I'm having trouble getting my head around Graphics objects and the paint method. Here's my predicament:

I have a class called DrawSurface which extends JPanel. The only thing that I changed was the paint method which I will use to draw on the DrawSurface. I have a bunch of coordinates that I want to draw onto the DrawSurface. It's not all going to fit on the screen, so I want to use a scrollbar to pan along the drawing. Is there a way that I can draw the entire drawing onto an offscreen Graphics object and then display a portion of that Graphics object on the DrawSurface depending on where the scrollbar is? I know that it's possible to draw a portion of an Image object onto a Graphics object, but what about Graphics to Graphics. Or is there an easier way that I'm overlooking?