Gallery problem - generating diferent size pictures from one?

[eluser]flash_back[/eluser]
I am making gallery for my tuning portal and I need some help.

Idea is that every register user can build and maintain there own gallery. Gallery is based on three levels and four album container. It's look something like this [mark -> model -> album > album content] or [BMW -> E30 - 318i ->photos].

So problem is that I need to generate from one uploaded photo 3 deferent size [thumb, medium and full size]. My idea is to build some function($photo_id) that will temporarily generate photo from original. Basically idea is to have just one original photo on server, and from that one just generating others.

can anybody help me whit some idea how to start that function? or some example will be nice too.