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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 ]
 fom Posts: 1,968 Registered: 12/4/12
Re: Calculating the area of a closed 3-D path or ring
Posted: Mar 16, 2013 1:30 PM

On 3/16/2013 10:33 AM, Math Guy wrote:
> fom used improper usenet message composition style by unnecessarily
> full-quoting:
>

>> When I had been trying to visualize the stated problem,
>> I assumed that a "ring" would be a convex star.

>
> I clearly stated in the first post that the ring resembled the perimeter
> of a horse saddle, or a potato chip.
>
> How does either of those resemble a star?
>

The sense of a star in this case is the
idea that there is some point in the
region which can form a line segment with
any given point of the region different
from itself such that every point of that
line segment is a point of the region.

Of course, with curved differentiable
surfaces, one would have to interpret
the sense of my statement in terms of
geodesics.

numerical methods and suggested that
the data available would be some finite
number of points on the boundary.

Assuming a Euclidean interpretation of
coordinates, the closest approximation
to a ring you could have is a polygonal
line closing upon itself. Hence corners.

Given the barycenter and triangular
regions formed with each consecutive
pair of points on the boundary, every
point of the region different from the
barycenter forms a line segment in the
surface.

Sadly, my choice of words is often not
as precise as I would like. But, it
can usually be reasonably clarified.
I hope I have done so.

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