tilePerim {deldir}

Calculate tile perimeters.

Description

Calculates the perimeters of all of the Dirichlet (Voronoi) tiles in a tessellation of a set of planar points. Also calculates the sum and the mean of these perimeters.

Usage

tilePerim(object,inclbdry=TRUE)

Arguments

object

An object of class tile.list (as produced by tile.list() specifying the Dirichlet (Voronoi) tiles in a tessellation of a set of planar points.

inclbdry

Logical scalar. Should boundary segments (edges of tiles at least one of whose endpoints lies on the enclosing rectangle rw (see deldir()) be included in the perimeter?

Value

A list with components

perimeters

A vector consisting of the values of the perimeters of the Dirichlet tiles in the tessellation.

totalPerim

The sum of perimeters.

meanPerim

The mean of perimeters.

perComps

A list whose entries are vectors consisting of the “components” of the perimeters of each tile. If/when the tiles are clipped, some tiles may be subdivided by the clipping into discontiguous parts. The components referred to above are the perimeters of this parts. If no subdivision has occurred then the vector in question has a single entry equal to the perimeter of the corresponding tile. If subdivision has occurred then the perimeter of the tile is the sum of the perimeters of the components.

Note

Function added at the request of Haozhe Zhang.

Author(s)

Rolf Turner [e-mail]

See Also

tile.list(), plot.tile.list()

Examples

    x <- runif(20)
    y <- runif(20)
    z <- deldir(x,y,rw=c(0,1,0,1))
    w <- tile.list(z)
    p1 <- tilePerim(w)
    p0 <- tilePerim(w,inclbdry=FALSE)
    p1$totalPerim - p0$totalPerim # Get 4 = the perimeter of rw.
    ss <- apply(as.matrix(z$dirsgs[,1:4]),1,
                function(x){(x[1]-x[3])^2 + (x[2]-x[4])^2})
    2*sum(sqrt(ss)) - p0$totalPerim # Get 0; in tilePerim() each interior
                                    # edge is counted twice.
    if(require(polyclip)) {
        CP <- list(x=c(0.49,0.35,0.15,0.20,0.35,0.42,
                       0.43,0.62,0.46,0.63,0.82,0.79),
                   y=c(0.78,0.86,0.79,0.54,0.58,0.70,
                       0.51,0.46,0.31,0.20,0.37,0.54))
        wc <- tile.list(z,clipp=CP)
        p2 <- tilePerim(wc) # Doesn't matter here if inclbdry is TRUE or FALSE.
        p2$perComps[["pt.6"]] # The tile for point 6 has got subdivided into
                              # two parts, a tetrahedron and a triangle.
        cul <- rainbow(10)[c(1,7,3:6,2,8:10)] # Rearranging colours to improve
                                              # the contrast between contiguous tiles.
        plot(wc,labelPts=TRUE,fillcol=cul)
    }