Creates an object of class `"tess"`

representing a tessellation
of a spatial region.

```
tess(..., xgrid = NULL, ygrid = NULL, tiles = NULL, image = NULL,
window=NULL, marks=NULL, keepempty=FALSE, unitname=NULL, check=TRUE)
```

An object of class `"tess"`

representing the tessellation.

- ...
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 (object of class

`"im"`

) 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"`

.- marks
Optional vector or data frame of marks associated with the tiles.

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

- unitname
Optional. Name of unit of length. Either a single character string, or a vector of two character strings giving the singular and plural forms, respectively. If this argument is missing or

`NULL`

, information about the unitname will be extracted from the other arguments. If this argument is given, it overrides any other information about the unitname.- check
Logical value indicating whether to check the validity of the input data. It is strongly recommended to use the default value

`check=TRUE`

.

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk.

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:

- rectangular:
tiles are rectangles, with sides parallel to the

`x`

and`y`

axes. They may or may not have equal size and shape. The arguments`xgrid`

and`ygrid`

determine the positions of the vertical and horizontal grid lines, respectively. (See`quadrats`

for another way to do this.)- tile list:
tiles are arbitrary spatial regions. The argument

`tiles`

is a list of these tiles, which are objects of class`"owin"`

.- pixel image:
Tiles are subsets of a fine grid of pixels. The argument

`image`

is a pixel image (object of class`"im"`

) with factor values. Each level of the factor represents a different tile of the tessellation. The pixels that have a particular value of the factor constitute a tile.

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, `tilenames`

to extract the names
of the tiles, and `tile.areas`

to compute their
areas.

The tiles may have marks, which can be extracted by
`marks.tess`

and changed by `marks<-.tess`

.

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

, `cut.ppp`

and
`by.ppp`

.

To construct particular tessellations, see
`quadrats`

, `hextess`

,
`dirichlet`

, `delaunay`

,
`venn.tess`

,
`polartess`

,
`quantess`

,
`bufftess`

and `rpoislinetess`

.

`marks.tess`

,
`plot.tess`

,
`[.tess`

,
`as.tess`

,
`tiles`

,
`intersect.tess`

,
`split.ppp`

,
`cut.ppp`

,
`by.ppp`

,
`bdist.tiles`

,
`tile.areas`

,
`as.function.tess`

.

To construct particular tessellations, see
`quadrats`

, `hextess`

,
`venn.tess`

,
`polartess`

,
`dirichlet`

, `delaunay`

, `quantess`

and `rpoislinetess`

.

To divide space into pieces containing equal
amounts of stuff, use `quantess`

.

To convert a tessellation to a function, for use as a spatial covariate
(associating a numerical value with each tile of the tessellation) use
`as.function.tess`

.

```
A <- tess(xgrid=0:4,ygrid=0:4)
A
plot(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)
plot(E)
G <- tess(image=v, marks=toupper(levels(v)), unitname="km")
G
```

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