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
fuzzythinker 35 days ago [-]
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?
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 :)
Sharlin 35 days ago [-]
The technique used in A Scanner Darkly is called rotoscoping, btw.
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.
mikhailfranco 34 days ago [-]
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).
alejohausner 34 days ago [-]
You don't have to use cones. Paraboloids work too.
"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."
rikroots 34 days ago [-]
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!
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
https://github.com/ajwerner/voronoi
https://github.com/gorhill/Javascript-Voronoi
I toyed with it here to have it move:
https://animations.adgent.com/voronoi.html
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 :)
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:
https://github.com/d3/d3-voronoi
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).
"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."
New discussion: https://github.com/KaliedaRik/Scrawl-canvas/discussions/120
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.
https://en.wikipedia.org/wiki/Jump_flooding_algorithm
I just did this with Common Lisp!