Also, I'd wonder whether directly backwards is part of the default, or would have to be added.
Good question. It makes less sense to exclude it here. OTOH, normally this square has to be empty, or it would have blocked the move. So it only becomes an issue for a burning Grasshopper move. As it seems quite unlikely anyone would use that, there seems little harm in excluding it. Just for uniformity with other continuation legs. It is easy enough to add it through ab, while it would be very hard to exclude it.
the description there doesn't match up with the explanation that I recall being given to me.
Well, I tried to generalize it. But I think I blew it, because I was thinking in terms of steps rather than moves when I wrote it.For the conventional 'orthogonal planar move', which we would write here as [vR.sR], the point is that the steps set up a grid (in this case containing every board square), and that you only have to consider what is on that grid. But (on an empty board) every square of the grid could be reached by zero-or-one move of the first kind plus zero-or-one move of the second kind. The area spanned by the move (which must be empty) consists of all squares that could be reached by fewer or shorter moves of both kinds.
I used the dot because I saw it as a multiplication. A comma could also be suitable, if you see it as coordinates.
The Ubi-Ubi is of course a sick piece. The problem is that the current implementation of the I.D. tabulates each angular realization of a given move, and for multi-leg moves that can freely change direction that quickly explodes. Even the Tenjiku area move, (a)2K, produces some 500 trajectories.
Good question. It makes less sense to exclude it here. OTOH, normally this square has to be empty, or it would have blocked the move. So it only becomes an issue for a burning Grasshopper move. As it seems quite unlikely anyone would use that, there seems little harm in excluding it. Just for uniformity with other continuation legs. It is easy enough to add it through ab, while it would be very hard to exclude it.
Well, I tried to generalize it. But I think I blew it, because I was thinking in terms of steps rather than moves when I wrote it.For the conventional 'orthogonal planar move', which we would write here as [vR.sR], the point is that the steps set up a grid (in this case containing every board square), and that you only have to consider what is on that grid. But (on an empty board) every square of the grid could be reached by zero-or-one move of the first kind plus zero-or-one move of the second kind. The area spanned by the move (which must be empty) consists of all squares that could be reached by fewer or shorter moves of both kinds.
I used the dot because I saw it as a multiplication. A comma could also be suitable, if you see it as coordinates.
The Ubi-Ubi is of course a sick piece. The problem is that the current implementation of the I.D. tabulates each angular realization of a given move, and for multi-leg moves that can freely change direction that quickly explodes. Even the Tenjiku area move, (a)2K, produces some 500 trajectories.