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Comment by hatthew | Hacker News Reader

I doubt I'm more geometrically inclined than the average HN user, but to me the general "accept-flip" method mentioned here seems trivial, obvious, and already solved, to the extent that I'm surprised it's worth writing more about or considering any alternatives.

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Generating random points uniformly in a circle without rejection is at least mildly more interesting, as you need to scale one factor by a square root:

    const r = sqrt(random()) * radius;
    const theta = random() * TAU;

Wait, wouldn't this result in the opposite of what you want? You want to shift the distribution out, not crowd the center, so you probably want to square your random instead.

Squaring numbers in (0,1) makes them smaller, pulling the random radius closer to center. As an example consider 0.9. Squaring it gets 0.81 vs 0.949 taking the square root.

Oh yes all of you are right. In my defense, I am stupid.

Because the numbers are less than 1 sqrt pulls them towards 1 (the edge)

assuming random() returns values 0<=r<=1, sqrt will shift the distribution outward

Yeah that would be at least nontrivial, but has been written about so much that the bar for a worthwhile article seems pretty high.

Obligatory xkcd: https://xkcd.com/1053/

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