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Area of inside contour of continuous function?

• To: mathgroup at smc.vnet.net
• Subject: [mg84229] Area of inside contour of continuous function?
• From: Gareth Russell <russell at njit.edu>
• Date: Fri, 14 Dec 2007 14:57:42 -0500 (EST)

Hi Group,

I have a two-parameter smooth continuous function f[x_,y_] that is 
unimodal (it's a log-likeihood function), and I know maxf, the height 
of the peak. I would like to calculate the area inside a contour that 
is a given number of units u below the peak. What is the easiest way to 
do this?

My own idea is to construct a separate function with discontinuities 
along the lines of

g[x_,y_]:=If[f[x,y]>(maxf-u),1,0]

And do numerical integration over a region big enough to contain the 
contour (which of course, I can see from a ContourPlot).

But am I missing something much easier? Searching the mathgroup 
archives I came across how to find the area of a discrete polygon, so I 
realize that another method would be to extract the contour data from 
the ContourPlot object and apply that, but it seems like a bit of hack!

Thanks,

Gareth

-- 
Gareth Russell
NJIT