# convexify

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##### Weil's Convexifying Operation

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

Keywords
utilities, spatial
##### 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.

convexhull for the convex hull of a window.

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

Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)

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