Questions tagged [voronoi-diagrams]

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Voronoi diagram. Status structure in Fortune's Algorithm

I'm trying to implement the Fortune's Algorithm, however I can't quite figure out how the status structure should be implemented. The following is extrapolated from my Computational Geometry book. ...
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Repeated nearest-neighbor queries

If I want to make N repeated (i.e. millions of) 2D nearest-neighbor queries on a pointset of size M, is traveling down into a KD-Tree most efficient or are there better ways to do this? (e.g. Voronoi?)...
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What is the runtime to compute the ordered higher-order Voronoi diagram?

The ordered order-k Voronoi diagram (sometimes written OOKVD) partitions the plane into regions such that the k closest sites are the same and in the same order for all the points in a region. I am ...
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Can breakpoints of the beachline move up in Fortune's algorithm?

In these slides describing Fortune's algorithm for constructing a Voronoi diagram, it is noted on page 7 that break points of the beach line can move upward. How is this so? In most of the cases I ...
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Voronoi diagram neighbors

I'm trying to find all the neighbors of a given cell in a voronoi diagram. For example, given the following diagram, if I want to find the neighbors of the cell 1, then I should be able to return the ...
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Voronoi Diagram Question

I am stuck on that question, it's about Voronoi diagrams Show that for some set of $n$ points, there can be $\Omega(n^2)$ intersections between the edges of the Voronoi diagram and the edges of ...
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Delaunay to Voronoi … and back?

Learning about Voronoi Diagrams, one quickly finds out that Delaunay Triangulations are clearly the easiest way to generate them from a set of points. How about the other way around? Given a ...
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Voronoi diagram of a set of simple polygons

The Voronoi diagram is a well-known data structure that helps solve various proximity problems. We have several nice algorithms that build this diagram for $n$ point in optimal time $O(n\log n)$. I ...