
Re: Question: Centroid given a distance metric
Posted:
Feb 11, 2013 12:45 PM


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 ndimensional 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 pseudorandom 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 ~= xcoordinate of the centroid of S, etc.
That's the Monte Carlo way.
A more advanced way is quasiMonte Carlo methods, which rely on special sequences of points that are sort of quasiperiodic (modulo something): a Halton sequence, a Sobol sequence, or a Faure sequence, for example:
http://en.wikipedia.org/wiki/QuasiMonte_Carlo_method
I don't have experience really with quasiMonte 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.

