Generating Voronoi diagrams using Fortune's algorithm
redpenguin101.github.ioI made an implementation in clojurescript that animates the algorithm as it goes a while back: https://voronoi.ajwerner.net/#/app-diagrams
It’s a very beautiful algorithm.
However, after that project I sort of came to dislike Fortune’s algorithm because it isn’t numerically stable with floating point numbers. If you have points that are colinear, or nearly colinear in fp, things can break. The delaunator is better in this regard iirc: https://github.com/mapbox/delaunator
The animation is the best I've seen. I see the "old" implementation link in the references page; any chance of open sourcing the current animation one?
It’s all open source, sorry there was no link!
A few years back I made this 3d visualisation https://x.com/KangarooPhysics/status/1253336959755251716
Wow, this made everything click for me. Really nice animation!
There is an implementation of that algorithm in JS by Raymond Hill (of uBlock Origin fame):
https://github.com/gorhill/Javascript-Voronoi
I toyed with it here to have it move:
Your animation reminded me of the style used in A Scanner Darkly (2006)
I wonder if it's possible to use video as an input to an algorithm that displays using Voronoi? Probably at that point it wouldn't be a Voronoi diagram, but it might look cool :)
The technique used in A Scanner Darkly is called rotoscoping, btw.
D3js has a new implementation
https://github.com/d3/d3-delaunay
at the bottom of that page is a discussion of the sweep algorithm used and a list of other (non-javascript) language implentations.
The original d3-voronoi is deprecated but can be found here:
If you are not interested in the edges, only painting the sites with different colors, you can use a variation of flood fill starting with the seeds and only stacking the pixel if that color has distance lower than the one already painted that pixel.
Build a 3D scene of distinctly colored right circular cones with their apexes at the 2D planar vertices, and their axes perpendicular to the plane.
Render a 2D orthographic view from 'above' the apexes.
The z-buffer will preserve pixels from the nearest apex.
(Yes, I now there are shadery ways to do this, but the classic 3D cones demo is trivial to understand and implement).
You don't have to use cones. Paraboloids work too.
Cool! Interesting that D3 moved away from Fortune's algorithm to https://mapbox.github.io/delaunator/ because it
"is 5-10× faster than d3-voronoi to construct the Delaunay triangulation or the Voronoi diagram, is more robust numerically, has Canvas rendering built-in, allows traversal of the Delaunay graph, and a variety of other improvements."
Oh - that's interesting! If D3 think delaunator is the best approach to this sort of effect, then there's no more excuses (beyond my natural procrastination) to stop me adding it to my canvas library: the current code I use to calculate tiles is painfully naive!
New discussion: https://github.com/KaliedaRik/Scrawl-canvas/discussions/120
This made me look up where Steve is these days. I knew him decades ago.
See also:
https://news.ycombinator.com/item?id=37998923 - Voronoi Diagram and Delaunay Triangulation in O(n log n) with Fortune's Algorithm (2020)
The previous article and discussion contain short summaries of other algorithms. My favorite is still the Jump Flooding Algorithm.
What’re the odds!
I just did this with Common Lisp!
Ah, the original latent space.
Houdini’s 3D Voronoi tools are fun.