# Let user move a frenet trihedron along a curve? How to "animate" a frenet trihedron along a given curve?

I believe this is similar to what I'm looking for:

http://www.math.byu.edu/~math302/cont...

but in the context of curves, because my task is to draw this curve:

c2: [0, 5] -> R^3, c2(t) = (e^t * cos(t), e^t * sin(t), e^t)


and give the user ability to move a frenet trihedron along that curve (using a parameter and @interact)

I know how to draw a curve and basics of interact:

show(parametric_plot3d( (e^t * cos(t), e^t * sin(t), e^t), (t, 0, 2*pi)));
@interact
...


But I don't have enough knowledge about frenet trihedron. If anyone could help me out I would appreciate it.

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I've given some thought to your question, as I'm also interested in such an animation. Some of the best advice I've seen on doing this kind of animation was just given today by niles at http://ask.sagemath.org/question/1437/animated-sphere.

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Here are some relevant interacts I've used in calc 3:

http://sagenb.org/home/pub/306/

http://sagenb.org/home/pub/256/ (I think this is currently broken...)

I also really like this demo: http://mrdoob.github.com/three.js/exa... (click "debug Normals" and the camera button, for example)

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