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Nearest Neighbour Graph and Locally Minimal Triangulation

  • Ivana KolingerováEmail author
  • Andrej Ferko
  • Tomáš Vomáčka
  • Martin Maňák
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10405)

Abstract

Nearest neighbour graph (NNG) is a useful tool namely for collision detection tests. It is well known that NNG, when considered as an undirected graph, is a subgraph of Delaunay triangulation (DT) and this relation can be used for efficient NNG computation. This paper concentrates on relation of NNG to the locally minimal triangulation (LMT) and shows that, although NNG can be proved not to be a LMT subgraph, in most cases LMT contains all or nearly all NNG edges. This fact can also be used for NNG computation, namely in kinetic problems, because LMT computation is easier.

Keywords

Nearest Neighbour Graph Locally Minimal Triangulation Delaunay triangulation Kinetic problem 

Notes

Acknowledgements

This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic, the project SGS-2016-013 Advanced Graphical and Computing Systems and the project PUNTIS (LO1506) under the program NPU I. We would like to thank to T. Bayer from the Charles University in Prague, Czech Republic for supplying us the real terrain data for the experiments.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ivana Kolingerová
    • 1
    • 3
    Email author
  • Andrej Ferko
    • 2
  • Tomáš Vomáčka
    • 1
  • Martin Maňák
    • 3
  1. 1.Department of Computer Science, Faculty of Applied SciencesUniversity of West BohemiaPilsenCzech Republic
  2. 2.Department of Algebra, Geometry and Didactics of Mathematics, Faculty of Mathematics, Physics and InformaticsComenius UniversityBratislavaSlovakia
  3. 3.New Technologies for the Information Society, Faculty of Applied SciencesUniversity of West BohemiaPilsenCzech Republic

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