Sorry Ted The code for the circle is in error, the radius distribution should be proportional to the circle area not uniform. Better / simple to sample from the (-1,1) square uniformly and reject where x^2+y^2 > 1 Heberto ________________________________________ From: r-help-boun...@r-project.org [r-help-boun...@r-project.org] On Behalf Of Ted Harding [ted.hard...@manchester.ac.uk] Sent: Friday, June 18, 2010 5:48 AM To: r-h...@stat.math.ethz.ch Subject: [R] [OOPS] Re: Drawing sample from a circle
OOPS: AN error on the code below! See in-line. Ted. On 18-Jun-10 09:33:04, Ted Harding wrote: > On 18-Jun-10 08:04:36, Ron Michael wrote: >> Hi, I would like to draw 10 uniformly distributed sample points from a >> circle with redius one and centered at (0,0). Is there any R function >> to do that? >> _ >> Thanks, > > You can quite easily write one. > > [A] > Sampling uniformly on the circumference of the circle: > > csamp <- function(n,rad=1,centre=c(0,0)){ > x0 <- centre[1] ; y0 <- centre[2] > u <- 2*pi*runif(n) > rad*cbind(x=cos(u)+x0, y=sin(u)+y0) > } > ># Returns an nx2 matrix whose two columns are the x and y coordinates CORRECTION: csamp <- function(n,rad=1,centre=c(0,0)){ x0 <- centre[1] ; y0 <- centre[2] u <- 2*pi*runif(n) cbind(x=rad*cos(u)+x0, y=rad*sin(u)+y0) } # Returns an nx2 matrix whose two columns are the x and y coordinates > [B] > Sampling uniformaly within the circle > > Csamp <- function(n,rad=1,centre=c(0,0)){ > x0 <- centre[1] ; y0 <- centre[2] > u <- 2*pi*runif(n) > r <- sqrt(runif(n)) > rad*cbind(x=r*cos(u)+x0, y=r*sin(u)+y0) > } > ># Returns an nx2 matrix whose two columns are the x and y coordinates CORRECTION: Csamp <- function(n,rad=1,centre=c(0,0)){ x0 <- centre[1] ; y0 <- centre[2] u <- 2*pi*runif(n) r <- sqrt(runif(n)) cbind(x=rad*r*cos(u)+x0, y=rad*r*sin(u)+y0) } # Returns an nx2 matrix whose two columns are the x and y coordinates > [C] > Examples: > > plot(csamp(100),asp=1) > > plot(Csamp(1000),asp=1) > > Ted. > > -------------------------------------------------------------------- > E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> > Fax-to-email: +44 (0)870 094 0861 > Date: 18-Jun-10 Time: 10:33:00 > ------------------------------ XFMail ------------------------------ > > ______________________________________________ > R-help@r-project.org 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. -------------------------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861 Date: 18-Jun-10 Time: 10:48:14 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@r-project.org 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. ______________________________________________ R-help@r-project.org 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.