rpoispp: Generate Poisson Point Pattern

Description

Generate a random point pattern using the (homogeneous or inhomogeneous) Poisson process. Includes CSR (complete spatial randomness).

Usage

rpoispp(lambda, lmax, win, ...)

Arguments

lambda

Intensity of the Poisson process. Either a single positive number, a function(x,y, ...), or a pixel image.

lmax

An upper bound for the value of lambda(x,y), if lambda is a function.

win

Window in which to simulate the pattern. An object of class "owin" or something acceptable to as.owin. Ignored if lambda is a pixel image.

...

Arguments passed to lambda if it is a function.

Value

The simulated point pattern (an object of class "ppp").

Details

If lambda is a single number, then this algorithm generates a realisation of the uniform Poisson process (also known as Complete Spatial Randomness, CSR) inside the window win with intensity lambda (points per unit area). If lambda is a function, then this algorithm generates a realisation of the inhomogeneous Poisson process with intensity function lambda(x,y,...) at spatial location (x,y) inside the window win. The function lambda must work correctly with vectors x and y. The value lmax must be given and must be an upper bound on the values of lambda(x,y,...) for all locations (x, y) inside the window win.

If lambda is a pixel image object of class "im" (see im.object), this algorithm generates a realisation of the inhomogeneous Poisson process with intensity equal to the pixel values of the image. (The value of the intensity function at an arbitrary location is the pixel value of the nearest pixel.) The argument win is ignored; the window of the pixel image is used instead. To generate an inhomogeneous Poisson process the algorithm uses ``thinning'': it first generates a uniform Poisson process of intensity lmax, then randomly deletes or retains each point, independently of other points, with retention probability $p(x,y) = \lambda(x,y)/\mbox{lmax}$.

Examples

Run this code

# uniform Poisson process with intensity 100 in the unit square
 pp <- rpoispp(100)
 
 # uniform Poisson process with intensity 1 in a 10 x 10 square
 pp <- rpoispp(1, win=owin(c(0,10),c(0,10)))
 # plots should look similar !
 
 # inhomogeneous Poisson process in unit square
 # with intensity lambda(x,y) = 100 * exp(-3*x)
 # Intensity is bounded by 100
 pp <- rpoispp(function(x,y) {100 * exp(-3*x)}, 100)

 # How to tune the coefficient of x
 lamb <- function(x,y,a) { 100 * exp( - a * x)}
 pp <- rpoispp(lamb, 100, a=3)

 # pixel image
 Z <- as.im(function(x,y){100 * sqrt(x+y)}, unit.square())
 pp <- rpoispp(Z)