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

*To*: mathgroup at smc.vnet.net*Subject*: [mg27283] Re: How can I find the closest distance between a specified point and an interpolation curve?*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Sun, 18 Feb 2001 02:52:16 -0500 (EST)*References*: <96is0i$dg6@smc.vnet.net> <pRIj6.5848$Rl5.43715@ralph.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Erich, Unfortunately, the use of the interpolation function spoils this approach. Even if the interpolation is linear -- when we will be looking for the nearest point on the line joining the points. Example: pt = {0,0} PointSet = {{-1,0}, {1,0}} But the FindMinimum method (Seth Chandler, Rasmus Debitsch) works: bestpoint[ptset_,pt_]:= With[{fc=Interpolation[ptset]}, ffc=fc; FindMinimum[With[{d={x,fc[x]}-pt},Sqrt[d.d]], Join[{x},{Min[First/@ptset],Max[First/@ptset]}]]] bestpoint[PointSet, pt] Interpolation::inhr: Requested order is too high; order has been reduced to {1}. {0., {x -> 0.}} Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Erich Mueller" <emuelle1 at uiuc.edu> wrote in message news:pRIj6.5848$Rl5.43715 at ralph.vnet.net... > Here is a brute force way: First calculate the square of the distance > from each point in "Pointset" to the given point > > distset = (# - pt).(# - pt) & /@ Pointset > > The result is > > {50, 52, 85, 101, 170, 293, 409, 1274} > > So the closest point is {0,0}. > > Erich > > On 16 Feb 2001, liwen liwen wrote: > > > 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/ > > > > > >