Add A way to get the length of the curve

[yolhan83]

Hi all,
In the $[a,b]->R^d$ case, it would be nice to recover the length easily, this would require calculating

$$L = \int_a^b || c'(s) ||_{R^d} ds$$

This may only interest me though so don't hesitate if it's not consider important here.

[SouthEndMusic]

You can of course make a SmoothArcLengthInterpolation with large m and take the last t. We can take a look at this per interpolation type to see what we can do analytically, but the integrals you have to compute are generally quite nasty.

[yolhan83]

Oh ok, basically, in BloodFlowTrixi.jl I take in 3d points then build an SPLine with parameter [0,1], calculate it's length (with quadgk) and finally build the arc length interpolation on [0,L]. It works great but I hate having quadgk only used in the extension which is why I wondered if it could be done here.
Yeah I understand that this integral may be nasty with some interpolations

[SouthEndMusic]

Can you explain exactly why you need QuadGK here (or, more specifically, why you want to compute the length of the spline curve)?

The arc length interpolation approximates the spline curve, so the length of the arc length interpolation approximates the length of the spline curve. The last t of the arc length interpolation is equal to its length essentially by definition.

[yolhan83]

Nevermind, I just realized how it works, thank you, I will make the changes in BFT when I can.