@article{13134,
  abstract     = {We propose a characterization of discrete analytical spheres, planes and lines in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently proposed alternative compact coordinate system, in which each integer triplet addresses some voxel in the grid. We define spheres and planes through double Diophantine inequalities and investigate their relevant topological features, such as functionality or the interrelation between the thickness of the objects and their connectivity and separation properties. We define lines as the intersection of planes. The number of the planes (up to six) is equal to the number of the pairs of faces of a BCC voxel that are parallel to the line.},
  author       = {Čomić, Lidija and Largeteau-Skapin, Gaëlle and Zrour, Rita and Biswas, Ranita and Andres, Eric},
  issn         = {0031-3203},
  journal      = {Pattern Recognition},
  number       = {10},
  publisher    = {Elsevier},
  title        = {{Discrete analytical objects in the body-centered cubic grid}},
  doi          = {10.1016/j.patcog.2023.109693},
  volume       = {142},
  year         = {2023},
}

@article{4125,
  abstract     = {Let S denote a set of n points in the plane such that each point p has assigned a positive weight w(p) which expresses its capability to influence its neighbourhood. In this sense, the weighted distance of an arbitrary point x from p is given by de(x,p)/w(p) where de denotes the Euclidean distance function. The weighted Voronoi diagram for S is a subdivision of the plane such that each point p in S is associated with a region consisting of all points x in the plane for which p is a weighted nearest point of S.

An algorithm which constructs the weighted Voronoi diagram for S in O(n2) time is outlined in this paper. The method is optimal as the diagram can consist of Θ(n2) faces, edges and vertices.
},
  author       = {Aurenhammer, Franz and Edelsbrunner, Herbert},
  issn         = {1873-5142},
  journal      = {Pattern Recognition},
  number       = {2},
  pages        = {251 -- 257},
  publisher    = {Elsevier},
  title        = {{An optimal algorithm for constructing the weighted Voronoi diagram in the plane}},
  doi          = {10.1016/0031-3203(84)90064-5},
  volume       = {17},
  year         = {1983},
}