Betza notation has four directional notation systems: for 4-fold or 8-fold atoms, and each of those in a degenerate (2 directions are equally 'forward') and a non-degenerate version. As specification for the initial direction, diagonals and obliques are degenerate, orthogonals and K/Q ('compounds') are not. XBetza uses the rule that continuation diections are always specified in an 8-fold system, to allow 45-degree turns.
The XBetza a-notation only allows continuation with the same atom, or a 'rotated' or 'range-toggled' version. With the bracket notation one can specify transitions between arbitrary atoms. We can divide the atoms into two groups: oblique and non-oblique. A simple rule is that a transition that stays within the group uses the non-degenerate 8-fold directional system, and transitions between leaps from a different group the degenerate 8-fold system. This avoids the nitpicking (= 'advanced geometry') for whether the adjacent diagonal or orthogonal is most forward after an oblique leap: they are made equivalen by definition even when in reality they are not. Just like in a transition between different obliques the one labeled 'forward' does not go in exactly the same direction. For a transition from orthogonal/diagonal to oblique the pairs of directions are truly equivalent.
If branching in an oblique to compound transition is not desired (which would usually be the case, as the two paths would not be symmetry equivalent), this can be solved by using an orthogonal or diagonal atom as continuation, rather than the compound. One direction in the pseudo-equivalent pair will always be orthogonal, the other diagonal. This avoids the need for using fl and fr, which would pick non-equivalent continuation for the adjacent directions in an oblique. (Which could be solved by using fq or fz instead, but most people would experience that as rather obscure.)
This 'chirality problem' would still exist if we wanted to indicate a continuation direction other than f in descriptions like [N-rR]: this would select moves of a different shape for the hlN and hrN chiral subsets, and would have to be written as [N-qR] for continuation in the 'outward' direction in the short dimension of the oblique leap.
A consequence of defining f as default in continuation legs is that it becomes difficult to indicate moves that can continue in arbitrary direction. Such as Tenjiku Shogi area moves or Lion hit-and-run captures. But since the function of the a has been taken over by the hyphen (or question mark), we can redefine its meaning inside the brackets as "any direction except exactly backwards". So a 3-step area move could be [K?aK?aK], and the Lion hit-and-run [cK-aK].
Betza notation has four directional notation systems: for 4-fold or 8-fold atoms, and each of those in a degenerate (2 directions are equally 'forward') and a non-degenerate version. As specification for the initial direction, diagonals and obliques are degenerate, orthogonals and K/Q ('compounds') are not. XBetza uses the rule that continuation diections are always specified in an 8-fold system, to allow 45-degree turns.
The XBetza a-notation only allows continuation with the same atom, or a 'rotated' or 'range-toggled' version. With the bracket notation one can specify transitions between arbitrary atoms. We can divide the atoms into two groups: oblique and non-oblique. A simple rule is that a transition that stays within the group uses the non-degenerate 8-fold directional system, and transitions between leaps from a different group the degenerate 8-fold system. This avoids the nitpicking (= 'advanced geometry') for whether the adjacent diagonal or orthogonal is most forward after an oblique leap: they are made equivalen by definition even when in reality they are not. Just like in a transition between different obliques the one labeled 'forward' does not go in exactly the same direction. For a transition from orthogonal/diagonal to oblique the pairs of directions are truly equivalent.
If branching in an oblique to compound transition is not desired (which would usually be the case, as the two paths would not be symmetry equivalent), this can be solved by using an orthogonal or diagonal atom as continuation, rather than the compound. One direction in the pseudo-equivalent pair will always be orthogonal, the other diagonal. This avoids the need for using fl and fr, which would pick non-equivalent continuation for the adjacent directions in an oblique. (Which could be solved by using fq or fz instead, but most people would experience that as rather obscure.)
This 'chirality problem' would still exist if we wanted to indicate a continuation direction other than f in descriptions like [N-rR]: this would select moves of a different shape for the hlN and hrN chiral subsets, and would have to be written as [N-qR] for continuation in the 'outward' direction in the short dimension of the oblique leap.
A consequence of defining f as default in continuation legs is that it becomes difficult to indicate moves that can continue in arbitrary direction. Such as Tenjiku Shogi area moves or Lion hit-and-run captures. But since the function of the a has been taken over by the hyphen (or question mark), we can redefine its meaning inside the brackets as "any direction except exactly backwards". So a 3-step area move could be [K?aK?aK], and the Lion hit-and-run [cK-aK].