Modeling rock fragmentation by coupling Voronoi diagram and discretized virtual internal bond

Time - Based Voronoi Diagram ∗

We consider a variation of Voronoi diagram, or time-based Voronoi diagram, for a set S of points in the presence of transportation lines or highways in the plane. A shortest time-distance path from a query point to any given point in S is a path that takes the least travelling time. The travelling speeds and hence travelling times of the subpaths along the highways and in the plane are differen...

Rounding Voronoi Diagram

Computational geometry classically assumes real-number arithmetic which does not exist in actual computers. A solution consists in using integer coordinates for data and exact arithmetic for computations. This approach implies that if the results of an algorithm are the input of another, these results must be rounded to match this hypothesis of integer coordinates. In this paper, we treat the c...

Saliency Detection with VORONOI Diagram

Many applications are serviced by the Voronoi tessellation required to split image into Voronoi regions. An automatic method to learn and detect salient region for color image with support of the Voronoi diagram is presented. Salient regions are modeled as flexible circumstance corresponding to centers of mass. The centers are predicted by local contrast-based representation with local maxima. ...

Hierarchical planar voronoi diagram approximations

Crystal Voronoi diagram and its applications

This paper studies the multiplicatively weighted crystal-growth Voronoi diagram, which describes the partition of the plane into crystals with different growth speeds. This type of the Voronoi diagram is defined, and its basic properties are investigated. The analytic equation describing the boundary curve is given for a simple case. For the general case, an approximation algorithm is proposed....