Introducing a new hobby for other people may inspire them to join with you. Reading, as one of mutual hobby, is considered as the very easy hobby to do. But, many people are not interested in this hobby. Why? Boring is the reason of why. However, this feel actually can deal with the book and time of you reading. Yeah, one that we will refer to break the boredom in reading is choosing concrete a...

Given two point sets in the plane, we study the minimization of the (lexiocographic) bottleneck distance between the smaller set and an equally-sized subset of the larger set under translations. We relate this problem to two Voronoi-type diagrams, which are of interest for related problems. Their complexity is shown to be polynomial in the sizes of the sets and algorithms for their construction...

1 The farthest-point Voronoi diagram of a set of n sites 2 is a tree with n leaves. We investigate whether arbi3 trary trees can be realized as farthest-point Voronoi di4 agrams. Given an abstract ordered tree T with n leaves 5 and prescribed edge lengths, we produce a set of n sites 6 S in O(n) time such that the farthest-point Voronoi di7 agram of S represents T . We generalize this algorithm...

Evolutionary algorithms have been applied to function identification problems with great success. This paper presents an approach in which the individuals represent a partition of the input space in Voronoi regions together with a set of local functions associated to each one of these regions. In this way, the solution corresponds to a combination of local functions over a spatial structure top...

1 This work has been partially supported by grant TIN2005-08863-C03 of the Spanish Ministry of Science and Education 2 Corresponding address: [email protected] Abstract – In this paper we present some techniques for obtaining non-photorealistc images with the aid of Voronoi diagrams, such as stained-glass images. We also show examples of their potential applications, including lossy image ...

We present a new type of Voronoi diagram in R that respects the anisotropy exerted on the plane by a given distance graph. It is based on a metric obtained by smoothly and injectively embedding R into R, and a scalar-valued function for re-scaling the distances. A spline representation of the embedding surface is constructed with the Gauß-Newton algorithm, which approximates the given distance ...

We present techniques for fast motion planning by using discrete approximations of generalized Voronoi diagrams, computed with graphics hardware. Approaches based on this diagram computation are applicable to both static and dynamic environments of fairly high complexity. We compute a discrete Voronoi diagram by rendering a three-dimensional distance mesh for each Voronoi site. The sites can be...

One of most famous theorems in computational geometry is the duality between Voronoi diagram and Delaunay triangulation in Euclidean space. This paper proposes an extension of that theorem to the Voronoi diagram and Delaunay-type triangulation in dually at space. In that space, the Voronoi diagram and the triangulation can be computed e ciently by using potential functions. We also propose high...

Voronoi diagrams are widely used to represent geographical distributions of information, but they are not readily stacked in a hierarchical fashion. We propose a simple mechanism whereby each index Voronoi cell contains the generators of several Voronoi cells in the next lower level. This allows various processes of indexing, paging, visualization and generalization to be performed on various t...

Given a two-dimensional space endowed with a divergence function that is convex in the firstargument, continuously differentiable in the second, and satisfies suitable regularity conditionsat Voronoi vertices, we show that orphan-freedom (the absence of disconnected Voronoi regions)is sufficient to ensure that Voronoi edges and vertices are also connected, and that the dual isa ...