[R] How to generate the random numbers uniformly distributed on the unit disc?

[Joerg van den Hoff]

S.Q. WEN wrote:
> Hi,
> I want to get  random number which is uniformly distributed  on the unit
> disc.
> How can I do that with R?
> 
> 
> Best wishes,
> WAN WAN
> 
> 	[[alternative HTML version deleted]]
> 
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the following function should put "N" uniformly distributed points into 
a disc of radius "R" (and plot the points in the (phi,rho) and (xx, yy) 
coordinate systems).

disc <- function (N = 10^4, R = 1) {
    phi <- runif(N) * 2 * pi
    rho <- R * sqrt(runif(N))
    xx <- rho * cos(phi)
    yy <- rho * sin(phi)
    layout(1:2)
    plot(phi, rho, pch = ".")
    plot(xx, yy, pch = ".", asp = 1)
    layout(1)
    invisible(list(phi = phi, rho = rho))
}

the trick is to transform a uniform distribution along `rho' in such a 
way that it gets "denser" towards the rim in such a way that the 
'smearing out' of the  points over the circumference is compensated.

regards

joerg