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Let user move a frenet trihedron along a curve?

asked 2012-05-21 06:56:19 -0500

dnizetic gravatar image

updated 2017-01-08 05:09:28 -0500

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 2012-05-22 16:31:39 -0500

calc314 gravatar image

updated 2012-05-22 16:32:03 -0500

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 2012-05-23 05:22:39 -0500

Jason Grout gravatar image

updated 2012-05-23 05:32:00 -0500

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: 2012-05-21 06:56:19 -0500

Seen: 377 times

Last updated: May 23 '12