See POV General thread (About PovRay 4) for context.

This is a still from an animation demonstrating the unit tangent 
(green), unit normal (light blue) and unit binormal (red) vectors to a 
vector-valued function (orange) at a point on the curve (dark blue.) 
The osculating circle (circle of curvature) is the tan circle, and the 
osculating (tangent) plane is the light gray circle.

The students had to calculate the equations for the unit tangent, normal 
and binormal (a good review of the quotient rule) and checked their work 
with Mathematica.

BTW the function is R(t) = <3cos(t), 3sin(3t + 2), 3sin(2t + 1)>

Dave Matthews

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