Here's a link to transcript of part of the programme 'Secret's of the Parthenon' which was on PBS. Is it possible that geometric mosaic patterns were set out using some of the ratio's mentioned there? Consider this, to set a geometric floor mosaic you need a team that is able to work stone and with at least one person who understands geometry. What about the builders that put the villa up in the first place? They have the skills and experience so, in some cases it might not be mosaicists arriving to do the floor, the builders just carried on.
Could they then have used certain measurements or ratios that they used in the architecture? This is a study that is marked down for some time in the future as you need to know the ratio's used in architecture. Was there a 'standard' set used in the building of a villa or, if there were specific ones, can these measurements be seen in any of the mosaics at that villa?