I'm assuming that the standard movement animation is not good enough.
So...
If you have a function to determine the trajectory then all you have to do is feed the input of your function into a point or a screen variable. Then, using a periodic event calculate (using your function, of course) the new top/left positions of your object.
For example, let's say your object is called "MyObj". You'd access it's top/left properties from CimBasic (in a screen script) as follows: