### The T-N-B Frame

How to use   ||   Examples   ||   Other Notes

How to use
• Enter functions f (t), g(t), and h(t) in the text input fields marked "f (t)=", "g(t)=", and "h(t)=".
(Example: f (t)=3cos t, g(t)=3sin t, h(t)=t/3)
• Click the "Graph" button (this button also refreshes the graph).
• Rotate the graph by clicking and dragging the mouse on the graph.
• Enter first derivative functions f '(t), g'(t), and h'(t) in the text input fields marked "f '(t)=", "g'(t)=", and "h'(t)=", and click the "Graph" button to refresh the graph. (Example: f '(t)=-3sin t, g'(t)=3cos t, h'(t)=1/3)
Examples
Helix: f (t)=3cos t, g(t)=3sin t, h(t)=t/3, with appropriate derivatives
Wavy circle: f (t)=3cos(t), g(t)=3sin(t), h(t)=sin(2t), with appropriate derivatives
Other Notes
The parametric path itself is shown in blue. The velocity vector v(t)=<f '(t), g'(t), h'(t)> and acceleration vector a(t)=<f ''(t), g''(t), h''(t)> are shown in orange. The standard unit tangent vector T is defined to be the unit vector in the direction of the velocity vector v(t). The standard unit normal vector N is defined to be the unit vector for which the acceleration vector a(t) lies in the T-N plane, with component aN (the length of the projection of a(t) onto N) being positive. The standard unit binormal vector B is defined so that B=TxN. The unit vectors T, N, and B are shown in green. Labels show the values of aT (the tangent component of a(t)) and aN (the normal component of a(t)).