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H. G. Muller wrote on Fri, Dec 3, 2021 02:00 PM UTC:

I extended XBetza notation to give new meaning to the use of the z and q modifier in continuation legs of multi-leg moves, where the original meaning of crooked and circular are not useful. The intention was to solve the problem that in a bent trajectory that contains an s (also in combinations fs / bs) the equivalence of l and r is broken. A move described as afs...W starts like the Xiangqi Horse (W, and from there diagonally outward). But in a description like afsafrW the next bend in the path is 45 degree to the right, irrespective of whether whether the first bend was taken to the left or right. It thus describes two different move shapes (Alfil-like or Camel-like), rather than two orientations of moves of identical shape. That is incovenient: it preclude the use of s for compactifying the notation, and forces one to write the two symmetry-equivalent paths separately (afraflWaflafrW for the Camel-like or 'crooked' version).

From now on this can be written as afsafzW. The z then indicates that the path bends in the opposit direction as the preceding s. A sequence of z legs would thus always describe a crooked path. Similarly, a q would indicate bending in the same direction as the previous bend, and a sequence of q legs would give a circular path. This new use of the modifiers allows the description of the Falcon move to be shortened to afafsKafsafzfK: the first atom describes a path that bends after 2 steps, the second atom one that bends immediately, and then either bends in opposit direction (fz) or goes straight on (f).

Note that on oblique atoms the symmetry is broken from the very start, even without the use of an s. Such moves are interpreted as if they started in their longest direction. (So g1-f3 would be a 'left' move.) You should thus never use l or r in continuation legs of an oblique atom, or after an s leg, but always use z or q instead.


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