Re: How to Calculatelength of an Spline curve between two points?

*To*: mathgroup at smc.vnet.net*Subject*: [mg104891] Re: How to Calculatelength of an Spline curve between two points?*From*: Mark Fisher <particlefilter at gmail.com>*Date*: Thu, 12 Nov 2009 06:07:57 -0500 (EST)*References*: <hdbhcp$jj4$1@smc.vnet.net>

On Nov 10, 6:04 am, alfaeco <alfa... 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? I'm assuming you want to compute the distance along the spline. In principle it should be easy, but because of a bug (that produces a kernel crash) it's a bit harder. Here's the setup: data = Table[{i, RandomReal[{-10, 10}]}, {i, 5}]; ifun = Interpolation[data, Method -> "Spline"]; Now let's simply use the formula for arc length to compute the distance from x = 1.5 to x = 3.1: NIntegrate[Sqrt[1 + ifun'[x]^2], {x, 1.5, 3.1}] But on my system (Windows XP, Mathematica Version 7.0.1) this crashes the kernel. So does FunctionInterpolation[ifun'[x], {x, 1, 5}], so that's out too. OK, we can do this "by hand": difun = Interpolation[Table[{x, ifun'[x]}, {x, 1, 5, .01}]] Then use the arc length formula: NIntegrate[Sqrt[1 + difun[x]^2], {x, 1.5, 3.1}] On the other hand, if this is not what you want, then never mind. --Mark

**Follow-Ups**:**Re: Re: How to Calculatelength of an Spline curve between***From:*DrMajorBob <btreat1@austin.rr.com>