Generate Poisson Point Pattern on Line Segments
Given a line segment pattern, generate a Poisson random point pattern on the line segments.
rpoisppOnLines(lambda, L, lmax = NULL, ..., nsim=1, drop=TRUE)
lambda |
Intensity of the Poisson process.
A single number, a |
L |
Line segment pattern (object of class |
lmax |
Optional upper bound (for increased computational efficiency).
A known upper bound for the values of |
... |
Additional arguments passed to |
nsim |
Number of simulated realisations to be generated. |
drop |
Logical. If |
This command generates a Poisson point process on the one-dimensional
system of line segments in L. The result is a point pattern
consisting of points lying on the line segments in L.
The number of random points falling on any given line segment follows
a Poisson distribution. The patterns of points on different segments
are independent.
The intensity lambda is the expected number of points
per unit length of line segment.
It may be constant, or it may depend on spatial location.
In order to generate an unmarked Poisson process,
the argument lambda may be a single number,
or a function(x,y), or a pixel image (object of class
"im").
In order to generate a marked Poisson process,
lambda may be a numeric vector, a list of functions,
or a list of images, each entry giving the intensity for
a different mark value.
If lambda is not numeric, then the (Lewis-Shedler)
rejection method is used.
The rejection method requires knowledge of lmax,
the maximum possible value of lambda. This should be either
a single number, or a numeric vector of the same length as
lambda. If lmax is not
given, it will be computed approximately, by sampling many values of
lambda.
If lmax is given, then it must be larger than
any possible value of lambda, otherwise the results of the
algorithm will be incorrect.
If nsim = 1, a point pattern
(object of class "ppp") in the same window
as L. If nsim > 1, a list of such point patterns.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
live <- interactive()
L <- psp(runif(10), runif(10), runif(10), runif(10), window=owin())
if(live) plot(L, main="")
# uniform intensity
Y <- rpoisppOnLines(4, L)
if(live) plot(Y, add=TRUE, pch="+")
# uniform MARKED process with types 'a' and 'b'
Y <- rpoisppOnLines(c(a=4, b=5), L)
if(live) {
plot(L, main="")
plot(Y, add=TRUE, pch="+")
}
# intensity is a function
Y <- rpoisppOnLines(function(x,y){ 10 * x^2}, L, 10)
if(live) {
plot(L, main="")
plot(Y, add=TRUE, pch="+")
}
# intensity is an image
Z <- as.im(function(x,y){10 * sqrt(x+y)}, unit.square())
Y <- rpoisppOnLines(Z, L, 15)
if(live) {
plot(L, main="")
plot(Y, add=TRUE, pch="+")
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