H. G. Muller wrote on Thu, Nov 15, 2018 06:56 AM UTC:
Ah, OK, he uses 45-degree rotated coordinates.
In that case, that the example that shows a Knight can move from a8 to c6 indecates that the blue areas should merely be considered inaccessible squares, i.e. like they are occupied by an uncapturable obstacle that cannot be moved by either player. But as a Knight jumps, it will ignore such obstacles, and moves as if they were normal, unoccupied board squares.
Although it is obvious what orthogonal and diagonal means in this board topology ('through sides' or 'through corners'), it is not so obvious what 'outward' means. After all, a Knight cannot make just any move that consists of an orthogonal plus a diagonal step. One could use the generalization that the diagonal step must go through a corner of the cell that was not an end-point of the side through which it entered the cell; this would allow it to go straight ahead in a triangular cell. Another generalization would be that the diagonal step can only be made throug the corner(s) farthest away from the side through which it entered; for cells with 2less than 3 or more than 4 corners this would make a difference.
Ah, OK, he uses 45-degree rotated coordinates.
In that case, that the example that shows a Knight can move from a8 to c6 indecates that the blue areas should merely be considered inaccessible squares, i.e. like they are occupied by an uncapturable obstacle that cannot be moved by either player. But as a Knight jumps, it will ignore such obstacles, and moves as if they were normal, unoccupied board squares.
Although it is obvious what orthogonal and diagonal means in this board topology ('through sides' or 'through corners'), it is not so obvious what 'outward' means. After all, a Knight cannot make just any move that consists of an orthogonal plus a diagonal step. One could use the generalization that the diagonal step must go through a corner of the cell that was not an end-point of the side through which it entered the cell; this would allow it to go straight ahead in a triangular cell. Another generalization would be that the diagonal step can only be made throug the corner(s) farthest away from the side through which it entered; for cells with 2less than 3 or more than 4 corners this would make a difference.