Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 ]
 Ray Koopman Posts: 3,383 Registered: 12/7/04
Re: Calculating the area of a closed 3-D path or ring
Posted: Mar 15, 2013 12:11 AM

On Mar 14, 8:24 am, Math Guy <M...@Guy.com> wrote:
> 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.

That's exactly what I suggested :)

You haven't said whether the ordering of the points around the loop is
given or not. Also, what do you want to do if the loop is not convex?
(Even if the loop "ought" to be convex, it's a biological system and
won't always behave as it "should", and there may also be measurement
errors.)

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