R help - Oct 2006 - How to generate the random numbers uniformly distributed on the unit disc?

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]]

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]]
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
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

"S.Q. WEN" <randsnews at gmail.com> writes:
> Hi,
> I want to get  random number which is uniformly distributed  on the unit
> disc.
> How can I do that with R?
Most easily, although perhaps not most efficiently, by using spherical
coordinates:

 N <- 10000
 r <- sqrt(runif(N))
 theta <- runif(N,0,2*pi)
 x <- r*cos(theta)
 y <- r*sin(theta)
 plot(x,y,pch=".")




-- 
   O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907