# 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.

Note that `countends`

requires the linear network `L`

to be given in the non-sparse matrix format (see the argument
`sparse`

in `linnet`

or `as.linnet`

)
while `lineardisc`

accepts both sparse and non-sparse formats.

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)
# }
```

*Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)*