Efficient generation of simple polygons for characterizing the shape of a set of points in the plane

被引:149
|
作者
Duckham, Matt [1 ]
Kulik, Lars [2 ]
Worboys, Mike [3 ]
Galton, Antony [4 ]
机构
[1] Univ Melbourne, Dept Geomat, Melbourne, Vic 3010, Australia
[2] Univ Melbourne, Dept Comp Sci & Software Engn, Melbourne, Vic 3010, Australia
[3] Univ Maine, Natl Ctr Geog Informat & Anal, Orono, ME 04469 USA
[4] Univ Exeter, Sch Engn Comp & Math, Exeter EX4 4QF, Devon, England
基金
美国国家科学基金会; 澳大利亚研究理事会;
关键词
convex hull; alpha shape; shape analysis; cartography; GIS;
D O I
10.1016/j.patcog.2008.03.023
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This paper presents a simple, flexible, and efficient algorithm for constructing a possibly non-convex, simple polygon that characterizes the shape of a set of input points in the plane, termed a characteristic shape. The algorithm is based on the Delaunay triangulation of the points. The shape produced by the algorithm is controlled by a single normalized parameter, which can be used to generate a finite, totally Ordered family of related characteristic shapes, varying between the convex hull at one extreme and a uniquely defined shape with minimum area. An optimal O(n log n) algorithm for computing the shapes is presented. Characteristic shapes possess a number of desirable properties, and the paper includes an empirical investigation of the shapes produced by the algorithm. This investigation provides experimental evidence that with appropriate parameterization the algorithm is able to accurately characterize the shape of a wide range of different point distributions and densities. The experiments detail the effects of changing parameter values and provide an indication of some "good" parameter values to use in certain circumstances. (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码:3224 / 3236
页数:13
相关论文
共 50 条
  • [1] ON THE SHAPE OF A SET OF POINTS IN THE PLANE
    EDELSBRUNNER, H
    KIRKPATRICK, DG
    SEIDEL, R
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1983, 29 (04) : 551 - 559
  • [2] On the shape of a set of points and lines in the plane
    van Kreveld, M.
    van Lankveld, T.
    Veltkamp, R. C.
    [J]. COMPUTER GRAPHICS FORUM, 2011, 30 (05) : 1553 - 1562
  • [3] On the shape of a set of points and lines in the plane
    Department of Information and Computing Sciences, Utrecht University, Netherlands
    [J]. Comput Graphics Forum, 5 (1553-1562):
  • [4] An efficient incremental algorithm for generating the characteristic shape of a dynamic set of points in the plane
    Zhong, Xu
    Duckham, Matt
    [J]. INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE, 2017, 31 (03) : 569 - 590
  • [6] Computing Simple Paths on Points in Simple Polygons
    Daescu, Ovidiu
    Luo, Jun
    [J]. COMPUTATIONAL GEOMETRY AND GRAPH THEORY, 2008, 4535 : 41 - +
  • [7] A simple approximation algorithm for the diameter of a set of points in an Euclidean plane
    Hong, Jieying
    Wang, Zhipeng
    Niu, Wei
    [J]. PLOS ONE, 2019, 14 (02):
  • [8] Generation of simple polygons from ordered points using an iterative insertion algorithm
    Zhang, Hongyun
    Zhao, Quanhua
    Li, Yu
    [J]. PLOS ONE, 2020, 15 (03):
  • [9] On recognizing and characterizing visibility graphs of simple polygons
    Ghosh, SK
    [J]. DISCRETE & COMPUTATIONAL GEOMETRY, 1997, 17 (02) : 143 - 162
  • [10] On recognizing and characterizing visibility graphs of simple polygons
    S. K. Ghosh
    [J]. Discrete & Computational Geometry, 1997, 17 : 143 - 162