lineardisc: Compute Disc of Given Radius in Linear Network
Description
Computes the disc of given radius and centre
in a linear network.
Usage
lineardisc(L, x = locator(1), r, plotit = TRUE,
cols=c("blue", "red","green"))
countends(L, x = locator(1), r)
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.
Value
The value of lineardisc is a list with two entries:
linesLine segment pattern (object of class "psp")
representing the interior disc
endpointsPoint pattern (object of class "ppp")
representing the relative boundary of the disc.
The value of countends is an integer giving the number of
points in the relative boundary.
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.
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.
To appear in Scandinavian Journal of Statistics.