Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the ‘disc’ of given radius and centre in a linear network.

1 2 3 4 |

`L` |
Linear network (object of class |

`x` |
Location of centre of disc.
Either a point pattern (object of class |

`r` |
Radius of disc. |

`plotit` |
Logical. Whether to plot the disc. |

`add` |
Logical. If |

`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 |

`internal` |
Argument for internal use by the package. |

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.

The value of `lineardisc`

is a list with two entries:

`lines ` |
Line segment pattern (object of class |

`endpoints` |
Point pattern (object of class |

The value of `countends`

is an integer giving the number of
points in the relative boundary.

Ang Qi Wei aqw07398@hotmail.com and \adrian

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
# 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)
plot(letterA)
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)
``` |

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