Computes the distribution of the orientation of vectors joining pairs of points at a particular range of distances.
pairorient(X, r1, r2, ..., cumulative=FALSE,
correction, ratio = FALSE,
unit=c("degree", "radian"), domain=NULL)A function value table (object of class "fv")
containing the estimates of the probability density or the
cumulative distribution function of angles,
in degrees (if unit="degree")
or radians (if unit="radian").
This algorithm considers all pairs of points in the pattern
X that lie more than r1 and less than r2
units apart. The direction of the arrow joining the points
is measured, as an angle in degrees or radians,
anticlockwise from the \(x\) axis.
If cumulative=FALSE (the default),
a kernel estimate of the probability density of the orientations
is calculated using circdensity.
If cumulative=TRUE, then the cumulative distribution
function of these directions is calculated.
This is the function \(O_{r1,r2}(\phi)\) defined
in Stoyan and Stoyan (1994), equation (14.53), page 271.
In either case the result can be plotted as a rose diagram by
rose, or as a function plot by plot.fv.
The algorithm gives each observed direction a weight,
determined by an edge correction, to adjust for the fact that some
interpoint distances are more likely to be observed than others.
The choice of edge correction or corrections is determined by the argument
correction. See the help for Kest for details
of edge corrections, and explanation of the options available.
The choice correction="none" is not recommended;
it is included for demonstration purposes only. The default is to
compute all corrections except "none".
It is also possible to calculate an estimate of the probability
density from the cumulative distribution function,
by numerical differentiation.
Use deriv.fv with the argument Dperiodic=TRUE.
Stoyan, D. and Stoyan, H. (1994) Fractals, Random Shapes and Point Fields: Methods of Geometrical Statistics. John Wiley and Sons.
Kest, Ksector, nnorient
rose(pairorient(redwood, 0.05, 0.15, sigma=8), col="grey")
plot(CDF <- pairorient(redwood, 0.05, 0.15, cumulative=TRUE))
plot(f <- deriv(CDF, spar=0.6, Dperiodic=TRUE))
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