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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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 Math Guy Posts: 20 Registered: 5/21/05
Re: Calculating the area of a closed 3-D path or ring
Posted: Mar 14, 2013 11:24 AM

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.

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