# 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

```
# NOT RUN {
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)
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*