Use for questions related to Voronoi diagram, such as computing its edges.
In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.
Source: Wikipedia
Questions tagged [voronoi-diagram]
97 questions
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What is the average number of sides of a cell of a Voronoi pattern on a flat torus?
Consider a random voronoi pattern with a uniform distribution on a large flat torus. What are the average number of sides of a cell. My guess is 6.
What about 3D or 4D?
My guess for 4D would be 24. For 3D I'm guessing somewhere between 12 and 13.
Is…
zooby
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What is the minimal and maximal number of sides of a polygon in a 2D voronoi diagram?
I'd assumed that the minimal and maximal number of sides of a polygon in a Voronoi diagram were 3 and 6 and almost wrote that in the History of Science and Mathematics SE question Why doesn't John Snow's Voronoi diagram look like one? How was the…
uhoh
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Intersection of Parabolas for Voronoi Diagram
I asked another question with the same title and relating to the same problem on Stack Overflow, here. In short, I am trying to implement Fortune's Algorithm for creating a Voronoi diagram and I can't figure out how to find the (x,y) intersection of…
HereForABit
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Proof that Generators of Centroidal Voronoi Tesselation are Given by Conditional Mean
I am trying to understand a proof in "Centroidal voronoi
tessellations: applications and algorithms" from Du et al. In particular, I do not understand Proposition 3.1, stating that a necessary condition for an "optimal" Voronoi tesselation its…
Gemini
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Voronoi Diagrams and Toxic Waste Dump Problem
I am struggling to understand/believe the idea that the center of the largest empty circle or optimal location for a "toxic waste dump" on a Voronoi diagram is on a vertex.
For example, if I have a Voronoi diagram with sites $A=(1,3), B=(6,4), C=…
Kat
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Equation for Determining if a Point Affects a Voronoi Diagram
Currently I am working on a Javascript program that plots a Voronoi diagram and am trying to find all of the points that form the points that form the region around a point. To make this clearer, here is an example of a potential scenario:
Point D…
Brendon Shaw
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Voronoi tessellation with known cell areas and unknown seeds
I would like to create a Voronoi tessellation inside a square of known dimensions. I know that I can plot a set of known seeds that will result in a set of cells with discrete areas; however, is it possible to find an unknown set of seeds that will…
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How to make voronoi diagram more random?
Classical voronoi diagram looks like biology cells. I want to make it more random. Like:
or the one on right (with some roundish borders):
Is it possible and how?
P.S. alternative algorithm suggestions are also welcome.
Janis Taranda
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How can I find the right parabola that intersects on a new site event for the fortune line algorithm?
I am trying to implement my own voronoï in Unity3d ( in C# ) as I am not satisfied with the existing libs that I found ( they always tend to miss a piece of information on the output and / or tend to be very difficult to understand ).
I did a…
