Reconstructing Space Curves From Curvature and Torsion

As already noted by previous answerers, in general one is unable or unwilling to obtain closed-form solutions for the differential equations that result from Frenet-Serret (except in the simplest cases, like helices). In practice, what one often does is to resort to numerical methods (e.g. Runge-Kutta) if all one wants is to see the curve with a given curvature and torsion function. The initial conditions for these differential equations are obtained by placing your Frenet trihedral in some convenient position. One common practice is to place the inital trihedral such that the curve passes through the origin, and the three vectors are coincident with the axes

Given $kappa (s)$ and $tau (s)$ and a frenet apparatus $lbrace T_0,N_0,B_0 rbrace$, how can you reconstruct a space curve?

I know I need to use the frenet-serret equations, but I can't put a finger on it. Thanks.

·OTHER ANSWER:

Given $kappa (s)$ and $tau (s)$ and a frenet apparatus $lbrace T_0,N_0,B_0 rbrace$, how can you reconstruct a space curve?

I know I need to use the frenet-serret equations, but I can't put a finger on it. Thanks.

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