Distributional properties of the three-dimensional Poisson Delaunay cell

被引:13
|
作者
Muche, L
机构
[1] Freiberg Univ. Mining and Technol., Institute of Stochastic
关键词
Delaunay tessellation; Poisson Delaunay cell; Poisson point process; probability density functions; moments;
D O I
10.1007/BF02179580
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
This paper gives distributional properties of geometrical characteristics of the Delaunay tessellation generated by a stationary Poisson point process in R(3). The considerations are based on a well-known formula given by Miles which describes the size and shape of the ''typical'' three-dimensional Poisson Delaunay cell. The results are the probability density functions for its volume, the area, and the perimeter of one of its faces, the angle spanned in a face by two of its edges, and the length of an edge. These probability density functions are given in integral form. Formulas for higher moments of these characteristics are given explicitly.
引用
收藏
页码:147 / 167
页数:21
相关论文
共 50 条
  • [31] The boundary recovery and sliver elimination algorithms of three-dimensional constrained Delaunay triangulation
    Guan, Zhenqun
    Song, Chao
    Gu, Yuanxian
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2006, 68 (02) : 192 - 209
  • [32] Delaunay Triangulation Based Key Distribution for Three-Dimensional Wireless Sensor Networks
    Saikia, Monjul
    JOURNAL OF INTERCONNECTION NETWORKS, 2021, 21 (01)
  • [33] A Robust Parallel Delaunay Mesh Generation Approach Suitable for Three-Dimensional TCAD
    Stimpfl, Franz
    Heinzl, Rene
    Schwaha, Philipp
    Selberherr, Siegfried
    SISPAD: 2008 INTERNATIONAL CONFERENCE ON SIMULATION OF SEMICONDUCTOR PROCESSES AND DEVICES, 2008, : 265 - 268
  • [34] Generation of Three-Dimensional Delaunay Meshes from Weakly Structured and Inconsistent Data
    Garanzha, V. A.
    Kudryavtseva, L. N.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2012, 52 (03) : 427 - 447
  • [35] Effect of Poisson's Ratio on Three-Dimensional Stress Distribution
    Abdulaliyev, Z.
    Ataoglu, S.
    JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 2009, 76 (01): : 1 - 3
  • [36] Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces
    Isokawa, Y
    ADVANCES IN APPLIED PROBABILITY, 2000, 32 (03) : 648 - 662
  • [37] Three-dimensional cylindrical Poisson solver with vacuum boundary conditions
    Moon, S.
    14TH INTERNATIONAL CONFERENCE ON NUMERICAL MODELING OF SPACE PLASMA FLOWS (ASTRONUM-2019), 2020, 1623
  • [38] A reliable estimation method of a dipole for three-dimensional Poisson equation
    Yamatani, K
    Ohnaka, K
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1998, 95 (1-2) : 139 - 151
  • [39] Efficient and accurate three-dimensional Poisson solver for surface problems
    Genovese, Luigi
    Deutsch, Thierry
    Goedecker, Stefan
    JOURNAL OF CHEMICAL PHYSICS, 2007, 127 (05):
  • [40] Chiral three-dimensional lattices with tunable Poisson's ratio
    Ha, Chan Soo
    Plesha, Michael E.
    Lakes, Roderic S.
    SMART MATERIALS AND STRUCTURES, 2016, 25 (05)