# nnorient

0th

Percentile

##### Nearest Neighbour Orientation Distribution

Computes the distribution of the orientation of the vectors from each point to its nearest neighbour.

Keywords
spatial, nonparametric
##### Usage
nnorient(X, ..., cumulative = FALSE, correction, k = 1,
domain = NULL, ratio = FALSE)
##### Arguments
X
Point pattern (object of class "ppp").
...
Arguments passed to circdensity to control the kernel smoothing, if cumulative=FALSE.
cumulative
Logical value specifying whether to estimate the probability density (cumulative=FALSE, the default) or the cumulative distribution function (cumulative=TRUE).
correction
Character vector specifying edge correction or corrections. Options are "none", "bord.modif", "good" and "best".
k
Integer. The $k$th nearest neighbour will be used.
ratio
Logical. If TRUE, the numerator and denominator of each edge-corrected estimate will also be saved, for use in analysing replicated point patterns.
unit
Unit in which the angles should be expressed. Either "degree" or "radian".
domain
Optional window. The first point $x_i$ of each pair of points will be constrained to lie in domain.
##### Details

This algorithm considers each point in the pattern X and finds its nearest neighbour (or $k$th nearest neighour). The direction of the arrow joining the data point to its neighbour 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 angles is calculated using circdensity. This is the function $\vartheta(\phi)$ defined in Illian et al (2008), equation (4.5.3), page 253.

If cumulative=TRUE, then the cumulative distribution function of these angles is calculated.

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.

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.

##### Value

• 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").

##### References

Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008) Statistical Analysis and Modelling of Spatial Point Patterns. Wiley.

pairorient
rose(nnorient(redwood, adjust=0.6), col="grey")
plot(CDF <- nnorient(redwood, cumulative=TRUE))