# Questions tagged [voronoi-diagrams]

For a given finite point set S, a voronoi diagram is a tessellation of a euclidean space. In the 2D case, it consists of conforming convex polygons surrounding each point such that for given a point p in S, any point in the enclosing polygon is closer to p than any other point in S.

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### Finding points inside cells of power (generalized Voronoi) diagram

Suppose we have a set of points $p_1,\ldots,p_n\in\mathbb R^d$ as well as a set of weights $w_1,\ldots,w_n\in\mathbb R$. Recall that the power cell associated to the pair $(p_k,w_k)$ is given by: \...
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### Fast Algorithms for the Simplicial Decomposition of a Convex Polytope in N-Dimensions

I'm in the process of constructing an algorithm which computes the Voronoi diagram of a set of points, but I now need a method to decompose each Voronoi cell into simplices. The information we have is:...
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### Fortune algorithm for voronoi diagram

Although there are many algorithms to construct Voronoi diagram, some of them are faster than others. Based on my knowledge Fortune algorithm is fastest for construct Voronoi diagram either in two ...