# convexify

##### Weil's Convexifying Operation

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"`

).

##### 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

```
# NOT RUN {
opa <- par(mfrow=c(1,2))
plot(letterR)
plot(convexify(letterR))
par(opa)
# }
```

*Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)*