[R] Concave hull

[(Ted Harding)]

Raising a rather general question here.

This is a tantalising discussion, but the notion of "concave hull"
strikes me as extremely ill-defined!

I'd like to see statement of what it is (generically) supposed to be.
The examples discussed so far seem to rely on a person's inner
feelings of what it is supposed to be.

Consider the following simple example (where I have drawn a "concave
hull" by hand, using sentimental criteria).

set.seed(54321)
X <- c(-1+rnorm(10),1+rnorm(10))
Y <- rnorm(20)
plot(X,Y,pch="+",col="blue",xlim=c(-4,4),ylim=c(-3,3))
for(i in (1:20)) text(X[i]+0.150,Y[i],i,cex=0.25)
## Find their convex hull:
ix0 <- chull(X,Y) ; n <- length(CH.ix0)
ix1 <- c(ix0,ix0[1]) # close it
lines(X[ix1],Y[ix1],col="green")
## Draw a "concave hull":
concix <- c(19,18,8,16,11,1,3,2,4,7,15,5,10,9,14,13,20,12,17,19)
lines(X[concix],Y[concix],col="red")


I have deliberately left the single point 6 "dangling", since
I am agonising over the choice between:

[A] Leaving it as it is, as in interior point, on the grounds
    that the resulting "concave hull" boundary is fairly smooth;

[B] Inserting it between c( ... ,2,4,7,6,15, ... ), which is
    the "least uncomfortable" of the two obvious possibilities;

[C] Inserting it between c( ... ,2,4,6,7,15, ... ), which is
    the "more uncomfortsable" of the two onvious possibilities.

Can someone provide counselling for me? I am hearing too many
voices about this!

Should I have tried to be less inclusive?

Ted.

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E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
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Date: 26-Nov-09                                       Time: 20:52:03
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