This demo includes tow windows.

The window "Curve: X(t)" displays a twice covered curve.

The window "Perturbed Tangential Image" displays the tangent vector T(t0) and a curve that it traces out. The tangent vector is perturbed slightly (with the magnitude of this perturbation controlled by parameter u) so that the curve that it traces out does not overlap itself.

The rotation index is the total change of direction angle from tmin to tmax divided by 2π, which is visualized in the "Perturbed Tangential Image" window.


Change the value of t0 and other variables as in earlier demos.
As in earlier demos, there are "Show entire curve" and "Show Color Spectrum" options.