Re: How to Calculatelength of an Spline curve between two

*To*: mathgroup at smc.vnet.net*Subject*: [mg104830] Re: [mg104819] How to Calculatelength of an Spline curve between two*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Wed, 11 Nov 2009 04:27:17 -0500 (EST)*References*: <200911101104.GAA20038@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

Here's an example: xvals = Flatten@{0, Sort@RandomReal[{0, 2 Pi}, 30], 2 Pi}; tbl = Table[{x, Sin@x + .05 RandomReal[]}, {x, xvals}]; sp = Interpolation[tbl, Method -> "Spline"]; Show[ListPlot@tbl, Plot[sp@x, {x, 0, 2 Pi}], PlotRange -> All] (Warning: splines can have VERY wild fluctuations.) Next solve for the curve length, from 0 to any x: Clear[x, len] len = len /. First@NDSolve[{len'[x] == Sqrt[1 + sp'[x]^2], len[0] == 0}, len, {x, 0, 2 Pi}]; Plot[len@x, {x, 0, 2 Pi}] Compute the arc length between two points: len[.7] - len[.2] 1.00597 Bobby On Tue, 10 Nov 2009 05:04:30 -0600, alfaeco <alfaeco at gmail.com> wrote: > I need some help. > > Given an Interpolating function with method-> Spline. > > sp = Interpolation[tbl, Method -> "Spline"]; > > How can I calculate the distance between two arbitrary points of the > splines? > -- DrMajorBob at yahoo.com

**References**:**How to Calculatelength of an Spline curve between two points?***From:*alfaeco <alfaeco@gmail.com>