Geodesic
On the Arc Length of Parametric Cubic Curves
Journal for geometry and graphics, Tome 3 (1999) no. 1, pp. 001-016.

Voir la notice de l'article provenant de la source Heldermann Verlag

We are seeking cubic parametric curves whose arc length can be expressed in a closed form. Based on the control points of a Bezier representation of parametric cubics, we provide a criterion to determine whether their arc length has a closed form or not. 
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     author = {Z. Bancsik and I. Juhasz},
     title = {On the {Arc} {Length} of {Parametric} {Cubic} {Curves}},
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Z. Bancsik; I. Juhasz. On the Arc Length of Parametric Cubic Curves. Journal for geometry and graphics, Tome 3 (1999) no. 1, pp. 001-016. http://geodesic.mathdoc.fr/item/JGG_1999_3_1_a0/