##### Voronoi mosaic

This function creates a Voronoi mosaic out of a given set of arbitraryly located points in the plane. Each cell of a voronoi mosaic is associated with a data point and contains all points \((x,y)\) closest to this data point.

- Keywords
- spatial

##### Usage

`voronoi.mosaic(x, y = NULL, duplicate = "error")`

##### Arguments

- x
vector containing \(x\) coordinates of the data. If

`y`

is missing`x`

should be a list or dataframe with two components`x`

and`y`

.`x`

can also be an object of class`triSht`

generated by`tri.mesh`

. In this case the internal triangulation step can be skipped.- y
vector containing \(y\) coordinates of the data. Can be omitted if

`x`

is a list with two components`x`

and`y`

.- duplicate
flag indicating how to handle duplicate elements. Possible values are:

`"error"`

-- default,`"strip"`

-- remove all duplicate points,`"remove"`

-- leave one point of the duplicate points.

##### Details

The function creates first a Delaunay triangulation (if not already given), extracts the circumcircle centers of these triangles, and then connects these points according to the neighbourhood relations between the triangles.

##### Value

An object of class `voronoi`

.

##### Note

This function is meant as a replacement for
`voronoi.mosaic`

from package `tripack`

.
Please note that the underlying triangulation uses a
different algorithm, see `tri.mesh`

. Contrary to
`tri.mesh`

this should not affect the result for non
unique triangulations e.g. on regular grids as the voronoi mosaic in
this case will still be unique.

The arguments are backward compatible, even the returned object should be
compatible with functions from package `tripack`

.

##### References

G. Voronoi, Nouvelles applications des parametres continus a la theorie des formes quadratiques. Deuxieme memoire. Recherches sur les parallelloedres primitifs, Journal fuer die reine und angewandte Mathematik, 1908, vol 134, p. 198-287

##### See Also

##### Examples

```
# NOT RUN {
data(franke)
fd <- franke$ds3
vr <- voronoi.mosaic(fd$x, fd$y)
summary(vr)
# }
```

*Documentation reproduced from package interp, version 1.0-33, License: GPL (>= 2)*