I have a regular curve, [itex]\underline{a}(s)[/itex], in ℝ(adsbygoogle = window.adsbygoogle || []).push({}); ^{N}(parameterised by its arc length, [itex]s[/itex]).

To a running point on the curve, I want to attach the (Frenet) frame of orthonormal vectors [itex]\underline{u}_1(s),\underline{u}_2(s),\dots, \underline{u}_N(s)[/itex]. However,looking in different books, I find different claims as to how these should be obtained. Specifically, some books suggest that Gram-Schmidt should be applied to:[tex]\underline{a}^{\prime}(s), \underline{a}^{\prime \prime}(s), \dots , \underline{a}^{(N-1)}(s)[/tex]while another book suggests that [itex]\underline{u}_{k+1}(s)[/itex] is obtained by applying Gram-Schmidt to [itex]\underline{u}_k^{\prime}(s)[/itex].

Which should I use?

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# How exactly to obtain Frenet Frame via Gram-Schmidt process?

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