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Is there an algorithm to find the center of a set of points in 3D-space?
It should minimize the distance to the furthermost point(s)
Thanks!
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sascha wrote:
> Is there an algorithm to find the center of a set of points in 3D-space?
> It should minimize the distance to the furthermost point(s)
>
Yes, there are algorithms for that (The problem ist equivalent to finding a
minimal sphere enclosing all points):
One by J.Ritter, see "An Efficient Bounding Sphere"
http://www1.acm.org/pubs/tog/GraphicsGems/authors.html#R_link
A more efficient one by E. Welzl:
Paper:
http://www.inf.ethz.ch/personal/emo/ps-files/SmallEnclDisks-LNCS555.ps
implementation can be found on
http://www.magic-software.com/Containment.html
--
POV-Ray Objects Collection: http://objects.povworld.org
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That's exactly what I was looking for, thanks a lot!!!
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sascha wrote:
>That's exactly what I was looking for, thanks a lot!!!
I guess it depends on the application, but isnt it generally more useful to
find the point from which the average distance is minimised? would be
equivalent to doing linear statistical analysis across 3 dimensions, I
think. Perhaps not.
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In article <web.3f6b1b8befaab55d85d37d7f0@news.povray.org>,
"neb" <neb### [at] qism org> wrote:
> sascha wrote:
> >That's exactly what I was looking for, thanks a lot!!!
>
> I guess it depends on the application, but isnt it generally more useful to
> find the point from which the average distance is minimised? would be
> equivalent to doing linear statistical analysis across 3 dimensions, I
> think. Perhaps not.
You're making it a bit too complicated...just average the points. The
result will be closer to most of the points, though it won't be the
center of the furthest extending points. Which method you choose depends
on what exactly you want.
--
Christopher James Huff <cja### [at] earthlinknet>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: chr### [at] tagpovrayorg
http://tag.povray.org/
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