2D spatial indexing question:
What do you call a data structure that is essentially an infinite* quadtree whose nodes contain neither absolute coordinates nor absolute scales -- in which the coordinate system of each node has been normalized to the unit square (0,0)-(1,1), and in which the top-level node is not fixed absolutely?
It's a quadtree, of course -- but what type of quadtree is it? (Is there a common name? I've seen dozens of types of quadtrees named and defined in the literature, but not this particular one.)
To render a scene, you are given some starting node (not necessarily the root), its size in pixels, and its location on the screen. You then draw all objects within the node by scaling their coordinates using a current transformation matrix, which you push on the stack and halve as you go down the tree. The absolute coordinates of the nodes are thus available only though temporary work variables during rendering, and are not contained within the data structure itself.
If an object within a node moves outside of the node (e.g., outside the unit square), you pass it to the parent for reassignment to another node. If an object becomes fragmented (for example, an asteroid hit by a bullet), the smaller portions are passed down to children nodes, who must scale the coordinates appropriately to maintain the unit-square normalization within each node.
The key difference here from traditional quadtree implementations used in spatial indexing is that the coordinates of objects are always relative to the coordinate system of the node within which they are contained. This relativism applies not only to position but also to scale.
* Infinite for the lack of absolute coordinates; even double-precision floating-point coordinates impart limits on position and size when used for absolute positioning.