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

```
nnorient(X, ..., cumulative = FALSE, correction, k = 1,
unit = c("degree", "radian"),
domain = NULL, ratio = FALSE)
```

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"`

).

- 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"`

. Alternatively`correction="all"`

selects all options.- 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`

.

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk

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`

.

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))
```

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