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Re: computing the area inside a contour plot

On Jun 1, 2005, at 6:03 AM, I. I. wrote:

> hi,
> I have a plot of data points on a set of x and y coordinate axes.   
> These data points form a contour (it sort of looks like a "blob" of  
> points).  I would like to compute the area inside this contour  
> using Mathematica.  Any help would be really appreciated.
> Thank you,
> I. I.

You can do this with a discrete version of Green's theorem, which in  
the continuous case says that

          area = 1/2 Integral of  x dy - y dx around the boundary

Here's an example of how this can be used to get an approximate area  
in the discrete case:

(*This computes points along the unit circle (note that the first and  
last points are the same). *)

         pts = Table[{Cos[t], Sin[t]}, {t, 0., 2*Pi, Pi/100}];

(*Now transpose to get separate lists of x and y coordinates.*)

         transpts = Transpose[pts];

(*Compute differences to obtain "dx" and "dy" values.*)

        diffs = ListCorrelate[{1,-1},#1]& /@ transpts ;

(*Compute sums as dot products.*)

       .5*( Rest[Last[transpts]].First[diffs] - Rest[First 

(* This gives 3.14108, a decent approximation of Pi. *)

Selwyn Hollis

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