1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
|
\name{connected.lpp}
\alias{connected.lpp}
\title{
Connected Components of a Point Pattern on a Linear Network
}
\description{
Finds the topologically-connected components of a point pattern on a
linear network, when all pairs of points closer than a threshold distance
are joined.
}
\usage{
\method{connected}{lpp}(X, R=Inf, \dots, dismantle=TRUE)
}
\arguments{
\item{X}{
A linear network (object of class \code{"lpp"}).
}
\item{R}{
Threshold distance. Pairs of points will be joined together
if they are closer than \code{R} units apart, measured
by the shortest path in the network.
The default \code{R=Inf} implies that points
will be joined together if they are mutually connected by any
path in the network.
}
\item{dismantle}{
Logical. If \code{TRUE} (the default), the network itself will be
divided into its path-connected components using
\code{\link{connected.linnet}}.
}
\item{\dots}{
Ignored.
}
}
\details{
The function \code{connected} is generic. This is the method for
point patterns on a linear network (objects of class \code{"lpp"}).
It divides the point pattern \code{X} into one or more groups of points.
If \code{R=Inf} (the default), then \code{X} is divided into groups
such that any pair of points in the same group
can be joined by a path in the network.
If \code{R} is a finite number, then two points of \code{X} are
declared to be \emph{R-close} if they lie closer than
\code{R} units apart, measured by the length of the shortest path in the
network. Two points are \emph{R-connected} if they
can be reached by a series of steps between R-close pairs of
points of \code{X}. Then \code{X} is divided into groups such that
any pair of points in the same group is R-connected.
If \code{dismantle=TRUE} (the default) the algorithm first checks
whether the network is connected (i.e. whether any pair of vertices
can be joined by a path in the network), and if not, the network is
decomposed into its connected components.
}
\value{
A point pattern (of class \code{"lpp"}) with marks indicating the
grouping, or a list of such point patterns.
}
\author{
\adrian.
}
\seealso{
\code{\link{thinNetwork}}
}
\examples{
## behaviour like connected.ppp
U <- runiflpp(20, simplenet)
plot(connected(U, 0.15, dismantle=FALSE))
## behaviour like connected.owin
## remove some edges from a network to make it disconnected
plot(simplenet, col="grey", main="", lty=2)
A <- thinNetwork(simplenet, retainedges=-c(3,5))
plot(A, add=TRUE, lwd=2)
X <- runiflpp(10, A)
## find the connected components
cX <- connected(X)
plot(cX[[1]], add=TRUE, col="blue", lwd=2)
}
\keyword{spatial}
\keyword{manip}
\concept{Linear network}
|
