The “distance function” of a set of points \(A\) is the
mathematical function \(f\) such that, for any
two-dimensional spatial location \((x,y)\),
the function value f(x,y)
is the shortest distance from \((x,y)\) to \(A\).
The command f <- distfun(X) returns a function
in the R language, with arguments x,y, 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. Alternatively x can be a
point pattern (object of class "ppp" or "lpp") of
locations at which the distance function should be computed (and then
y should be missing).
This should be contrasted with the related command distmap
which computes the distance function of X
on a grid of locations, and returns the distance
values in the form of a pixel image.
The distance values returned by f <- distfun(X); d <- f(x)
are computed using coordinate geometry; they are more accurate,
but slower to compute, than the distance values returned by
Z <- distmap(X); d <- Z[x]
which are computed using a fast recursive algorithm.
The result of f <- distfun(X) also belongs to the class
"funxy" and to the special class "distfun".
It can be printed and plotted immediately as shown in the Examples.
A distfun object can be converted to a pixel image
using as.im.