# tileArea: Area of a Dirichlet tile. In deldir: Delaunay Triangulation and Dirichlet (Voronoi) Tessellation

## Description

Calculates the area of a Dirichlet tile, applying a discrete version of Stoke's theorem.

## Usage

 `1` ```tileArea(x, y, rw) ```

## Arguments

 `x` The `x`-coordinates of the vertices of the tile, in anticlockwise direction. The last coordinate should not repeat the first. `y` The `y`-coordinates of the vertices of the tile, in anticlockwise direction. The last coordinate should not repeat the first. `rw` A vector of length 4 specifying the rectangular window in which the relevant tessellation was construced. See `deldir()` for more detail. Actually this can be any rectangle containing the tile in question.

## Details

The heavy lifting is done by the Fortran subroutine `stoke()` which is called by the `.Fortran()` function.

## Value

A positive scalar.

## Author(s)

Rolf Turner r.turner@auckland.ac.nz

## See Also

`deldir()` `tilePerim()`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```set.seed(42) x <- runif(20) y <- runif(20) z <- deldir(x,y,rw=c(0,1,0,1)) w <- tile.list(z) with(w[[1]],tileArea(x,y,rw=z\$rw)) sapply(w,function(x,rw){tileArea(x\$x,x\$y,attr(w,"rw"))}) x <- c(0.613102,0.429294,0.386023,0.271880,0.387249,0.455900,0.486101) y <- c(0.531978,0.609665,0.597780,0.421738,0.270596,0.262953,0.271532) # The vertices of the Dirichlet tile for point 6. tileArea(x,y,rw=c(0,1,0,1)) tileArea(x,y,rw=c(-1,2,-3,4)) # Same as above. ```

deldir documentation built on Feb. 17, 2021, 1:08 a.m.