Today’s invention is a way to carpet an irregularly-shaped room, without having to get fitters involved in the work.
A small, Roomba-like robot traverses the floor, recording its position accurately. Eventually, it develops an internal map of the room and can order up carpet tiles which will fit exactly …no cutting required. This device would map tiles to floor so as to ensure that there were no ridiculous 1cm-wide tiles required at the edges, for example.
These tiles need no longer be all of the same size and shape, they could be made to scale in size from some central point like the seeds in a sunflower or the segments of a nautilus shell.
Recarpeting is then just a matter of dialling up new tiles to fit the known geometry.