# periodify

##### Make Periodic Copies of a Spatial Pattern

Given a spatial pattern (point pattern, line segment pattern, window, etc) make shifted copies of the pattern and optionally combine them to make a periodic pattern.

##### Usage

```
periodify(X, ...)
## S3 method for class 'ppp':
periodify(X, nx = 1, ny = 1, ...,
combine=TRUE, warn=TRUE, check=TRUE,
ix=(-nx):nx, iy=(-ny):ny,
ixy=expand.grid(ix=ix,iy=iy))
## S3 method for class 'psp':
periodify(X, nx = 1, ny = 1, ...,
combine=TRUE, warn=TRUE, check=TRUE,
ix=(-nx):nx, iy=(-ny):ny,
ixy=expand.grid(ix=ix,iy=iy))
## S3 method for class 'owin':
periodify(X, nx = 1, ny = 1, ...,
combine=TRUE, warn=TRUE,
ix=(-nx):nx, iy=(-ny):ny,
ixy=expand.grid(ix=ix,iy=iy))
```

##### Arguments

- X
- An object representing a spatial pattern (point pattern, line segment pattern or window).
- nx,ny
- Integers.
Numbers of additional copies of
`X`

in each direction. The result will be a grid of`2 * nx + 1`

by`2 * ny + 1`

copies of the original object. (Overruled by`ix, iy, ixy`

). - ...
- Ignored.
- combine
- Logical flag determining whether the copies should be superimposed
to make an object like
`X`

(if`combine=TRUE`

) or simply returned as a list of objects (`combine=FALSE`

). - warn
- Logical flag determining whether to issue warnings.
- check
- Logical flag determining whether to check the validity of the combined pattern.
- ix, iy
- Integer vectors determining the grid positions of the copies
of
`X`

. (Overruled by`ixy`

). - ixy
- Matrix or data frame with two columns, giving the
grid positions of the copies of
`X`

.

##### Details

Given a spatial pattern (point pattern, line segment pattern, etc)
this function makes a number of shifted copies of the pattern
and optionally combines them. The function `periodify`

is
generic, with methods for various kinds of spatial objects.

The default is to make a 3 by 3 array of copies of `X`

and
combine them into a single pattern of the same kind as `X`

.
This can be used (for example) to compute toroidal or periodic
edge corrections for various operations on `X`

.

If the arguments `nx`

, `ny`

are given
and other arguments are missing,
the original object will be copied `nx`

times to the right
and `nx`

times to the left, then `ny`

times upward and
`ny`

times downward, making `(2 * nx + 1) * (2 * ny + 1)`

copies altogether, arranged in a grid, centred on the original object.
If the arguments `ix`

, `iy`

or `ixy`

are specified,
then these determine the grid positions of the copies of `X`

that will be made. For example `(ix,iy) = (1, 2)`

means a
copy of `X`

shifted by the vector `(ix * w, iy * h)`

where
`w,h`

are the width and height of the bounding rectangle of `X`

.

If `combine=TRUE`

(the default) the copies of `X`

are
superimposed to create an object of the same kind as `X`

.
If `combine=FALSE`

the copies of `X`

are returned as a list.

##### Value

- If
`combine=TRUE`

, an object of the same class as`X`

. If`combine=FALSE`

, a list of objects of the same class as`X`

.

##### See Also

##### Examples

```
data(cells)
plot(periodify(cells))
a <- lapply(periodify(cells$window, combine=FALSE),
plot, add=TRUE,lty=2)
```

*Documentation reproduced from package spatstat, version 1.34-1, License: GPL (>= 2)*