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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

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 Ray Koopman Posts: 3,383 Registered: 12/7/04
Re: Calculating the area of a closed 3-D path or ring
Posted: Mar 18, 2013 1:09 AM

On Mar 17, 4:33 pm, Math Guy <M...@Guy.com> wrote:
> Ray Koopman wrote:
>> 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.

>
> How do the polygon area plots compare with the more simple area
> method (sum of triangles using computed centroid) ?

As predicted, the sum of the triangle areas is always greater than
the polygon area, but plots of the areas as functions of time are very
similar. Plotting one area against the other shows a hysteresis-like
pattern. Plotting the difference between the two areas against the
smallest singular value of the centered 3D coordinates shows a similar
pattern.

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