Computational geometry: an introduction
Computational geometry: an introduction
An improved algorithm for constructing kth-order voronoi diagrams
IEEE Transactions on Computers
A new duality result concerning Voronoi diagrams
Discrete & Computational Geometry
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Algorithmic geometry
Discrete Applied Mathematics
On k-Nearest Neighbor Voronoi Diagrams in the Plane
IEEE Transactions on Computers
Two-site Voronoi diagrams in geographic networks
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Proceedings of the twenty-fifth annual symposium on Computational geometry
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The triangle-perimeter 2-site distance function defines the "distance" from a point x to two other points p, q as the perimeter of the triangle whose vertices are x, p, q. Accordingly, given a set S of n points in the plane, the Voronoi diagram of S with respect to the triangleperimeter distance, is the subdivision of the plane into regions, where the region of the pair p, q ∈ S is the locus of all points closer to p, q (according to the triangle-perimeter distance) than to any other pair of sites in S. In this paper we prove a theorem about the perimeters of triangles, two of whose vertices are on a given circle. We use this theorem to show that the combinatorial complexity of the triangle-perimeter 2- site Voronoi diagram is O(n2+ε) (for any ε 0). Consequently, we show that one can compute the diagram in O(n2+ε) time and space.