# tess

##### Create a Tessellation

Creates an object of class `"tess"`

representing a tessellation
of a spatial region.

##### Usage

```
tess(..., xgrid = NULL, ygrid = NULL, tiles = NULL, image = NULL,
window=NULL, keepempty=FALSE)
```

##### Arguments

- ...
- Ignored.
- xgrid,ygrid
- Cartesian coordinates of vertical and horizontal lines determining a grid of rectangles. Incompatible with other arguments.
- tiles
- List of tiles in the tessellation.
A list, each of whose elements is a window
(object of class
`"owin"`

). Incompatible with other arguments. - image
- Pixel image which specifies the tessellation. Incompatible with other arguments.
- window
- Optional.
The spatial region which is tessellated (i.e. the union of all the tiles).
An object of class
`"owin"`

. - keepempty
- Logical flag indicating whether empty tiles should be retained or deleted.

##### Details

A tessellation is a collection of disjoint spatial regions
(called *tiles*) that fit together to form a larger spatial
region. This command creates an object of class `"tess"`

that
represents a tessellation.

Three types of tessellation are supported: [object Object],[object Object],[object Object]

The optional argument `window`

specifies the spatial region
formed by the union of all the tiles. In other words it specifies the
spatial region that is divided into tiles by the tessellation.
If this argument is missing or `NULL`

, it will be determined by
computing the set union of all the tiles. This is a time-consuming
computation. For efficiency it is advisable to specify the window.
Note that the validity of the window will not be checked.

Empty tiles may occur, either because one of the entries in the list
`tiles`

is an empty window, or because one of the levels of the
factor-valued pixel image `image`

does not occur in the pixel data.
When `keepempty=TRUE`

, empty tiles are permitted.
When `keepempty=FALSE`

(the default), tiles are not allowed to be
empty, and any empty tiles will be removed from the tessellation.

There are methods for `print`

, `plot`

, `[`

and `[<-`

for tessellations. Use `tiles`

to extract the list of
tiles in a tessellation, or `tile.areas`

to compute their
areas.

Tessellations can be used to classify the points of
a point pattern, in `split.ppp`

, `cut.ppp`

and
`by.ppp`

.

##### Value

- An object of class
`"tess"`

representing the tessellation.

##### See Also

`plot.tess`

,
`[.tess`

,
`as.tess`

,
`tiles`

,
`intersect.tess`

,
`split.ppp`

,
`cut.ppp`

,
`by.ppp`

,
`quadrats`

,
`bdist.tiles`

,
`tile.areas`

.

##### Examples

```
A <- tess(xgrid=0:4,ygrid=0:4)
A
B <- A[c(1, 2, 5, 7, 9)]
B
v <- as.im(function(x,y){factor(round(5 * (x^2 + y^2)))}, W=owin())
levels(v) <- letters[seq(length(levels(v)))]
E <- tess(image=v)
E
```

*Documentation reproduced from package spatstat, version 1.31-3, License: GPL (>= 2)*