Math Guy <Math@Guy.com> writes: >Math Guy wrote: > >> A closed loop (an irregular ring) is defined by a set of n points >> in space. >> >> The way I see it, there are two ways to understand the concept of >> the area of this ring... > >Thanks for all the responses. > >The points are markers on the mitral valve annulus of research subjects. > >The desired area is thus the aperture or opening of the valve. > >We will probably go with calculating a centroid and then summing the >areas of the triangles formed from the centroid to the perimeter >markers. > >The more "elegant" method (I would think, given the objective) would be >to project this opening to a flat plane, and then measure the area of >the projection. One way to imagine this plane is the "plane of best >fit" from the given points (a plane where the sum of the squared >differences of the distances from each point to the plane is minimized). > >Once the plane is known, the points are translated to the coordinate >system of the plane, their Z coordinates are ignored or dropped, and >this becomes a 2-dimensional area calculation.
use something like odrpack from netlib (or in this simple case, the svd ) compute the plane of least sum of orthogonal distances squared , project your points to this plane, compute the centroid, construct the triangles (in the plane now) and you get a lower bound for the surface in question with such a small number of points you might use this here: http://numawww.mathematik.tu-darmstadt.de in the section ''least squares'' there is the svd solution to compute the plane. hth peter