find (X0,Y0,Z0) to minimise the maximum of f(x,y,z)=Sqrt( (x-X0)^2 +(y-Y0)^2 +(z-Z0)^2 ) with a set of data (x,y,z)

[xgatc]

Hi, Experts :

I have a set of data (x,y,z),  and the distance of each set (x,y,z) to a centre  (X0,Y0,Z0) is caluclated by 

   f(x,y,z)=Sqrt( (x-X0)^2 +(y-Y0)^2 +(z-Z0)^2 )

I need to find a  set of (X0,Y0,Z0), which can minimise the maximum of f(x,y,z)  

in Excel, I can use Solver and take Mean(x,y,z) as  start values for  (X0,Y0,Z0),

using GRG nonlinear Method, I can find a minimum set of (X0,Y0,Z0).  see aattched zip file for data and Excel file.

is there any way I can use LabView to do the same?  

 could Nonlinear curve Fit  be used? and how to implement?

any suggestion is more than welcome.

thanks for your time 

Xiaofeng

[DFGray]

Check out the Mathematics>>Optimization palette. My choice would be the Downhill Simplex, but there are several other VIs on that palette which would also work.

[xgatc]

thanks for your quick reply. I did try Downhill Simplex, but could not  fingure out how to setup the VI.

see my trial one.   any suggestion?

[altenbach]

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xgatc wrote:

I have a set of data (x,y,z),  and the distance of each set (x,y,z) to a centre  (X0,Y0,Z0) is caluclated by 

   f(x,y,z)=Sqrt( (x-X0)^2 +(y-Y0)^2 +(z-Z0)^2 )

I need to find a  set of (X0,Y0,Z0), which can minimise the maximum of f(x,y,z)  

---

What do you mean by "minimize the maximum"? (There will be several maxima in the solution).

Maybe you want do fit to a sphere instead?

[xgatc]

Hi,

Yes, it is actually to find minimum radius for sphere. I am using LV2012, and I could not find  this call

any idea where I can get this?

many thanks.

[altenbach]

It had been in LabVIEW forever. Do you only have LabVIEW base? Look in the math..fitting palette. However, this will not give you the minimum radius, but a best fit for the data.. ~50% will be inside.

[altenbach]

Search wikipedia for "bounding sphere". It lists a collection of algorithms that can be implemented easily.

[xgatc]

HI, altenbach

you are right,   the "fitting on a sphere fit.vi " is not what I am after.

thanks for the suggestion. I will have a look .