Oh phew, thank you so much for making that! I was trying to make something like that too but a bit different, and some of those symmetries were starting to make me feel Very cross-eyed.
Basically I was thinking that a table for all the tiling types (both wallpaper and Frieze) with the following visual guides would be useful: 1. The base tile guide with no transformation indicators 2. The base tile guide with indicators (use can toggle indicators on and off) 3. The preview when creating the guide (either what you did here, or Thorsten's previews) 4. An outline preview of extra tiles (can be toggled on and off, shows basically the outline of those extra tiles as you've made here) 5. My idea was to also make base tile guides that show you which tile side ends up reflected on which side. This is meant to help a person who wants to program the "guide points" feature: - Two "corresponding" sides will be represented by dotted lines of the same colours. (example: for simple translation, the left and right sides would be dotted lines of one colour, and the up and down sides of another colour). An arrow marks the "direction" of each side. - Each side that transforms onto itself is represented by a full line. It is marked either by a single arrow (if the transformation is in the same direction) or two arrows in opposite directions (if the tile is flipped) 6. Base tiles again, this time with examples of guide points and guide segments.
(yeah, that makes a lot...)
I do have to throw out there at this point, the proposed UI for tiling at http://wiki.inkscape.org/wiki/index.php/Tiling_tool%C2%A0 is incredibly complex. One of the benefits to a dedicated tool is actually being able to manipulate parameters on-canvas.
Are you reading the latest version (there were many versions...)? Because all the things that can be manipulated on canvas Are manipulated on-canvas... The dialogue is only choosing options (there are a lot of options... much more than your average LPE, even), the number of copies, and hitting "apply" (none of which are really on-canvas interactions).
I've thought of the use of tile shadow outlines to help users see what will be rendered. The problem is dynamics. They make the tile outlines unpredictable in the first place... That's why I came up with extra render "target" options, so users can choose to render over a specific, non-rectangular area, or even better, to render as a target's pattern (if .svg allows that), so users can then manually control any offsets with the pattern tool.
Now, I was actually thinking about on-canvas handles for manipulating dynamics, but that's a whole other can of worms... (and given the time needed to render dynamic tiles, I'm not so sure it's such a good idea to have them updated live...)
I'm open to suggestions though. I've made a number of mock-ups proposals for tilings until now, and this is just the latest iteration (the... fifth I think? If I count the few ideas I first had a few years ago). If someone has a general direction in mind (beyond "it has to be a tool"), I can try to see if I can work out something.