
Re: Calculating the area of a closed 3D 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 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. > > 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 hysteresislike pattern. Plotting the difference between the two areas against the smallest singular value of the centered 3D coordinates shows a similar pattern.

