interesting...
Different boards
It would be pretty hard to define how various types of pieces move, on such boards where not every cell is equivalent.

Some linear and circular moves are shown in here:
http://scrybqj.com/images_diversen/board_rect_tri_2_r1_moves.jpg
http://scrybqj.com/images_diversen/board_rect_tri_2_r1.jpg
http://scrybqj.com/images_diversen/board_rect_tri_1_r1.jpg