Geometriae Dedicata

, Volume 27, Issue 1, pp 65-75

Geometric relations among Voronoi diagrams

  • F. AurenhammerAffiliated withInstitutes for Information Processing, Technical University of Graz and Austrian Computer Society
  • , H. ImaiAffiliated withDepartment of Computer Science and Communication Engineering, Kyushu University

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Two general classes of Voronoi diagrams are introduced and, along with their modifications to higher order, are shown to be geometrically related. This geometric background, on the one hand, serves to analyse the size and combinatorial structure and, on the other, implies general and efficient methods of construction for various important types of Voronoi diagrams considered in the literature.