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curve-length approximation #106

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@ebo

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@ebo

I have a question or two about the implementation of the curve lengths and fairing.

If I understand the documentation correctly, you use the Euclidean distance summed across some arbitrary evaluation points, is that correct?

I was reading some papers on using NURBS for CNC machining and came across one [1] that uses an adaptive quadrature method based on Simpson׳s rule [2] for greater accuracy.

Also, do you have smoothing (fairing) functions where I can minimize high order derivatives (jerk, or maybe up the ladder to snap, crackle, or pop).

[1] Xu Du, Jie Huang, Li-Min Zhu, A complete S-shape feed rate scheduling approach for NURBS interpolator, Journal of Computational Design and Engineering, Volume 2, Issue 4, October 2015, Pages 206–217, https://doi.org/10.1016/j.jcde.2015.06.004

[2] Lei W.T., Sung M.P., Lin L.Y., Huang J.J. Fast real-time NURBS path interpolation for CNC machine tools. International Journal of Machine Tools and Manufacture 2007;47(10)1530–41.

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