weetabixharry
- 111
- 0
I have a regular curve, \underline{a}(s), in ℝN (parameterised by its arc length, s).
To a running point on the curve, I want to attach the (Frenet) frame of orthonormal vectors \underline{u}_1(s),\underline{u}_2(s),\dots, \underline{u}_N(s). 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:\underline{a}^{\prime}(s), \underline{a}^{\prime \prime}(s), \dots , \underline{a}^{(N-1)}(s)while another book suggests that \underline{u}_{k+1}(s) is obtained by applying Gram-Schmidt to \underline{u}_k^{\prime}(s).
Which should I use?
To a running point on the curve, I want to attach the (Frenet) frame of orthonormal vectors \underline{u}_1(s),\underline{u}_2(s),\dots, \underline{u}_N(s). 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:\underline{a}^{\prime}(s), \underline{a}^{\prime \prime}(s), \dots , \underline{a}^{(N-1)}(s)while another book suggests that \underline{u}_{k+1}(s) is obtained by applying Gram-Schmidt to \underline{u}_k^{\prime}(s).
Which should I use?