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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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 fom Posts: 1,968 Registered: 12/4/12
Re: Calculating the area of a closed 3-D path or ring
Posted: Mar 16, 2013 3:33 AM

On 3/16/2013 2:27 AM, Ray Koopman wrote:
> On Mar 14, 9:36 pm, Math Guy <M...@Guy.com> wrote:
>> Ray Koopman wrote:
>>>
>>> You haven't said whether the ordering of the points around the
>>> loop is given or not.

>>
>> The user will specify the markers to be used (there are other markers
>> on the heart which will not be involved in this ring). A routine will
>> identify the order by picking one point and then determine which of
>> the remaining points is closest, and will piece-wise work it's way
>> around the ring. This should avoid any errors if the user gives the
>> order incorrectly.
>>

>>> Also, what do you want to do if the loop is not convex?
>>
>> Do you mean what if the loop looks like a potato chip with a bite taken
>> out of it?
>>
>> I don't see how that would affect the proposed area calculation method.

>
> It won't affect the plane of best fit, but it may make it harder to
> identify the loop. I would give the 2D coordinates to a convex hull
> routine. If the hull uses all the points then it's your loop. But
> if some points are inside the hull then a simple nearest-neighbor
> approach can sometimes connect the points in the wrong order.
>

Absolutely.

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

Good point!

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