Varying the Path Turn Angle

Each animation below shows how a path configuration evolves as the path turn angle is changed. In the image on the left the polynomial is a cubic; the one on the right is a quartic. In each case, there is a root at t = -1. This corresponds to an angle of 45 degrees in the Lill diagram with right angle turns. In both animations, the configuration that is shown corresponds to this root. In particular, the paths coincide at the final point throughout the animation.

Cubic polynomial
Quartic polynomial