I redid the whole thing... again. http://wiki.inkscape.org/wiki/index.php/Tiling_tool
This is the first among my proposals with a consistent behavior from start to finish (at least, I think so), and doesn't look like a badly-proportioned three-headed Frankenstein.
A picture is worth a thousand words so.... this is the target behavior: http://wiki.inkscape.org/wiki/images/Tiling_interface_examples.png
In fact, I now divide the tiling "tool" into 2 parts (then further divided the whole proposal into hopefully more manageable sub-parts):
1. A general tiling guide tool whose only interacting with the tiling process is to send it coordinates (the type that no-one wants to input manually). http://wiki.inkscape.org/wiki/images/Tiling_Guide_Toolbar.png
2. The tiling -process- is back in a dialogue. This is because no matter what I did, it wouldn't stuff into a toolbar, and having separate "tools" was becoming a bit ridiculous. However, all the things that need to be "on-canvas" (the guide, basically) is now on-canvas. The only numerical values you need to input manually are intuitive ones like the number of clones and maybe a start and finish angle. And values for dynamics, but I haven't figured out an on-canvas way to handle those as the same time as basic tile information... http://wiki.inkscape.org/wiki/images/Tiling_dialogue_proposal.png
Also, this interface allows you to stack tilings, and could also integrate into whatever future Effects Stacking interface Inkscape comes up with.
From a single tile, you can define not only the interior tiles, but "edge"
scenarios as well. The feature involved here is actually a simple cut, delete and join operation: Inkscape cuts the pattern along certain guides, deletes the parts that need deleting, and does a "Select all nodes" and "Join" operation. (of course, on this occasion, I discovered that Inkscape can't actually cut groups of objects yet, oh well)
If you placed all the tile elements in a way to create seamless tiles (that's where Guide Points are supposed to help), then all the tiles will proceed to join up seamlessly, even with small variations (though not big ones).
Hopefully this is a good start for others to come up with even better possibilities. Thoughts?
You have covered the topic very well. Another example to look at is the Kali applet:
http://www.scienceu.com/geometry/handson/kali/index.cgi?group=wt
For Tiling along the Path you could support the seven Frieze groups and for Rotational tiling you could support the Rosette groups.
In the guides for a given symmetry group, you could show the rotation points (along with their degree) as well as reflection lines, glide reflection lines and translation directions and lengths. I think you briefly describe these ideas in your document but since there is quite a lot going on here it may be useful to spell it out in detail for each symmetry group. The user should be able to move these guide lines and points as long as they stay within the constraints of the chosen symmetry group.
Below is a picture of guides for symmetry p6m (colours just used for visibility but should conform to guidelines elsewhere):
http://inkscape.13.n6.nabble.com/file/n4628619/wallpaper.png
The book "The Symmetry of Things" by Conway, Burgiel and Goodman-Straus has some very nice visualizations for reference.
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Valerie
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veronika