Let P be a planar n-point set in general position. For k ∈ {1, . . . , n − 1}, the Voronoi diagram of order k is obtained by subdividing the plane into regions such that points in the same cell have the same set of nearest k neighbors in P . The (nearest point) Voronoi diagram (NVD) and the farthest point Voronoi diagram (FVD) are the particular cases of k = 1 and k = n − 1, respectively. It is...

The use of Voronoi diagrams in GIS-oriented spatiotemporal databases is considered. The Voronoi algorithms generate appropriate meshes for data interpolation. We illustrate the data representation in this database generated from a point-based spatiotemporal relation in the National Agricultural Statistics Service (NASS) database.

No wonder you activities are, reading will be always needed. It is not only to fulfil the duties that you need to finish in deadline time. Reading will encourage your mind and thoughts. Of course, reading will greatly develop your experiences about everything. Reading concrete and abstract voronoi diagrams is also a way as one of the collective books that gives many advantages. The advantages a...

The MIR Voronoi diagram appears with the notion of good illumination introduced in [3, 4]. This illumination concept generalizes well-covering [7] and triangle guarding [9]. The MIR Voronoi diagram merges the notions of proximity and convex dependency. Given a set S of planar light sources, for each point q in the plane we search for the subset Sq ⊂ S nearest to q and such that q is an interior...

We study the Hausdorff Voronoi diagram of a set S of polygonal objects in the plane, a generalization of Voronoi diagrams based on the maximum distance of a point from a polygon, and show that it is equivalent to the Voronoi diagram of S under the Hausdorff distance function. We investigate the structural and combinatorial properties of the Hausdorff Voronoi diagram and give a divide and conque...

The Voronoi diagram is a widely used partition of space which may be implemented in a variety of unconventional computing prototypes, sharing in common the uniform propagation of information via fronts emanating from data point sources. The giant single-celled amoeboid organism Physarum polycephalum constructs minimising transport networks but can also approximate the Voronoi diagram using two ...

In robot motion planning in a space with obstacles, the goal is to find a collision-free path of robot from the starting to the target position. There are many fundamentally different approaches, and their modifications, to the solution of this problem depending on types of obstacles, dimensionality of the space and restrictions for robot movements. Among the most frequently used are roadmap me...

The aim of districting problems is to get an optimized partition of a territory into smaller units, called districts or zones, subject to some side constraints such as balance, contiguity, and compactness. Logistics districting problems usuually involve additional optimization criteria and constraints. Districting problems are called continuous when the underlying space, both for facility sites...

The farthest line segment Voronoi diagram shows properties different from both the closest-segment Voronoi diagram and the farthest-point Voronoi diagram. Surprisingly, this structure did not receive attention in the computational geometry literature. We analyze its combinatorial and topological properties and outline an O(n log n) time construction algorithm that is easy to implement. No restr...

One of the basic concerns of Geographic Information Systems and their application is the spatial relationships between objects on the map. This has been attacked from two directions: by the construction/linking of polygon boundary segments; and by including spatial operators within data-base retrieval requests. In both cases only an incomplete picture has been obtained due to the lack of any co...