# rpoisppOnLines

##### Generate Poisson Point Pattern on Line Segments

Given a line segment pattern, generate a Poisson random point pattern on the line segments.

##### Usage

`rpoisppOnLines(lambda, L, lmax = NULL, ..., nsim=1)`

##### Arguments

- lambda
Intensity of the Poisson process. A single number, a

`function(x,y)`

, a pixel image (object of class`"im"`

), or a vector of numbers, a list of functions, or a list of images.- L
Line segment pattern (object of class

`"psp"`

) on which the points should be generated.- lmax
Optional upper bound (for increased computational efficiency). A known upper bound for the values of

`lambda`

, if`lambda`

is a function or a pixel image. That is,`lmax`

should be a number which is known to be greater than or equal to all values of`lambda`

.- …
Additional arguments passed to

`lambda`

if it is a function.- nsim
Number of simulated realisations to be generated.

##### Details

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.

##### Value

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.

##### See Also

##### Examples

```
# NOT RUN {
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="+")
}
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*