Hacker News Reader

Comment by eru | Hacker News Reader

And it _is_ a random point in a circle. Just not a uniformly distributed one.

Btw, here's a way to sample a uniform random point on the edge of a circle without trigonometric functions:

Sample x and y coordinates from a standard normal distribution. Then project the result on the circle, by normalising the distance.

(You can approximate normal distributions fairly easily. Or your favourite computing environment might have specialised optimized machinery built-in.)

View on HN

> Sample x and y coordinates from a standard normal distribution. Then project the result on the circle, by normalising the distance.

I wonder if that's uniform...

I expect that you would have more points mapped to the corners.

It appears to be uniform. I tested empirically in Python: https://pastebin.com/raw/ca03uywJ

https://codepen.io/toxicfork/pen/OJQzLba

This says otherwise

Normal distribution is not the same as uniform distribution. I edited in a normal distribution sampler in your codepen example.

https://pastebin.com/raw/CP4yNRE9

I see, thanks!

Btw, the following two are equivalent (in JavaScript syntax):

    var a = Math.max(Math.random(), Math.random());
    var b = Math.sqrt(Math.random());

Curious, how come? Does it become a statistical thing?

Well, not sure whether you'd call it statistics. It's a mathematical fact from probability theory. And it doesn't matter how often you sample: the distributions themselves are the same.

I came across that one in the other direction, when trying to work out how to make weighted rendezvous hashing work. See https://en.wikipedia.org/wiki/Rendezvous_hashing

I meant to show the output of my code, but Pasteboard was down at the time: https://gcdnb.pbrd.co/images/f8bgGZMW3deq.png?o=1

It's a well-known method to uniformly sample the surface of an n-dimensional sphere.

I guess/think you misread the “standard normal” part in that sentence as “uniform”.

The logic is that independent standard normals on each axis make up the multivariate standard normal, and the multivariate standard normal is rotationally invariant and therefore has the same density at any angle.

Reply on news.ycombinator.com