# spokes

##### Spokes pattern of dummy points

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

`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.

##### See Also

`quad.object`

,
`quadscheme`

,
`inside.owin`

,
`gridcentres`

,
`stratrand`

##### Examples

```
dat <- runifrect(10)
plot(dat)
dum <- spokes(dat$x, dat$y)
points(dum$x, dum$y, pch=".")
Q <- quadscheme(dat, dum)
```

*Documentation reproduced from package spatstat, version 1.9-3, License: GPL version 2 or newer*