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1

The link in the comment is excellent. To plot TNB frame to a point you need to a line/arrow from point ($\vec{r}(t)$ to relevant vector, e.g. $\vec{r}(t)+\vec{T}(t)$. There are some indeterminate points (at piecewise junctions but the desired points are well defined). Just for illustration: tang[t_] := r'[t]/Sqrt[r'[t].r'[t]] norm[t_] := ...


2

Here's a minimally-changed working version of what you want, I think: Do[ Do[ If[ (Subscript[B, i][[j]] == {20} && Subscript[B, i][[j + 1]] == {10}) || (Subscript[B, i][[j]] == {10} && Subscript[B, i][[j + 1]] == {20}) , Subscript[new, i] = Module[ {a = Subscript[B, i]} , ReplacePart[a, {j -> a[[j + ...



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