# 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, ...)`

##### Arguments

- lambda
- Intensity of the Poisson process.
A single number, a
`function(x,y)`

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

). - L
- Line segment pattern (object of class
`"psp"`

) on which the points should be generated. - lmax
- Maximum possible value of
`lambda`

if it is a function or a pixel image. - ...
- Additional arguments passed to
`lambda`

if it is a function.

##### 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.

The argument `lambda`

may be a single number,
or a `function(x,y)`

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

). In the two latter cases, the rejection method is used.

The rejection method requires knowledge of `lmax`

,
the maximum possible value of `lambda`

. If `lmax`

is not
given, it will be computed approximately, by sampling many values of
`lambda`

.

##### Value

- A point pattern (object of class
`"ppp"`

) in the same window as`L`

.

##### See Also

##### Examples

```
L <- psp(runif(10), runif(10), runif(10), runif(10), window=owin())
plot(L, main="")
# uniform intensity
Y <- rpoisppOnLines(4, L)
plot(Y, add=TRUE, pch="+")
# intensity is a function
Y <- rpoisppOnLines(function(x,y){ 10 * x^2}, L, 10)
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, 10)
plot(L, main="")
plot(Y, add=TRUE, pch="+")
```

*Documentation reproduced from package spatstat, version 1.19-2, License: GPL (>= 2)*