Re: How can I find the closest distance between a specified point and an interpolation curve?

• To: mathgroup at smc.vnet.net
• Subject: [mg27276] Re: How can I find the closest distance between a specified point and an interpolation curve?
• From: "Seth Chandler" <SChandler at Central.UH.Edu>
• Date: Sat, 17 Feb 2001 03:30:49 -0500 (EST)
• Organization: University of Houston
• References: <96is0i\$dg6@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```The following should work in your case, although in general it will only
find local minima

bestpoint[ptset_,pt_]:=
With[{fc=Interpolation[ptset]},
FindMinimum[With[{d={x,fc[x]}-pt},Sqrt[d.d]],
Join[{x},{Min[First/@ptset],Max[First/@ptset]}]]]

Example:

bestpoint[{{0,0},{1,1},{3,4},{4,5},{6,8},{7,12},{8,15},{12,30}},{5,-5}]

{7.02196,{x\[Rule]0.333778}}

Seth J. Chandler
University of Houston Law Center

"liwen liwen" <gzgear at yahoo.com> wrote in message
news:96is0i\$dg6 at smc.vnet.net...
> Dear friends,
> Here is a curve that is produced by
> Interpolation[PointSet] function,
> Pointset={{0,0},{1,1},{3,4},{4,5},{6,8},{7,12},{8,15},{12,30}}.
>
> Fc=Interpolation[PointSet].
> the specified point is:
> pt={5,-5}
> I want to find the closest distance between the point
> of pt and Fc ?
>
>
> Best regards,
>              Liwen    2/15/2001
>
> __________________________________________________
> Do You Yahoo!?
> Get personalized email addresses from Yahoo! Mail - only \$35
> a year!  http://personal.mail.yahoo.com/
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```

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