# Sample uniformly within a fixed radius.

May 16, 2014
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I was asked how to do this today and thought that I would share the answer:

`## Sample points uniformly within a fixed radiusnrand=1000maxstep=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 coordinatestempdat\$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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