lineardisc
Compute Disc of Given Radius in Linear Network
Computes the ‘disc’ of given radius and centre in a linear network.
- Keywords
- spatial
Usage
lineardisc(L, x = locator(1), r, plotit = TRUE,
cols=c("blue", "red","green")) countends(L, x = locator(1), r, toler=NULL)
Arguments
- L
Linear network (object of class
"linnet").- x
Location of centre of disc. Either a point pattern (object of class
"ppp") containing exactly 1 point, or a numeric vector of length 2.- r
Radius of disc.
- plotit
Logical. Whether to plot the disc.
- cols
Colours for plotting the disc. A numeric or character vector of length 3 specifying the colours of the disc centre, disc lines and disc endpoints respectively.
- toler
Optional. Distance threshold for
countends. See Details. There is a sensible default.
Details
The ‘disc’ \(B(u,r)\) of centre \(x\) and radius \(r\) in a linear network \(L\) is the set of all points \(u\) in \(L\) such that the shortest path distance from \(x\) to \(u\) is less than or equal to \(r\). This is a union of line segments contained in \(L\).
The relative boundary of the disc \(B(u,r)\) is the set of points \(v\) such that the shortest path distance from \(x\) to \(u\) is equal to \(r\).
The function lineardisc computes the
disc of radius \(r\) and its relative boundary,
optionally plots them, and returns them.
The faster function countends simply counts the number of
points in the relative boundary.
The optional threshold toler is used to suppress numerical
errors in countends.
If the distance from \(u\) to a network vertex \(v\)
is between r-toler and r+toler, the vertex
will be treated as lying on the relative boundary.
Value
The value of lineardisc is a list with two entries:
Line segment pattern (object of class "psp")
representing the interior disc
Point pattern (object of class "ppp")
representing the relative boundary of the disc.
References
Ang, Q.W. (2010) Statistical methodology for events on a network. Master's thesis, School of Mathematics and Statistics, University of Western Australia.
Ang, Q.W., Baddeley, A. and Nair, G. (2012) Geometrically corrected second-order analysis of events on a linear network, with applications to ecology and criminology. Scandinavian Journal of Statistics 39, 591--617.
See Also
Examples
# NOT RUN {
# letter 'A'
v <- ppp(x=(-2):2, y=3*c(0,1,2,1,0), c(-3,3), c(-1,7))
edg <- cbind(1:4, 2:5)
edg <- rbind(edg, c(2,4))
letterA <- linnet(v, edges=edg)
lineardisc(letterA, c(0,3), 1.6)
# count the endpoints
countends(letterA, c(0,3), 1.6)
# cross-check (slower)
en <- lineardisc(letterA, c(0,3), 1.6, plotit=FALSE)$endpoints
npoints(en)
# }