
Re: Calculating the area of a closed 3D 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 numericalmethods 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 tabdelimited > 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 pathorder from 1 to 9 > (and back to 1).
This set of data seems quite well conditioned. All the projections into the bestfit 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.

