Re: Re: How to Calculatelength of an Spline curve between

• To: mathgroup at smc.vnet.net
• Subject: [mg104930] Re: [mg104891] Re: How to Calculatelength of an Spline curve between
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Fri, 13 Nov 2009 05:57:08 -0500 (EST)
• References: <hdbhcp\$jj4\$1@smc.vnet.net> <200911121107.GAA19061@smc.vnet.net>

```I get the same kernel crash here.

Bobby

On Thu, 12 Nov 2009 05:07:57 -0600, Mark Fisher <particlefilter at gmail.com>
wrote:

> 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
>

--
DrMajorBob at yahoo.com

```

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