seing this kind of visualisations helped me a lot in gfx. always much respect for ppl who understand it well enough to make these things. after a long time tinkering i am still not there for sure :D.
> Consider when the algorithm places a point p and then samples its annulus to get a new point q.
I was confused for a while thinking p and q were swapped here, relative to the visualization below. [0] However I now think what I missed is that that the visualization is showing two points that are already firmly-established, and the question is where a potential third (unseen, unnamed) point could be placed.
So metaphorically speaking, it's about picking a new direction of travel that isn't guaranteed to be into your own recent footsteps.
[0] You might say I have problems minding my p's and q's.
I love these kinds of problems, because they try to produce what humans perceive as random instead of something truly random. Another great example of this is blue noise
funny you mention. blue noise was also the first one that popped in my mind. spent a lot of time looking for blue noise without knowing it at some point ::) while working on a system that was also using poisson disk sampling.
For a low-discrepancy sequence you are usually trying to generate one point at a time, up to some arbitrary number. Here the goal is to generate (roughly) a specific number of points that fill a whole region.
So you probably could figure out a way to use this method to make a low-discrepancy sequence but it's probably not going to be particularly suitable compared to alternatives.
That's the the difference between a low-discrepancy sequence and low-discrepancy set. The first can generate an infinite number of points, the later targets exactly a specific number. You can often get lower discrepancy if you know up front exactly how many points you'll want.
All that said, there's definitely been research into samplers that combine low-discrepancy with blue noise properties (often including retaining those properties even in lower-dimensional projections produced by dropping axis).
Still one of the most satisfying debug UIs I ever came up with.
https://akkartik.name/post/2023-11-04-devlog
seing this kind of visualisations helped me a lot in gfx. always much respect for ppl who understand it well enough to make these things. after a long time tinkering i am still not there for sure :D.
thanks, these are great!
The third one especially is both (really) cool looking and legible!
Possibly interesting post from Casey Muratori, regarding random placement of grass in games: https://caseymuratori.com/blog_0013, using blue noise.
Also Casey, but his much cooler/deterministic solution to grass placement, to avoid lines
https://caseymuratori.com/blog_0011
Folks may find https://observablehq.com/@fil/poisson-distribution-generator... useful
Also fun: https://observablehq.com/@jrus/spheredisksample
Never found a way to do this per-pixel in a shader, Bridson's needs the active list. Ended up hashing cells and jittering inside them instead.
TFA links to PixelPie as a GPU implementation https://www.cs.umd.edu/gvil/projects/pixelpie.shtml
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Off-topic but I quite like another post about relationships on this site: https://stripeacross.com/posts/no-bf-22/
> Consider when the algorithm places a point p and then samples its annulus to get a new point q.
I was confused for a while thinking p and q were swapped here, relative to the visualization below. [0] However I now think what I missed is that that the visualization is showing two points that are already firmly-established, and the question is where a potential third (unseen, unnamed) point could be placed.
So metaphorically speaking, it's about picking a new direction of travel that isn't guaranteed to be into your own recent footsteps.
[0] You might say I have problems minding my p's and q's.
I love these kinds of problems, because they try to produce what humans perceive as random instead of something truly random. Another great example of this is blue noise
funny you mention. blue noise was also the first one that popped in my mind. spent a lot of time looking for blue noise without knowing it at some point ::) while working on a system that was also using poisson disk sampling.
Oh, that’s rather a different sort of disk sampling than I imagined.
I'm wondering if it can be used as a low-discrepancy sequence
For a low-discrepancy sequence you are usually trying to generate one point at a time, up to some arbitrary number. Here the goal is to generate (roughly) a specific number of points that fill a whole region.
So you probably could figure out a way to use this method to make a low-discrepancy sequence but it's probably not going to be particularly suitable compared to alternatives.
That's the the difference between a low-discrepancy sequence and low-discrepancy set. The first can generate an infinite number of points, the later targets exactly a specific number. You can often get lower discrepancy if you know up front exactly how many points you'll want.
All that said, there's definitely been research into samplers that combine low-discrepancy with blue noise properties (often including retaining those properties even in lower-dimensional projections produced by dropping axis).
I found this very satisfying to look at. Especially the one with the "tree" rendering!
I see the generated points often form lines which would cause aliasing in computer graphics, why not use low discrepancy sequences instead?
I immidiately thought of ggplot's geom_jitter.
Love the interactive visuals in this post!
Magical algorithm
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