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A Practical Algorithm for Degree-k Voronoi Domains of Three-Dimensional Periodic Point Sets

Part of the Lecture Notes in Computer Science book series (LNCS,volume 13598)


Degree-k Voronoi domains of a periodic point set are concentric regions around a fixed centre consisting of all points in Euclidean space that have the centre as their k-th nearest neighbour. Periodic point sets generalise the concept of a lattice by allowing multiple points to appear within a unit cell of the lattice. Thus, periodic point sets model all solid crystalline materials (periodic crystals), and degree-k Voronoi domains of periodic point sets can be used to characterise the relative positions of atoms in a crystal from a fixed centre. The paper describes the first algorithm to compute all degree-k Voronoi domains up to any degree \(k\ge 1\) for any two or three-dimensional periodic point set.


  • Degree-k Voronoi Domains
  • Periodic point sets
  • Crystals

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Correspondence to Philip Smith or Vitaliy Kurlin .

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Smith, P., Kurlin, V. (2022). A Practical Algorithm for Degree-k Voronoi Domains of Three-Dimensional Periodic Point Sets. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2022. Lecture Notes in Computer Science, vol 13598. Springer, Cham.

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  • Print ISBN: 978-3-031-20712-9

  • Online ISBN: 978-3-031-20713-6

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