Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


Math Forum » Discussions » sci.math.* » sci.math.num-analysis.independent

Topic: Calculating the area of a closed 3-D path or ring
Replies: 23   Last Post: Mar 25, 2013 4:54 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

As for your description, you asked for
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
Read Calculating the area of a closed 3-D path or ring
Math Guy
3/13/13
Read Re: Calculating the area of a closed 3-D path or ring
Ray Koopman
3/13/13
Read Re: Calculating the area of a closed 3-D path or ring
Nicolas Neuss
3/13/13
Read Re: Calculating the area of a closed 3-D path or ring
Peter Spellucci
3/13/13
Read Re: Calculating the area of a closed 3-D path or ring
Shmuel (Seymour J.) Metz
3/13/13
Read Re: Calculating the area of a closed 3-D path or ring
Frederick Williams
3/13/13
Read Re: Calculating the area of a closed 3-D path or ring
Brian Q. Hutchings
3/14/13
Read Re: Calculating the area of a closed 3-D path or ring
fom
3/14/13
Read Re: Calculating the area of a closed 3-D path or ring
fom
3/14/13
Read Re: Calculating the area of a closed 3-D path or ring
Math Guy
3/15/13
Read Re: Calculating the area of a closed 3-D path or ring
Ray Koopman
3/15/13
Read Re: Calculating the area of a closed 3-D path or ring
Math Guy
3/15/13
Read Re: Calculating the area of a closed 3-D path or ring
fom
3/16/13
Read Re: Calculating the area of a closed 3-D path or ring
Ray Koopman
3/16/13
Read Re: Calculating the area of a closed 3-D path or ring
fom
3/16/13
Read Re: Calculating the area of a closed 3-D path or ring
Math Guy
3/16/13
Read Re: Calculating the area of a closed 3-D path or ring
fom
3/16/13
Read Re: Calculating the area of a closed 3-D path or ring
Ray Koopman
3/15/13
Read Re: Calculating the area of a closed 3-D path or ring
Peter Spellucci
3/16/13
Read Re: Calculating the area of a closed 3-D path or ring
Math Guy
3/17/13
Read Re: Calculating the area of a closed 3-D path or ring
Ray Koopman
3/17/13
Read Re: Calculating the area of a closed 3-D path or ring
Math Guy
3/18/13
Read Re: Calculating the area of a closed 3-D path or ring
Ray Koopman
3/25/13
Read Re: Calculating the area of a closed 3-D path or ring
Gib Bogle

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.