rpoispoly {spagmix}

Generate a Poisson point pattern in a polygonal window

Description

Generates a single realisation of a spatial Poisson point process based on a pixel image and a polygonal owin.

Usage

rpoispoly(z, w = NULL, correction = 1.1, maxpass = 50)

Arguments

z

A pixel image of class im defining the spatial intensity function of the points. The number of points generated, n, will be found as a randomly generated Poisson variate with mean parameter equal to the integral of z.

w

A polygonal window of class owin. See ‘Details’.

correction

An adjustment to the number of points generated at the initial pass of the internal loop in an effort to minimise the total number of passes required to reach n points. See ‘Details’ and ‘Warning’.

maxpass

The maximum number of passes allowed before the function exits. If this is reached before n points are found that fall within w, a warning is issued.

Details

This is a wrapper function for rimpoly that operates much like rpoispp, but with artificial corrections at the edges of boundary pixels. This allows the user to generate a realisation of a 2D Poisson point process using a supplied pixel image as the spatial intensity function, but return the result with a polygonal owin instead of a binary image mask.

Let n be a randomly generated integer from a Poisson distribution with mean given by the integral of the intensity function z. When the user specifies their own polygonal window in w, a while loop is called and repeated as many times as necessary (up to maxpass times) to find n points inside w (when w = NULL, then the union of the pixels of z is used, obtained via as.polygonal(Window(z))). The loop is necessary because the standard behaviour of rpoispp can (and often does) yield points that sit in corners of pixels which lie outside a corresponding irregular polygon w.

The correction argument is used to determine how many points are generated initially, which will be ceiling(correction*n); to minimise the number of required passes over the loop this is by default set to give a number slightly higher than the requested n.

An error is thrown if Window(z) and w do not overlap.

Value

An object of class ppp containing the Poisson-generated points, defined with the polygonal owin, w.

Warning

Note that this is an artificial correction that forces the Poisson-generated number of n points to be found inside any supplied polygon w (even if w only partially covers the domain of z). As such, this function only makes sense in terms of the theory of a Poisson point process if the polygon w corresponds exactly to the pixellised intensity. For practical intents and purposes, it therefore must be assumed in using this function that a supplied polygon w is/was the original basis for the discretisation into the pixel image for the purposes of producing the intensity z, and hence that any adverse effects arising from imposing w as the window of the final result are negligible. See ‘Examples’.

Author(s)

T.M. Davies

References

Diggle, P.J. (2014) Statistical Analysis of Spatial and Spatiotemporal Point Patterns, 3rd Ed, Chapman & Hall, Boca Raton, USA.

See Also

rpoint, rimpoly, rpoispp

Examples

mn <- cbind(c(0.25,0.8),c(0.31,0.82),c(0.43,0.64),c(0.63,0.62),c(0.21,0.26))
v1 <- matrix(c(0.0023,-0.0009,-0.0009,0.002),2)
v2 <- matrix(c(0.0016,0.0015,0.0015,0.004),2)
v3 <- matrix(c(0.0007,0.0004,0.0004,0.0011),2)
v4 <- matrix(c(0.0023,-0.0041,-0.0041,0.0099),2)
v5 <- matrix(c(0.0013,0.0011,0.0011,0.0014),2)
vr <- array(NA,dim=c(2,2,5))
for(i in 1:5) vr[,,i] <- get(paste("v",i,sep=""))
intens <- sgmix(mean=mn,vcv=vr,window=toywin,p0=0.1,int=500)

aa <- rpoispp(intens) # Default spatstat function
bb <- rpoispoly(intens) # No polygon supplied; just uses pixel union
cc <- rpoispoly(intens,w=toywin) # Original irregular polygon

plot(intens,log=TRUE)
plot(aa,main=paste("aa\nn =",npoints(aa)))
plot(bb,main=paste("bb\nn =",npoints(bb)))
plot(cc,main=paste("cc\nn =",npoints(cc)))