spatstat (version 1.37-0)

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. Scandinavian Journal of Statistics 39, 591--617.

See Also

linnet

Examples

Run this code
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

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