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Let user move a frenet trihedron along a curve?

asked 12 years ago

dnizetic gravatar image

updated 4 years ago

FrédéricC gravatar image

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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answered 12 years ago

calc314 gravatar image

updated 12 years ago

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.

You also mention wanting more info on the Frenet frame. The wikipedia page has good information: http://en.wikipedia.org/wiki/Frenet–Serret_formulas.

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answered 12 years ago

Jason Grout gravatar image

updated 12 years ago

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...)

(see also http://wiki.sagemath.org/interact/cal... for working example of 3d motion)

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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Asked: 12 years ago

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Last updated: May 23 '12