Examples from Section 13.3
The following examples use the trefoil knot for the space curve. Our
scaling and choice of coordinates gives:
x = sin(t) + 2 sin(2t)
y = sin(3t)
z = cos(t) - 2 cos(2t)
The first animation below shows three vectors: The red vector is position,
the velocity vector is yellow and the acceleration is green. The lengths
correspond to the magnitude of each:
![Trefoil Knot, Figure 1](TNB_PosVelAccelNoScale.gif)
The next animation shows the vectors scaled back for better viewing.
Again, red is position, yellow is velocity, acceleration is green.
![Trefoil Knot, Figure 1](TNB_PosVelAccelScaled.gif)
The next animation shows the Frenet frame (a.k.a. TNB frame) for
the trefoil knot- The unit tangent is red, the unit normal is yellow,
and the binormal vector is green.
![Trefoil Knot, Figure 1](TNBAnimation01.gif)