[R] determine upper convex hull, 2-dimensional case
Richard and Barbara Males
rbmales at gmail.com
Mon Mar 22 22:35:22 CET 2010
For an environmental planning example that involves looking at the
relative efficiencies of one plan over another, I need to determine
the pareto-efficient plans (which I have done), and then, within that
set of plans, determine the convex hull representing the outer upper
boundary of those points. I have a dataframe, dfPlans, as follows,
representing the pareto-efficient cost and benefit of different
environmental restoration plans out of a larger set of plans, where
A1, EC, A6, and A4 are identifiers for the plans.
Cost Benefit
A1 0.00 0.000
EC 0.00 7821.689
A6 76783.19 16094.142
A4 78703.73 22245.760
I am interesting in determining what I believe is called the upper
convex hull, i.e. the upper outer boundary if I plot benefit on the y
axis, cost on the x axis. This should be plans A1, EC, and A4, and
not point A6. I have used chull, which returns all of the points,
including A6, and have tried to use convhulln with the QU option, but
I am unclear as to how to interpret the results, which are returned as
follows:
> chull(dfPlans)
[1] 1 2 3 4
> convhulln(dfPlans,option="QU")
[,1] [,2]
[1,] 3 2
[2,] 3 4
[3,] 1 2
[4,] 1 4
Any assistance greatly appreciated, any way to accomplish my goal
(need not use convhulln or chull).
Thanks in advance.
--
Richard M. Males
Cincinnati, OH USA
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