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Topic: Question: Centroid given a distance metric
Replies: 14   Last Post: Feb 12, 2013 1:04 PM

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David Bernier

Posts: 3,366
Registered: 12/13/04
Re: Question: Centroid given a distance metric
Posted: Feb 11, 2013 12:45 PM
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On 02/11/2013 12:17 PM, Andrey Savov wrote:
> Was wondering if you guys can point me in the right direction.
>
> Are there any known/studied methods to calculate a centroid (geometric center) of finite set of points in n-dimensional real Euclidean space by only knowing a distance metric f(x,y): R^n x R^n -> R ?


Suppose the figure S can be enclosed in a box of volume V.

Then you can generate pseudo-random points in the box
and when the point P falls inside S, do:
( count=0;
xSum= ySum = zSum = 0 initially )

count = count+1;
xSum = xSum + x_P
ySum = ySum + y_P
zSum = zSum + z_P


Then, xbar = xSum/count is ~= x-coordinate of the centroid of S,
etc.

That's the Monte Carlo way.


A more advanced way is quasi-Monte Carlo methods,
which rely on special sequences of points that are
sort of quasi-periodic (modulo something):
a Halton sequence, a Sobol sequence, or a Faure sequence,
for example:

http://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method

I don't have experience really with quasi-Monte Carlo methods.

dave


--
dracut:/# lvm vgcfgrestore
File descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID
993: sh
Please specify a *single* volume group to restore.



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