# lineardisc

0th

Percentile

##### 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)
##### 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
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.
##### 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.

##### 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.

##### 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.

linnet

• lineardisc
• countends
##### Examples
example(linnet)
lineardisc(letterA, c(0,3), 1.6)
# count the endpoints
countends(letterA, c(0,3), 1.6)
# cross-check (slower)
lineardisc(letterA, c(0,3), 1.6, plotit=FALSE)$endpoints$n
Documentation reproduced from package spatstat, version 1.25-1, License: GPL (>= 2)

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