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

• To: mathgroup at smc.vnet.net
• Subject: [mg27272] Re: How can I find the closest distance between a specified point and an interpolation curve?
• From: "Rasmus Debitsch" <debitsch at zeiss.de>
• Date: Sat, 17 Feb 2001 03:30:44 -0500 (EST)
• References: <96is0i\$dg6@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

you can try FindMinimum:

Pointset = {
{0, 0}, {1, 1}, {3, 4}, {4, 5}, {6, 8},
{7, 12}, {8, 15}, {12, 30}
};
Fc = Interpolation[Pointset];
pt = {5, -5};

res = FindMinimum[(p = {x, Fc[x]} - pt; Sqrt[p . p]),  {x, {0, 1}}]

Out[32]=  (12:43:04 on 2/16/01)
{7.02196, {x -> 0.333778}}

ps = {x, Fc[x]} /. res[[2]]
Out[16]=  (12:39:40 on 2/16/01)
{0.333778, 0.247309}

Plot[Fc[x], {x, 0, 5.2},
Epilog -> {PointSize[0.02],
RGBColor[1, 0, 0], Point[pt],
RGBColor[0, 1, 0],  Point[ps]
},
PlotRange -> {-5.5, 5.5},
AspectRatio -> 1
]

--

Rasmus Debitsch
Carl Zeiss Lithos GmbH
Carl Zeiss Strasse
D-73447 Oberkochen

eMail : debitsch at zeiss.de

"liwen liwen" <gzgear at yahoo.com> schrieb im Newsbeitrag
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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