Re: computing the area inside a contour plot

*To*: mathgroup at smc.vnet.net*Subject*: [mg57622] Re: [mg57580] computing the area inside a contour plot*From*: Selwyn Hollis <sh2.7183 at earthlink.net>*Date*: Thu, 2 Jun 2005 05:17:00 -0400 (EDT)*References*: <200506011003.GAA24462@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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 [transpts]].Last[diffs]) (* This gives 3.14108, a decent approximation of Pi. *) -------------- Selwyn Hollis http://www.appliedsymbols.com

**References**:**computing the area inside a contour plot***From:*"I. I." <ibrahiim@email.uc.edu>