> 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.