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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

 Messages: [ Previous | Next ]
 Peter Spellucci Posts: 221 Registered: 11/9/09
Re: Calculating the area of a closed 3-D path or ring
Posted: Mar 15, 2013 12:57 PM

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:
in the section ''least squares'' there is the svd solution to compute the plane.
hth
peter

Date Subject Author
3/12/13 Math Guy
3/13/13 Ray Koopman
3/13/13 Narasimham
3/14/13 Narasimham
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