When you call repaint(), for example, repaintComponent(Graphics) gets called, and then you can call it from outside the class without the parameter Graphics.
I'd like to have a function that takes more parameters I'm using, but I still want to be able to draw with it, so I need to be able to make a call like that (eg repaint() calls repaintComponent(Graphics)) or get access to Graphics to call the function, assuming it would get repainted by explicitly calling repaintComponent() anyway.
I've been thinking about putting the data in the object and then drawing, but I'm not sure if it'd work and it would be pretty complicated, I think.