convexmetric: Distance Metric Defined by Convex Set

Description

Create the distance metric associated with a given convex polygon.

Usage

convexmetric(K)

Arguments

Convex set defining the metric. A polygon that is symmetric about the origin. See Details.

Value

An object of class "metric".

Details

This function creates the distance metric associated with the convex set K so that the unit ball of the metric is equal to K. It returns an object of class "metric" representing the metric (see metric.object).

The argument K must be a window (class "owin"). It will be converted to a polygon. It must be convex, and symmetric about the origin.

To perform distance calculations (for example, nearest-neighbour distances) using this metric instead of the Euclidean metric, first check whether the standard function for this purpose (for example nndist.ppp) has an argument named metric. If so, use the standard function and add the argument metric; if not, use the low-level function invoke.metric.

To see which operations are currently supported by the metric, use summary, as shown in the examples.

Examples

Run this code

# NOT RUN {
  K <- owin(poly=list(x=c(2.5,2,0.5,-2.5,-2,-0.5),y=c(0,1,2,0,-1,-2)))
  plot(K)
  points(0,0)
  m <- convexmetric(K)
  m
  summary(m)

  ## show redwood data and identify point number 43
  plot(redwood, main="")
  plot(redwood[43], pch=16, add=TRUE)

  ## compute nearest neighbour distances and identifiers
  ##   using the distance metric m
  nd <- nndist(redwood, metric=m)
  nw <- nnwhich(redwood, metric=m)

  ## Nearest neighbour distance for point number 43 is nd[43]; verify
  B43 <- disc(radius=nd[43], centre=redwood[43], metric=m)
  plot(B43, add=TRUE)

  ## nearest neighbour for point number 43 is point number nw[43]; verify
  plot(redwood[nw[43]], pch=3, col="red", add=TRUE)
# }