If two single-valued continuous functions κ(s) (curvature) and τ(s) (torsion) are given for s>0, then there exists exactly one space curve, determined except for orientation and position in space (i.e., up to a Euclidean motion), where s is the arc length, κ is the curvature, and τ is the torsion.

arc length | curvature | Euclidean motion | fundamental theorem of plane curves | torsion