Consider operations of splitting and merging rectangles to form new rectangles. Motivation is for a tiling window manager.
Nicer subset is hierarchical: a rectangle can be divided into multiple like a tic tac toe grid. Merges only permitted if nodes share the same immediate parent.
Not hierarchical: arbitrarily split lines, almost arbitrary merges: a tricky task to decide what may be merged and form a rectangle.
Interesting operations: extend line (perhaps rejoining with an original line that got split). Shift line (or only a portion of a line, perhaps non connected). Shift vertex, moving two lines at once. Proportional shift: shift a line keeping proportions within a region the same.