Failing to grok mappings of QGraphicsScene, QGraphicsView, etc.

[ubuntourist]

I have a UI that I designed with Qt-Designer. My code (Python / PySide) expands it to full screen via

   self.setWindowFlags(Qt.FramelessWindowHint)
   self.showFullScreen()

So, I don't know the final dimensions of stuff before-hand. I have a QGroupBox that I want to have a QGraphicsItem centered in, and I want to be able to move the QGraphicsItem within the QGroupBox. I don't want to scroll off in any direction. I just want to center an SVG in a box and move it within the box.

When I look at the explanation of how things map and QPaintEvents, I just go cross-eyed. Is there a straightforward way to just use the geometry of the QGroupBox after it has resized, as both the coordinate system and boundary / bounding box of my SVG image?

If I have a background that is computationally drawn -- say for example a circle that fits inside the QGroupBox, is there a way to avoid redrawing it constantly as the SVG image moves around inside it?