library(spatial)
#help(package=spatial)

towns <- ppinit("towns.dat")
par(pty="s")
plot(Kfn(towns, 10), type="b", xlab="distance", ylab="L(t)")
title("Kfunction for towns data",cex=.5)

Kfunc <- Kfn(towns, 10)
Kfunc

plot(Kfn(towns, 10), type="b", xlab="distance", ylab="L(t)")
for(i in 1:10) lines(Kfn(Psim(69), 10), lty=3)
lims <- Kenvl(10,100,Psim(69))
lines(lims$x,lims$l, lty=2, col="green", lwd=3) # lty=2: dotted lines
lines(lims$x,lims$u, lty=2, col="green", lwd=3)
title("Kfunction with envelope and simulation Poisson Models",cex=.5)

plot(Kfn(towns, 10), type="b", xlab="distance", ylab="L(t)")
for(i in 1:10) lines(Kfn(Strauss(69,0.5,3.5), 10), lty=3)
lines(Kaver(10,25,Strauss(69,0.5,3.5)), col="red", lwd=3)
title("Kfunction with Simulations and Average Strauss Model",cex=.5)

#############################################################
#
# Psim:
# Simulate Binomial spatial point process.
#
# Kfn:
# Computes Ripley's K function for a set of case locations
#     (Actually computes L = sqrt(K/pi).)
#
# Kaver:
# Forms the average of a series of (usually simulated) 
#     K-functions. 
#
# Kenvl:
# Computes envelope (upper and lower limits) and average 
#     of simulations of K-fns 
#
#############################################################