Voronoi Tessellation Neighbor Algorithm

Working on some fun coding project, and I've been looking on the internet as best I can, and either the keywords I'm using are crap, or the info is really esoteric, so I'm asking here.

Is there a simple way of determining if two 'atoms' share an edge on a Voronoi tessellation. I haven't studied math or anything, so I don't understand half the stuff on the papers about this topic.

Thanks!

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๐Ÿ‘ค๏ธŽ u/A_Wild_Turtle
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Crafting Organic Patterns With Voronoi Tessellations georgefrancis.dev/writingโ€ฆ
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Grids 2D : Grids 2D is an easy to use, highly optimized and flexible grid generator and territory/cell highlighter/fader.**Features** - Configurable, fully interactive and flexible grid generation, including Voronoi tessellation, boxed, rectangular and hexagonal types. - Produces highly optimized assetstore.unity.com/packโ€ฆ
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Voronoi tessellation

So I was playing around with Voronoi tessellation for fun and I think I accidentally invented WiFi :D

https://i.redd.it/ynljqzxq4ze71.gif

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๐Ÿ‘ค๏ธŽ u/mordigan228
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Voronoi Tessellation on a plane

I've been looking to find how to create a voronoi pattern with faces on a mesh (not with texture nodes), and I saw this image from a houdini tutorial, where they called it voronoi tessellation. I was wondering if there was a good way to do this in blender.

I've tried Cell fracture, but I need to to affect a plane, and I cant have the gaps that cell fracture makes.

https://preview.redd.it/ql7c11ilvpy51.png?width=684&format=png&auto=webp&s=cc106c61d28e89d5857f04eef617610d0e264f0d

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๐Ÿ‘ค๏ธŽ u/Conor074
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A website that lets you find your local football team using Voronoi tessellations guushoekman.com/local-fooโ€ฆ
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๐Ÿ‘ค๏ธŽ u/qpolask
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Using Voronoi tessellations to make caves - my last two weeks. wick.works/wicklog-6-voroโ€ฆ
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Chess set print, 3D Voronoi volume tessellation made in Rhino/grasshopper (Shapeways) imgur.com/qIiC5Mr
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Voronoi Diagram (A Voronoi tessellation emerges by radial growth from seeds outward.) - https://commons.wikimedia.org/wiki/User:Jahobr
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Algorithm for constructing 3D Voronoi Tessellations

I'm currently working on a MD coding project that requires the construction of a Voronoi Tessellation at the beginning of a simulation based on a set of "anchor points" that the user provides. The anchors serve as the individual Voronoi cell generating points. I've run into a few problems trying to code this. One of them being that the Voronoi Tessellation is required to be 3 dimensional, so using Fortune's algorithm is unfortunately out of the question. The other one is that I have to perform this calculation in my underlying C++ source code, as the Voronoi tessellation has to be able to be changed throughout the simulation. I'm coding an OpenMM plugin, so I can't change any part of the simulation from the python level once the simulation has started (to my knowledge). I was looking into using boost, but I don't think boost's Voronoi Tessellation library supports 3D Voronoi Tessellation construction. Thanks a lot for the help and let me know if you need any more info!

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๐Ÿ‘ค๏ธŽ u/astokely
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[A] Voronoi tessellation
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๐Ÿ‘ค๏ธŽ u/aloofloofah
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I made a Voronoi Tessellation Generator and I want to share it with all of you. (x-post from /r/proceduralgeneration)

Hey /r/gamedev

For a game I'm working on, I created this program that generates the voronoi tessellation of random points on the surface of a sphere. I use it to generate buildings and clouds on the surface of a spherical planet. I'm sure you can find some uses for it too.

I put a lot of work into making it fast. The first version was incredibly slow, but now it can generate a tessellation for 1,000,000 points in under 20 seconds on my desktop. I wrote an article about optimizing it on my blog.

I also struggled with numerical stability when the number of points is large. You can read about how I fixed that too.

Here are some videos showing what I used it for.

http://youtu.be/nFah9_xSyvo

http://youtu.be/Rr6x4L3oha0

Feel free to modify the code and use it for whatever you want. Let me know if you use it for something cool! If you have any requests to modify it or add features let me know!

You can find the source code here.

And you can download it here!

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๐Ÿ‘ค๏ธŽ u/Octahedro
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I just got my Voronoi tessellations working with cellular automata to make caves! giphy.com/gifs/crescent-lโ€ฆ
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Voronoi tessellation inside geometric bounds

I've been trying to generate Voronoi tessellations inside convex polygons. Basically I want to be able to have a fractal tesselation, where I have multiple scales. So I would like to re-tesselate individual polygons from the Voronoi with new random points at a finer scale. I'm using qhull via scipy.spatial at the moment.

My current approach is:

  1. Generate random points using a variety of distributions.
  2. Use the point in polygon formula to exclude random points outside the polygon (https://wrf.ecse.rpi.edu//Research/Short_Notes/pnpoly.html)
  3. Create mirror points across the perpendicular vectors to the two lines attached to the nearest vertex in the bounding polygon. Add these points to the Voronoi diagram and recompute. This gives me straight lines on my bounding polygon.
  4. Clip the added points from the Voronoi object.
  5. Relax the Voronoi diagram with ~3 cycles of Lloyd's algorithm.

I'm just sitting here though and thinking, surely there's a smart, faster way to generate bounded Voronoi diagrams?. Perhaps there is and I'm just not searching for the right keywords on Google?

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๐Ÿ‘ค๏ธŽ u/robert_mcleod
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Understanding Voronoi Tessellation (resource allocation, path finding, breakable geometry, ...) alanzucconi.com/?p=3090
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Voronoi Map (Thiessen polygons) of Australia with State Capitals as Centroids [OC] [4000x3282]
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[OC] Map of the World but Capitals are Voronoi Centroids
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๐Ÿ‘ค๏ธŽ u/njanakiev
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Voronoi tessellation
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๐Ÿ‘ค๏ธŽ u/aloofloofah
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FXGL (game framework) 0.3.8 is out! New: Heroku leaderboard server, Voronoi tessellation. github.com/AlmasB/FXGL
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Voronoi sphere tessellation, spheric maze generation youtube.com/watch?v=_JYSKโ€ฆ
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FXGL game framework 0.3.8 (Heroku leaderboard server, Voronoi tessellation, particle interpolators) github.com/AlmasB/FXGL
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Creating Voronoi Tessellations from Images codegolf.stackexchange.coโ€ฆ
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Using Voronoi tessellations to make caves (x-post from r/proceduralgeneration) wick.works/wicklog-6-voroโ€ฆ
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Voronoi Tessellations datagenetics.com/blog/mayโ€ฆ
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Voronoi tessellation in linear time asserttrue.blogspot.com/2โ€ฆ
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Voronoi/Delaunay Tessellation for Spatial Construction

My blog post on the concept of Spatial Construction, which is the theory of deriving the spatial knowledge. I released PyDelaunay - an efficient Python implementation of Voronoi/Delaunay Tessellation, which can be served as the Basic Map of the neighbourhood concept.

http://bennycheung.github.io/model-of-spatial-construction

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image voronoi tessellation [OC][howto in comments]
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A Three-Tiered Reorganization of the Lower 48 States Based on a Voronoi Tesselation from 30 Capitals reddit.com/gallery/p1a43e
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Voronoi Tessellation of the Last Month of Earthquakes in the Five Most Active States [OC] igotcharts.tumblr.com/posโ€ฆ
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Interlocking puzzle pieces from Voronoi tessellation mathematica.stackexchangeโ€ฆ
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๐Ÿ‘ค๏ธŽ u/mathshare
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Voronoi Tessellation of National Cancer Institute Cancer Centers [2158 x 1449] [OC]
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๐Ÿ‘ค๏ธŽ u/shivasprogeny
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A deflation of Voronoi tiles (LHS) using the centroids of the original triangulation set (RHS)
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๐Ÿ‘ค๏ธŽ u/jphsd
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I've got Delaunay triangulation and the centroids of the triangles working. Now, how do I turn this into Voronoi regions?
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๐Ÿ‘ค๏ธŽ u/hiulit
๐Ÿ“…๏ธŽ Jun 04 2020
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On the left, Voronoi cells using circumcenter. On the right, Voronoi cells using centroid. Which one do you like the most?
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๐Ÿ‘ค๏ธŽ u/hiulit
๐Ÿ“…๏ธŽ Jun 18 2020
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[OC] Map of the World but Capitals are Voronoi Centroids
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๐Ÿ‘ค๏ธŽ u/Hexidian
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Extract neighbors from first shell of Voronoi tesselation

Iโ€™m assuming the best answer to this question requires using VoronoiDelaunay.jl, but Iโ€™m also open to other packages/approaches.

If I have a set of points in 2D (or 3D? Though not Iโ€™m not sure this is possible with the package VoronoiDelaunay.jl
), what is the fastest way to get each of their nearest neighbors in a Voronoi-tesselation sense (e.g the neighbors within the โ€˜first Voronoi shellโ€™)? I am also not really confident on the mathematics behind this or how it relates to Delaunay triangulation.

The data structure doesnโ€™t matter too much to me, but letโ€™s just assume the data is stored in a 2D array of type Array{Float64,2} called my_points, whose size is (nDims, nPoints), and nDims
is 2 or 3, and nPoints is the number of points. Letโ€™s say I want to have the output be an edge list of some kind, e.g. array of arrays called edge_list (Array{Array{Int64,1}}) where each element i of edge_list stores the indices of those points that are Voronoi neighbors of the focal point i
(whose coordinates are stored in my_points[:,i]).

Any ideas?

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๐Ÿ‘ค๏ธŽ u/mccl30d
๐Ÿ“…๏ธŽ Jul 10 2020
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[OC] Bombay Suburban Rail catchment areas according to Voronoi Tesselations
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๐Ÿ‘ค๏ธŽ u/jedipro
๐Ÿ“…๏ธŽ Apr 14 2020
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I made a Voronoi Tessellation Generator and I want to share it with all of you.

Hey /r/proceduralgeneration

For a game I'm working on, I created this program that generates the voronoi tessellation of random points on the surface of a sphere. I use it to generate buildings and clouds on the surface of a spherical planet. I'm sure you can find some uses for it too.

I put a lot of work into making it fast. The first version was incredibly slow, but now it can generate a tessellation for 1,000,000 points in under 20 seconds on my desktop. I wrote an article about optimizing it on my blog.

I also struggled with numerical stability when the number of points is large. You can read about how I fixed that too.

Here are some videos showing what I used it for.

http://youtu.be/nFah9_xSyvo

http://youtu.be/Rr6x4L3oha0

Feel free to modify the code and use it for whatever you want. Let me know if you use it for something cool! If you have any requests to modify it or add features let me know!

You can find the source code here.

And you can download it here!

๐Ÿ‘๏ธŽ 27
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๐Ÿ‘ค๏ธŽ u/Octahedro
๐Ÿ“…๏ธŽ Dec 01 2014
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