TNB-Frame (Frenet-Serret Frame) with GeoGebra 3D

  Рет қаралды 5,769

turksvids

turksvids

4 жыл бұрын

In this video we use GeoGebra to create a TNB-frame for a parametrically defined curve. The way we create it you can change the component functions and watch things change. To make it all happen we first: define the component functions individually, define the curve parametrically, create the unit tangent vector, create a function for the unit tangent vector, create the unit normal vector, graph the osculating plane, and then finally create the unit binormal vector. The three vectors, T, N, and B make up a nice little 3D coordinate system that moves along with our point. It's fun to make and fun to watch move around!
You can play around with GeoGebra in your web browser at GeoGebra.org.

Пікірлер: 11
@dpmike32819
@dpmike32819 2 жыл бұрын
That was FANTASTIC
@poo2uhaha
@poo2uhaha 3 жыл бұрын
Nice vid, really useful tutorial for people new to geogebra and frenet serret co-ords
@BrownPen_BluePen
@BrownPen_BluePen 4 жыл бұрын
This is so clear, thank you!
@klingonxxxxxx
@klingonxxxxxx 4 жыл бұрын
Amazing visualization. Thanx
@mirandabluff836
@mirandabluff836 3 жыл бұрын
This video saved my ass on a computer graphics project! Thanks
@uhhmir
@uhhmir 2 жыл бұрын
thank you! this was so helpful
@anandarunakumar6819
@anandarunakumar6819 Жыл бұрын
Nice, motivates to learn diff geom visually. Thank you.
@ermiasawoke192
@ermiasawoke192 4 ай бұрын
Thank you
@dpmike32819
@dpmike32819 2 жыл бұрын
Thank You..THANK YOU
@user-cd8yi4dk6p
@user-cd8yi4dk6p 2 жыл бұрын
couldn't you've defined the curve b as a'(t)/d(t) ?
@tedsheridan8725
@tedsheridan8725 Жыл бұрын
Cool video. Question - is there any way to reduce the amount of redundant calculations when plotting a curve like 'b'? I'm working on similar (but more complicated) parametric service which involves the unit normal vector of a curve. I have something similar to your curve 'b', and I'm finding that all the redundant calculations really slows Geogebra down, especially as functions get nested. For the life of me I can't find a way to get Geogebra to store a vector in the while drawing a curve or surface so it will use the current numerical vector instead of going back and recalculating the vector by function definitions. Any help? Thanks!
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