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

Compute the distance function of a point pattern on a linear network.

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`X` |
A point pattern on a linear network
(object of class |

`k` |
An integer. The distance to the |

`...` |
Extra arguments are ignored. |

On a linear network *L*, the “geodesic distance function”
of a set of points *A* in *L* is the
mathematical function *f* such that, for any
location *s* on *L*,
the function value `f(s)`

is the shortest-path distance from *s* to *A*.

The command `distfun.lpp`

is a method for the generic command
`distfun`

for the class `"lpp"`

of point patterns on a linear network.

If `X`

is a point pattern on a linear network,
`f <- distfun(X)`

returns a *function*
in the **R** language that represents the
distance function of `X`

. Evaluating the function `f`

in the form `v <- f(x,y)`

, where `x`

and `y`

are any numeric vectors of equal length containing coordinates of
spatial locations, yields the values of the distance function at these
locations. More efficiently `f`

can be called in the form
`v <- f(x, y, seg, tp)`

where `seg`

and `tp`

are the local
coordinates on the network. It can also be called as
`v <- f(x)`

where `x`

is a point pattern on the same linear
network.

The function `f`

obtained from `f <- distfun(X)`

also belongs to the class `"linfun"`

.
It can be printed and plotted immediately as shown in the Examples.
It can be
converted to a pixel image using `as.linim`

.

A `function`

with arguments `x,y`

and optional
arguments `seg,tp`

.
It also belongs to the class `"linfun"`

which has methods
for `plot`

, `print`

etc.

.

To identify *which* point is the nearest neighbour, see
`nnfun.lpp`

.

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