I am trying to define the movement of an object for a danmaku game I am making. Here is a link to some example gameplay (not my game, but a popular series in this genre made by Zun). Basically, I was thinking that any object's movement (in a 2-dimensional plane) can be defined using just two functions. This is a 2d game and so there are two axes. It will have a velocity in pixels/secs for the x-axis and for the y-axis with positive numbers being velocity going right for the x-axis and going up for the y-axis. I was thinking that no matter how complex the pattern of the object, I can define it using two functions. Maybe it isn't practical to define their movement this way, but I was wondering if it is theoretically possible.
I hope that my question was explained clearly enough. Also, if you know of any books that deal with this sort of thing that would be nice to know about as well. I also did not now what tags to put on this so some of these may be wrong.