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When one have a curve $\beta(s)$ which is parametrized by arc length (has natural parametrization) one is able to obtain the tangent, normal and binormal vectors by using Frenet-Serret frame equations:

$T = \beta'(s)$, $N=\frac{T'(s)}{|T'(s)|}$, $B = T \times N$

But are those formulas valid for non-regular parametrizations when one normalizes the tangent vector?

$T=\frac{\beta'(s)}{|\beta'(s)|}$, $N$ and $B$ are calculated as above.

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Yes, as the Wikipedia article says at the end.

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  • $\begingroup$ Oh, silly me. Did not see that, thank you! :) $\endgroup$ – MasterM Jun 24 '12 at 19:47

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