I know solving the Frenet-Serret equations for a given curvature and torsion is possible, but only analytically possible under special cases like plane curves. Is there something I can exploit to calculate a unit-speed curve where, for instance, $\kappa(s)=\tau(s)=\sqrt{2}/(1+s^2)$?

## 1 Answer

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See my answer on StackExchange: https://math.stackexchange.com/questions/28925/explicit-formula-for-space-curves/28931#28931