Premium
Aspects of the Facet‐Edge Data Structure for the Construction of Voronoi Cells
Author(s) -
Weber Christoph,
Loehnert Stefan,
Wriggers Peter
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010315
Subject(s) - delaunay triangulation , bowyer–watson algorithm , voronoi diagram , pitteway triangulation , constrained delaunay triangulation , centroidal voronoi tessellation , surface triangulation , dual graph , triangulation , minimum weight triangulation , computer science , data structure , enhanced data rates for gsm evolution , facet (psychology) , algorithm , mathematics , planar graph , graph , theoretical computer science , geometry , artificial intelligence , psychology , social psychology , personality , big five personality traits , programming language
The construction of Voronoi diagrams has two main aspects: The construction algorithm and the data structure. For the construction of planar Voronoi diagrams e.g. the well known plane sweep algorithm can be applied. Another efficient method is the incremental construction of the Delaunay triangulation by using the quad‐edge data structure. Within this data structure the Delaunay triangulation is treated as a planar graph. Incremental construction implies that manipulations of the triangulation are allowed. Its Voronoi diagram is obtained simply by accessing the triangulation's dual graph. We extend this method to tree dimensions, by implementing a 3D Delaunay triangulation on the facet‐edge data structure. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)