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Topic: How to find a bounding line?
Replies: 39   Last Post: Jul 12, 2013 5:39 AM

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quasi

Posts: 10,202
Registered: 7/15/05
Re: How to find a bounding line?
Posted: Jul 10, 2013 5:13 PM
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ols6000 wrote:
>
>This has not been proved.


I think it has.

>Only the fact that a "best" bounding line must pass through at
>least one point has been shown (by quasi).
>
>If it turns out to be true that said line must pass through at
>least two points, then we have an O(n^2) method, which is too
>slow for practical use.
>
>The convex hull may be found in O(n) time, given that the data
>is already sorted, but even if the optimum line(s) pass through
> two points on the hull (and this hasn't yet been proved),


I claim it _has_ been proved.

>the method is still O(n^2).
>
>The hypothesis that an optimum line must pass through two
>neighboring points of the original data is incorrect, as shown
>by counter-example.
>
>It may be that an optimum line must pass through two
>neighboring points of the convex hull, but this has not been
>proved.


It's a triviality (draw a picture).

If a bounding line passes through two points of the convex hull
it must pass through two _consecutive_ points of the convex hull.

Thus, the task is O(N).

quasi


Date Subject Author
7/7/13
Read How to find a bounding line?
Woody
7/7/13
Read Re: How to find a bounding line?
Scott Berg
7/7/13
Read Re: How to find a bounding line?
Peter Percival
7/7/13
Read Re: How to find a bounding line?
Woody
7/7/13
Read Re: How to find a bounding line?
quasi
7/7/13
Read Re: How to find a bounding line?
quasi
7/8/13
Read Re: How to find a bounding line?
quasi
7/8/13
Read Re: How to find a bounding line?
Woody
7/8/13
Read Re: How to find a bounding line?
quasi
7/8/13
Read Re: How to find a bounding line?
LudovicoVan
7/8/13
Read Re: How to find a bounding line?
LudovicoVan
7/10/13
Read Re: How to find a bounding line?
Woody
7/10/13
Read Re: How to find a bounding line?
quasi
7/8/13
Read Re: How to find a bounding line?
Leon Aigret
7/8/13
Read Re: How to find a bounding line?
Woody
7/10/13
Read Re: How to find a bounding line?
Leon Aigret
7/10/13
Read Re: How to find a bounding line?
Leon Aigret
7/10/13
Read Re: How to find a bounding line?
Woody
7/10/13
Read Re: How to find a bounding line?
RGVickson@shaw.ca
7/10/13
Read Re: How to find a bounding line?
Woody
7/10/13
Read Re: How to find a bounding line?
quasi
7/7/13
Read Re: How to find a bounding line?
quasi
7/7/13
Read Re: How to find a bounding line?
quasi
7/7/13
Read Re: How to find a bounding line?
quasi
7/8/13
Read Re: How to find a bounding line?
William Elliot
7/8/13
Read Re: How to find a bounding line?
Peter Percival
7/8/13
Read Re: How to find a bounding line?
quasi
7/11/13
Read Re: How to find a bounding line?
Woody
7/11/13
Read Re: How to find a bounding line?
quasi
7/11/13
Read Re: How to find a bounding line?
LudovicoVan
7/11/13
Read Re: How to find a bounding line?
quasi
7/11/13
Read Re: How to find a bounding line?
Leon Aigret
7/11/13
Read Re: How to find a bounding line?
Woody
7/11/13
Read Re: How to find a bounding line?
Leon Aigret
7/12/13
Read Re: How to find a bounding line?
Woody
7/12/13
Read Re: How to find a bounding line?
Leon Aigret
7/11/13
Read Re: How to find a bounding line?
Woody
7/12/13
Read Re: How to find a bounding line?
quasi
7/12/13
Read Re: How to find a bounding line?
Woody
7/12/13
Read Re: How to find a bounding line?
quasi

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