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Topic: Calculating the area of a closed 3-D path or ring
Replies: 23   Last Post: Mar 25, 2013 4:54 PM

 Messages: [ Previous | Next ]
 Ray Koopman Posts: 3,383 Registered: 12/7/04
Re: Calculating the area of a closed 3-D path or ring
Posted: Mar 17, 2013 5:12 PM

On Mar 16, 6:42 pm, Math Guy <M...@Guy.com> wrote:
> Math Guy wrote:
>> A closed loop (an irregular ring) is defined by a set of n points
>> in space.
>>
>> I am looking for a numerical-methods formula or algorythm to
>> calculate the "area" of such a ring...

>
> In case anyone's interested, here is some example data:
>
> http://www.fileden.com/files/2008/7/19/2010361/data.xls
>
> http://www.fileden.com/files/2008/7/19/2010361/data.txt
>
> They contain the same data - the txt file is just a tab-delimited
> ascii text dump of the data in the xls file.
>
> First column is time, the next 27 columns are the {x,y,z} sets
> for 9 marker coordinates.
>
> About 260 rows representing about 1.7 seconds worth of data.
>
> The markers are numbered in correct path-order from 1 to 9
> (and back to 1).

This set of data seems quite well conditioned. All the projections
into the best-fit planes give convex polygons, with their vertices
in the order given. The areas of the polygons range from 699 to 933.
A plot of the areas as a function of time makes it obvious that the
264 points cover 3 beats of the heart. This can also be seen if you
view the polygons successively, as a movie.

Date Subject Author
3/12/13 Math Guy
3/13/13 Ray Koopman
3/13/13 Nicolas Neuss
3/13/13 Peter Spellucci
3/13/13 Shmuel (Seymour J.) Metz
3/13/13 Frederick Williams
3/13/13 Brian Q. Hutchings
3/14/13 fom
3/14/13 fom
3/14/13 Math Guy
3/15/13 Ray Koopman
3/15/13 Math Guy
3/15/13 fom
3/16/13 Ray Koopman
3/16/13 fom
3/16/13 Math Guy
3/16/13 fom
3/16/13 Ray Koopman
3/15/13 Peter Spellucci
3/16/13 Math Guy
3/17/13 Ray Koopman
3/17/13 Math Guy
3/18/13 Ray Koopman
3/25/13 Gib Bogle