I don't think the adjective supernumerary makes much sense for pieces that affect other pieces. The latter doesn't have anything to do with a number. In the context of chess engines I always use the term 'supernumerary pieces' to refer to the situation where you have more pieces of a certain type than were initially present, e.g. 2 Queens or 3 Knights.
The page does't really stress that how a piece moves and what it can do otherwise are really independent properties, which could be combined arbitrarily. E.g. you can have immobilizing Knights or Gold Generals. I would refer to this as 'additional powers' (as opposed to 'power of movement'). In the Interactive Diagram description I use the term 'influence' or 'spell' for affecting other pieces without moving the piece itself (like immobilizing enemies, or move induction in friendly pieces, or passive burning as in Tenjiku Shogi).
I agree that a Windmill fits best in the hopper class. Unless hoppers are considered a sub-group of an even broader class of pieces that could acquire moves through the presence of other pieces. (As opposed to riders, which only lose moves by the presence of pieces in their path, where it should be taken for granted that any piece would lose moves to a square occupied by a friendly piece.) Matts Winther's bifurcator pieces are examples of this, by changing direction at, just before or just after the first obstacle in their initial path. I always considered these pieces 'deflecting hoppers'.
In fact hopping is a somewhat independent property of leaping or riding; we have sliding hoppers as well as leaping hoppers (e.g. the equi-hopper), as well as mixtures like the Grasshopper (which starts riding, bot only leaps after the mount).
I don't think the adjective supernumerary makes much sense for pieces that affect other pieces. The latter doesn't have anything to do with a number. In the context of chess engines I always use the term 'supernumerary pieces' to refer to the situation where you have more pieces of a certain type than were initially present, e.g. 2 Queens or 3 Knights.
The page does't really stress that how a piece moves and what it can do otherwise are really independent properties, which could be combined arbitrarily. E.g. you can have immobilizing Knights or Gold Generals. I would refer to this as 'additional powers' (as opposed to 'power of movement'). In the Interactive Diagram description I use the term 'influence' or 'spell' for affecting other pieces without moving the piece itself (like immobilizing enemies, or move induction in friendly pieces, or passive burning as in Tenjiku Shogi).
I agree that a Windmill fits best in the hopper class. Unless hoppers are considered a sub-group of an even broader class of pieces that could acquire moves through the presence of other pieces. (As opposed to riders, which only lose moves by the presence of pieces in their path, where it should be taken for granted that any piece would lose moves to a square occupied by a friendly piece.) Matts Winther's bifurcator pieces are examples of this, by changing direction at, just before or just after the first obstacle in their initial path. I always considered these pieces 'deflecting hoppers'.
In fact hopping is a somewhat independent property of leaping or riding; we have sliding hoppers as well as leaping hoppers (e.g. the equi-hopper), as well as mixtures like the Grasshopper (which starts riding, bot only leaps after the mount).