`csr.Rd`

Generate completely spatially random points on a polygon.

`csr(poly,npoints)`

- poly
A polygon data set.

- npoints
The number of points to generate.

A point data set consisting of `npoints`

points distributed randomly,
i.e. as an independent random sample from the uniform distribution
in the polygon defined by `poly`

.

`csr`

generates points randomly in the bounding box of `poly,`

then uses
`pip`

to extract those in the polygon. If the number of points remaining is
less than that required, `csr`

generates some more points in the
bounding box until at least `npoints`

remain inside the polygon. If too many
points are generated then the list of points is truncated.

Uses `runif()`

to generate random numbers and so updates `.Random.seed`

,
the standard S random number generator seed.

Rowlingson, B. and Diggle, P. 1993 Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627-655; the original sources can be accessed at: https://www.maths.lancs.ac.uk/~rowlings/Splancs/. See also Bivand, R. and Gebhardt, A. 2000 Implementing functions for spatial statistical analysis using the R language. Journal of Geographical Systems, 2, 307-317.

```
data(cardiff)
nsim <- 29
emp.Ghat <- Ghat(as.points(cardiff), seq(0,30,1))
av.Ghat <- numeric(length(emp.Ghat))
U.Ghat <- numeric(length(emp.Ghat))
L.Ghat <- numeric(length(emp.Ghat))
U.Ghat <- -99999
L.Ghat <- 99999
for(i in 1:nsim) {
S.Ghat <- Ghat(csr(cardiff$poly, length(cardiff$x)), seq(0,30,1))
av.Ghat <- av.Ghat + S.Ghat
L.Ghat <- pmin(S.Ghat, L.Ghat)
U.Ghat <- pmax(S.Ghat, U.Ghat)
}
av.Ghat <- av.Ghat/nsim
plot(av.Ghat, emp.Ghat, type="l", xlim=c(0,1), ylim=c(0,1),
xlab="Simulated average G", ylab="Empirical G")
lines(c(0,1),c(0,1),lty=2)
lines(U.Ghat,emp.Ghat,lty=3)
lines(L.Ghat,emp.Ghat,lty=3)
```