R: Weil's Convexifying Operation

convexify {spatstat} | R Documentation

## Weil's Convexifying Operation

### Description

Converts the window `W` into a convex set by rearranging the edges, preserving spatial orientation of each edge.

### Usage

     convexify(W, eps)

### Arguments

`W` | A window (object of class `"owin"`).
`eps` | Optional. Minimum edge length of polygonal approximation, if `W` is not a polygon.

### Details

Weil (1995) defined a convexification operation for windows W that belong to the convex ring (that is, for any W which is a finite union of convex sets). Note that this is not the same as the convex hull.

The convexified set f(W) has the same total boundary length as W and the same distribution of orientations of the boundary. If W is a polygonal set, then the convexification f(W) is obtained by rearranging all the edges of W in order of their spatial orientation.

The argument `W` must be a window. If it is not already a polygonal window, it is first converted to one, using `simplify.owin`. The edges are sorted in increasing order of angular orientation and reassembled into a convex polygon.

### Value

A window (object of class `"owin"`).

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk

### References

Weil, W. (1995) The estimation of mean particle shape and mean particle number in overlapping particle systems in the plane. Advances in Applied Probability 27, 102–119.

### See Also

`convexhull` for the convex hull of a window.

### Examples

      opa <- par(mfrow=c(1,2))
      plot(letterR)
      plot(convexify(letterR))
      par(opa)

[Package spatstat version 1.63-3 Index]