊, 田慧敏.一种基于边指针搜索及区域划分的三角剖分算法.自动化学报, 2021, 47(1): 100-107 doi: 10.16383/j.aas.c190155
Zhang Jun, Tian Hui-Min. A triangulation algorithm based on edge-pointer search and region-division. Acta Automatica Sinica, 2021, 47(1): 100-107 doi: 10.16383/j.aas.c190155
Citation: Zhang Jun, Tian Hui-Min. A triangulation algorithm based on edge-pointer search and region-division. Acta Automatica Sinica, 2021, 47(1): 100-107 doi: 10.16383/j.aas.c190155

一种基于边指针搜索及区域划分的三角剖分算法

doi: 10.16383/j.aas.c190155
基金项目: 

国家自然科学基金 61571466

详细信息
    作者简介:

    张俊  中南大学自动化学院教授. 2004年获得日本东北大学机械智能工学博士学位.主要研究方向为三维图形芯片即处理器软件, 图形图像处理加速FPGA设计, 电机驱动控制器FPGA设计, SOC系统集成芯片.E-mail: zhangjun1000@hotmail.com

    通讯作者:

    田慧敏  中南大学计算机学院硕士研究生.主要研究方向为三维点云数据处理, 计算机视觉.本文通信作者.E-mail: thuimin2018@126.com

  • 本文责任编委 刘艳军

A Triangulation Algorithm Based on Edge-pointer Search and Region-division

Funds: 

National Natural Science Foundation of China 61571466

More Information
    Author Bio:

    ZHANG Jun   Professor at the School of Automation, Central South University. He received his Ph. D. degree in Mechanical Intelligence Engineering from Tohoku University, Japan in 2004. His research interest covers 3D graphics chip and processor software, graphics image processing accelerated FPGA design, motor drive controller FPGA design, and SOC system integrated chip

    Corresponding author: TIAN Hui-Min  Master student at the School of Computer Science and Engineering, Central South University. Her research interest covers 3D point cloud data processing, and computer vision. Corresponding author of this paper
  • Recommended by Associate Editor LIU Yan-Jun
  • 摘要: 针对大规模数据处理时Delaunay三角剖分过于耗时的问题, 本文提出了一种基于边指针搜索及区域划分的三角剖分算法.基于边指针设计了一种能够反映三角形之间位置关系的数据结构, 并优化了目标三角形的搜索路径.基于该数据结构, 利用区域划分进一步降低目标三角形的搜索深度.超级三角形所在的正方形被划分成具有相同尺寸的区域, 目标三角形的搜索从插入点所在的区域的入口三角形开始, 这大大缩小了目标三角形的搜索范围.实验证明, 与传统的Delaunay三角剖分算法相比, 该算法的效率显著提升.
    Recommended by Associate Editor LIU Yan-Jun
    1)  本文责任编委 刘艳军
  • 图  1  三角形数据结构

    Fig.  1  Data structure of triangle

    图  2  点与三角形位置关系判断

    Fig.  2  Judgment of positional relationship between point and triangle

    图  3  点$V$的目标三角形的搜索路径

    Fig.  3  Search path for target triangle of point $V$

    图  4  结构体关系图

    Fig.  4  Structure diagram

    图  5  搜索点$V$的目标三角形

    Fig.  5  Searching for target triangle of point $V$

    图  6  入口三角形及边指针的更新

    Fig.  6  Update of entry triangle and edge-pointer

    图  7  执行时间比较

    Fig.  7  Comparison of run time

    表  1  基于边指针及区域划分的算法数据结构

    Table  1  Data structure of algorithm based on edge-pointer and region-division

    Structure
    POINT $ x $ $ y $ entry_flag
    EDGE $ V_1 $ $ V_2 $
    TRIANGLE $ V_1 $, $ V_2 $, $ V_3 $ *$ p_1 $, *$ p_2 $, *$ p_3 $ entry $ X, Y $
    REGION valid *entrytri
    下载: 导出CSV

    表  2  算法的执行时间(s)

    Table  2  Running time of algorithms (s)

    散点数量 2万 3.5万 5万 7万 10万
    TD 113.515 298.687 756.656 1 943.39 3 972.81
    CGAL 1.719 3.074 4.281 6.265 8.594
    EPD 0.563 1.547 2.562 3.218 6.172
    EPRDD 0.117 0.234 0.325 0.531 0.813
    下载: 导出CSV

    表  3  算法的平均搜索深度

    Table  3  Average search depth of algorithms

    散点数量 2万 3.5万 5万 7万 10万
    TD 10 003 17 543 24 989 34 893 49 854
    EPD 108 229 233 247 278
    EPRDD 8 11 13 15 18
    下载: 导出CSV
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  • 收稿日期:  2019-03-13
  • 录用日期:  2019-05-23
  • 刊出日期:  2021-01-29

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