Weil's Convexifying Operation
Converts the window W into a convex set by rearranging
the edges, preserving spatial orientation of each edge.
convexify(W, eps)
W |
A window (object of class |
eps |
Optional. Minimum edge length of polygonal approximation,
if |
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.
A window (object of class "owin").
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
Rolf Turner r.turner@auckland.ac.nz
and Ege Rubak rubak@math.aau.dk
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.
opa <- par(mfrow=c(1,2)) plot(letterR) plot(convexify(letterR)) par(opa)
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