Hi,
To be honest, what you mean by "a (linear) lower envelope" becomes less
and less clear to me. Take any cloud of 2-d points. The convex hull
consists of a number of these points - or alternatively, of a number of
line segments between successive ones of these points. Thus, every one
of these segments defined by a pair of points on the bottom half of the
convex hull would, if prolonged to infinity, define a line with all your
points in the half-space above the line, which sounds a lot like what
you seem to look for - in which case, "the" lower envelope would not be
well-defined.
Or does your cloud of points have two points A and B such that all
points are to the right of A and to the left of B and above the line AB?
In this case, you could call the segment AB "the lower envelope" in your
sense, but finding such A and B (if they exist) is trivial: look for the
leftmost point, if there are multiple ones of these, take the bottom
one, that's A, and the same for B.
Life would be easier for us if you provided a small reproducible example
and told us what you expect the result to be.
HTH
Stephan
Asha Sharma schrieb:
Hi,
Thanks to both of you for taking the time to answer my question. I was
maybe not very clear in the way I framed my question. By plot, I meant
an x-y plot with a cloud of points which should have a linear lower
envelope. Is there a way to both plot as well as get the parameters of
the lower envelope (intercept, slope, etc.) and to also set the
percentage of points outside it?
Thanks!
Asha
Stephan Kolassa wrote:
Hi,
one possibility would be to calculate the convex hull using chull(). I
believe that the hull points are returned by chull() in a clockwise
order (?), so the points between the rightmost and the leftmost point
in the chull() result are the lower half of the convex hull. Remove
these points from the original dataset (a variant of "peeling convex
hulls") and iterate until you have removed your prespecified
percentage of points - these all lie outside of the final lower hull
(though the percentage will, of course, only be approximated, but you
should be able to modify this to taste).
HTH
Stephan
David Winsemius schrieb:
On Jun 30, 2010, at 2:05 PM, Asha Sharma wrote:
Hi,
I am looking for a way to find the lower envelope of points on a
plot, preferably specifying what percentage of points should be
allowed to lie outside the envelope. There must be a straightforward
way to do this, but I do not seem to be able to find it. I would
greatly appreciate any help.
You probably want something like the "lower half" of the convex hull.
You should find quite a bit of code with your favorite r search
engine on the topic of "convex hull".
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