ScreenSaver: resolution change screws up margins

I created a screensaver. Basically, I have a couple of characters sitting right outside the viewable part of the screen. On particular times, the characters begin to move and gradually appear moving from the outside the monitor into the viewable part of the screen. It works perfectly when the resolution is at 600x800.

However, I notice that if the screen saver is displayed on a computer with a different resolution, the characters are no long gradually moving into the viewable part of the screen. Instead, they are basically re-positioned inside the viewable part of the screen screwing up the entire effect.

How do I set it up so that the characters gradually move into the viewable section of the monitor REGARDLESS OF A PERSONS SCREEN RESOLUTION? I tried changing a bunch of settings under "window"/etc, but I can't seem to figure it out.

Any help would be GREATLY appreciated. Thanks in advance.

Just make the characters invisible until you use them. Make them reappear, and then make them invisible again when they're not being used.

My fault.. I should have done a better job explaining it.

Basically... this is what I did:
1. At a specific time, I have the system "create" the cartoon character at a specific location (i.e. located just outside the margins of the monitor) and then the character moves along the path (basically slowly creeping along the edge of the monitor after they enter the viewable part of the screen).
2. Then when the character reaches the end of the path, the character is destroyed.
3. At designated times the above repeats.

PROBLEM: I am telling the system to create the characters at precise measurements (just outside the viewable portion of my screen -- my resolution on my computer is at 600x800). However, I suspect the problem is that if somebody has a higher resolution, the measurements I entered for the character to appear is actually more in the center of the screen that if somebody has a resolution only at 600x800 -- whereas I only want the characters to basically follow the same path and creep along the edge of the monitor regardless of what a persons resolution is.

I did see an option to have the character be created "relative" to another object.. but that won't work either for the above reasons.

Anybody know how to tell the system to create the characters at a precise location just outside the margins of the screen if the resolutions change?

Hopefully this makes more sense now. Thanks again.