[Date Index]
[Thread Index]
[Author Index]
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
Prev by Date:
**Re: mml files**
Next by Date:
**Re: Re: Limit of list**
Previous by thread:
**computing the area inside a contour plot**
Next by thread:
**Re: computing the area inside a contour plot**
| |