(This article was first published on

**Quantitative Ecology**, and kindly contributed to R-bloggers)I was asked how to do this today and thought that I would share the answer:

## Sample points uniformly within a fixed radius

nrand=1000

maxstep=10## Sample data## NB: To get a truly uniform sample over the circle, you must## sample the square of the distance and then transform back.

tempdat<-data.frame(X0=0,Y0=0, bearing0=0,

bad.dist=runif(nrand)*maxstep,

dist2=sqrt(runif(nrand)*maxstep^2),

turningangle=runif(nrand)*2*pi-pi)##convert Turning angle to bearing (in this case no change)

tempdat$bearing=tempdat$bearing0+tempdat$turningangle## Convert from polar to cartesian coordinates

tempdat$X<-tempdat$X0+tempdat$dist2*sin(tempdat$bearing)

tempdat$Y<-tempdat$Y0+tempdat$dist2*cos(tempdat$bearing)

tempdat$Xbad<-tempdat$X0+tempdat$bad.dist*sin(tempdat$bearing)

tempdat$Ybad<-tempdat$Y0+tempdat$bad.dist*cos(tempdat$bearing)##make plotspng(filename="sampleplots.png",width=500,height=1000)par(mfrow=c(2,1))plot(Ybad~Xbad, data=tempdat, asp=1, main="Center is oversampled")plot(Y~X, data=tempdat, asp=1, main="Uniform across space")dev.off()

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