Knutson-Tao Tiles

Have you played around with these tiles?
Well, you should.
Go ahead, mouse around with different buttons below this line:

A very simple interface:

The idea is that you move the mouse around, and the keyboard acts like a very large number of mouse buttons, generally taking an action at the current mouse location.
Tile placing commands
Press '1' to place a red triangle.
Press '2' to place a blue triangle.
Press '3' to place a rhombus.
Edge painting commands
Press 'b' to make the mouse location be a blue edge.
Press 'r' to make the mouse location be a red edge.
Press 'c' to to make the mouse location be a crossing edge (a rhombus).
Your three mouse buttons act the same as these three keys.
Hold down shift to only give a blue or red "hint". (defined below)
Holding down shift when laying a rhombus instead lays a "not-rhombus" tile boundary.
Press 'y' to mark an edge as being a boundary between a rhombus and a triangle, oriented towards the blunt middle of the rhombus.
Press 'u' (or ',' or '<' or backspace) to undo the last information laid down.
Press 'z' to undo the restriction next to the mouse (will undo and then redo all more recent restrictions -- do not be alarmed).
Other commands
Press '?' to try all possible local configurations at the vertex where the mouse is, and then apply any conclusions that are reached in all cases.
Press 'a' to search for a full solution automatically, starting where the mouse is. (The screen will only update once every few seconds if it takes a huge amount of trial and error. Check the status bar to see how much it has tried and erred so far.)
Press 'q' to stop the search.

What do the markings mean?