# spokes: Spokes pattern of dummy points In spatstat.geom: Geometrical Functionality of the 'spatstat' Family

## Description

Generates a pattern of dummy points in a window, given a data point pattern. The dummy points lie on the radii of circles emanating from each data point.

## Usage

 `1` ``` spokes(x, y, nrad = 3, nper = 3, fctr = 1.5, Mdefault = 1) ```

## Arguments

 `x` Vector of x coordinates of data points, or a list with components `x` and `y`, or a point pattern (an object of class `ppp`). `y` Vector of y coordinates of data points. Ignored unless `x` is a vector. `nrad` Number of radii emanating from each data point. `nper` Number of dummy points per radius. `fctr` Scale factor. Length of largest spoke radius is `fctr * M` where `M` is the mean nearest neighbour distance for the data points. `Mdefault` Value of `M` to be used if `x` has length 1.

## Details

This function is useful in creating dummy points for quadrature schemes (see `quadscheme`).

Given the data points, the function creates a collection of `nrad * nper * length(x)` dummy points.

Around each data point `(x[i],y[i])` there are `nrad * nper` dummy points, lying on `nrad` radii emanating from `(x[i],y[i])`, with `nper` dummy points equally spaced along each radius.

The (equal) spacing of dummy points along each radius is controlled by the factor `fctr`. The distance from a data point to the furthest of its associated dummy points is `fctr * M` where `M` is the mean nearest neighbour distance for the data points.

If there is only one data point the nearest neighbour distance is infinite, so the value `Mdefault` will be used in place of `M`.

If `x` is a point pattern, then the value returned is also a point pattern, which is clipped to the window of `x`. Hence there may be fewer than `nrad * nper * length(x)` dummy points in the pattern returned.

## Value

If argument `x` is a point pattern, a point pattern with window equal to that of `x`. Otherwise a list with two components `x` and `y`. In either case the components `x` and `y` of the value are numeric vectors giving the coordinates of the dummy points.

## Author(s)

and \rolf

`quad.object`, `quadscheme`, `inside.owin`, `gridcentres`, `stratrand`
 ```1 2 3 4 5``` ``` dat <- runifrect(10) dum <- spokes(dat\$x, dat\$y, 5, 3, 0.7) plot(dum) Q <- quadscheme(dat, dum, method="dirichlet") plot(Q, tiles=TRUE) ```