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 ? > > Please help! > > 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/ > >