## Friday, May 16, 2014

### Sample uniformly within a fixed radius.

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,
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)

##make plots
png(filename="sampleplots.png",width=500,height=1000)
par(mfrow=c(2,1))
plot(Y~X, data=tempdat, asp=1, main="Uniform across space")
dev.off()
```

#### 1 comment:

Mark T Patterson said...

Hi Forester,
Thanks for your post! Here's different solution for uniform sampling that's a bit more slipshod (you end up having less control), but I thought you'd be interested in the nature of the solution:

Mark

df = data.frame(
x1 = runif(1000,-1,1),
y1 = runif(1000,-1,1)
)

df\$ok = apply(df,1,function(x){as.numeric(x[1]^2 + x[2]^2 < 1)})

sub = df[df\$ok == 1,]

plot(sub\$x1, sub\$y1)