# rshift.ppp

##### Randomly Shift a Point Pattern

Randomly shifts the points of a point pattern.

##### Usage

```
## S3 method for class 'ppp':
rshift(X, \dots, which=NULL, group)
```

##### Arguments

- X
- Point pattern to be subjected to a random shift.
An object of class
`"ppp"`

- ...
- Arguments that determine the random shift. See Details.
- group
- Optional. Factor specifying a grouping of the points of
`X`

, or`NULL`

indicating that all points belong to the same group. Each group will be shifted together, and separately from other groups. By default, points in - which
- Optional. Identifies which groups of the pattern will be shifted,
while other groups are not shifted. A vector of levels of
`group`

.

##### Details

This operation randomly shifts the locations of the points in a point pattern.

The function `rshift`

is generic. This function `rshift.ppp`

is the method for point patterns.

The most common use of this function is to shift the points in a multitype point pattern. By default, points of the same type are shifted in parallel (i.e. points of a common type are shifted by a common displacement vector), and independently of other types. This is useful for testing the hypothesis of independence of types (the null hypothesis that the sub-patterns of points of each type are independent point processes).

In general the points of `X`

are divided into groups,
then the points within a group are shifted by a common
random displacement vector. Different groups of points are shifted
independently. The grouping is determined as follows:

- If the argument
`group`

is present, then this determines the grouping. - Otherwise, if
`X`

is a multitype point pattern, the marks determine the grouping. - Otherwise, all points belong to a single group.

`group`

should be a factor, of length equal to the
number of points in `X`

. Alternatively `group`

may be `NULL`

,
which specifies that all points of `X`

belong to a single group. By default, every group of points will be shifted.
The argument `which`

indicates that only some of the groups
should be shifted, while other groups should be left unchanged.
`which`

must be a vector of levels of `group`

(for example, a vector of types in a multitype pattern)
indicating which groups are to be shifted.

The displacement vector, i.e. the vector
by which the data points are shifted,
is generated at random.
Parameters that control the randomisation
and the handling of edge effects are passed through
the `...`

argument. They are
[object Object],[object Object],[object Object]
If the window is a rectangle, the *default* behaviour is
to generate a displacement vector at random with equal probability
for all possible displacements. This means that the $x$ and
$y$ coordinates of the displacement vector are independent random
variables, uniformly distributed over the range of possible coordinates.

Alternatively, the displacement vector can be generated by
another random mechanism, controlled by the arguments
`radius`

, `width`

and `height`

.
[object Object],[object Object]

The argument `edge`

controls what happens when
a shifted point lies outside the window of `X`

.
Options are:
[object Object],[object Object],[object Object]
The optional argument `clip`

specifies a smaller window
to which the pattern should be restricted.

##### Value

- A point pattern (object of class
`"ppp"`

).

##### See Also

##### Examples

```
data(amacrine)
# random toroidal shift
# shift "on" and "off" points separately
X <- rshift(amacrine)
# shift "on" points and leave "off" points fixed
X <- rshift(amacrine, which="on")
# shift all points simultaneously
X <- rshift(amacrine, group=NULL)
# maximum displacement distance 0.1 units
X <- rshift(amacrine, radius=0.1)
# shift with erosion
X <- rshift(amacrine, radius=0.1, edge="erode")
```

*Documentation reproduced from package spatstat, version 1.10-3, License: GPL version 2 or newer*