Trajectory spline 3D illusion

While playing around with 2D quadratic splines of a trajectory, I sometimes perceive the resulting curve rotating "in 3D" when changing the parameters. Here is a crude GIF example:

And another example. (The jerks are due to my poor video editing).

• INTV is the difference in the parameter t between each pair of consecutive points.
• DIR_X and DIR_Y are the initial slopes in each coordinate.

Why is this so? Is there any mathematical explanation of this phenomenon?

edit. If it's of any use, I can provide the source of the program.

• DIR_X and DIR_Y appear to be tracking your mouse movements. Unless this is a popular program with certain users (not me), how is anyone supposed to know without the code? – David Peterson Feb 16 '14 at 4:59