Generate completely spatially random points on a polygon

Generate completely spatially random points on a polygon.

csr(poly,npoints)

Arguments

poly

A polygon data set.

npoints

The number of points to generate.

Value

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.

Details

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.

References

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.

Examples

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)