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).
INTVis the difference in the parameter t between each pair of consecutive points.DIR_XandDIR_Yare 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.
Clearly there is some 3D curve and some rotational motion that would produce the results you are seeing, when projected into 2D. So, your mind does not reject the idea that the curve might be rotating in 3D.
The way you are drawing the curve (with the yellow disks in front of the orange ones) strongly suggests that the curve is 3D. If you change the drawing order, or make all the disks the same color, I think the 3D illusion will be greatly reduced.