Geodesic
Shapes of Space Curves
Journal for geometry and graphics, Tome 7 (2003) no. 2, pp. 145-156 Cet article a éte moissonné depuis la source Heldermann Verlag

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We study an ordered pair of functions which determines a regular space curve up to a direct similarity. The first function is called a shape curvature and the second one a shape torsion. We prove an extension of the fundamental theorem of space curves relating to the group of direct similarities. We also propose a direct way for recovering a space curve from its shape curvature and shape torsion.
Classification : 53A55, 53A04
Mots-clés : space curves, direct similarities, differential-geometric invariants 
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     author = {R. Encheva and G. Georgiev},
     title = {Shapes of {Space} {Curves}},
     journal = {Journal for geometry and graphics},
     pages = {145--156},
     year = {2003},
     volume = {7},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2003_7_2_JGG_2003_7_2_a2/}
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R. Encheva; G. Georgiev. Shapes of Space Curves. Journal for geometry and graphics, Tome 7 (2003) no. 2, pp. 145-156. http://geodesic.mathdoc.fr/item/JGG_2003_7_2_JGG_2003_7_2_a2/