deldir (version 0.2-9)

tileArea: Area of a Dirichlet tile.

Description

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

Usage

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.

Value

A positive scalar.

Details

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

See Also

deldir() tilePerim()

Examples

# NOT RUN {
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.
# }