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Old   December 7, 2000, 03:57
Default Arc length approximation
Stefan Maehlmann
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Hello, i'm looking for a high order method to calculate the arc length of a 2d curve. Is it possible to use chebychev or legendre polynoms for this task?

Thanks in advance.

Stefan Maehlmann
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Old   December 7, 2000, 10:11
Default Re: Arc length approximation
Brian Gribben
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That's a very good question. I suggest you search the news group "" (you could use the Discussions section of to do this for example) for "spline length" or similar, I know there are a lot of postings on the subject.

Recently I was trying to find a way of calculating the length of parametric cubic splines. I concluded that there was no closed-form analytic solution. Since speed was not an issue for me, I broke up the spline into successively-finer polylines and calculated their lengths until convergence.

I am sure there is a more elegant solution using interpolating polynomials as you suggest. I think I read something on it once, maybe at netlib?

Good luck and please let us know if you find anything useful

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