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.