> If I take a plane, I can draw a 9x9 board on it or a 19x19 board on > it. I can also draw the previously mentioned circular / cylindrical > board on it. Could you explain how you propose to extract the topology > of these, given only the fact that I have drawn them on a plane?
excellent point. :) i overstated my point quite a bit. let me be more specific and more careful and say that if you draw a grid that completely covers the surface of, say, a torus, where every crossing point in the mesh represents a point on the board, you cannot hope to do so in a way that makes the board act like a board drawn with those same restrictions on, say, the surface of a sphere. there is torus-ness embedded in your game board that you can't remove. the same goes for a covering mesh on a projective plane, a sphere with two handles and one cusp, etc.. the topology of the surface is important. on the other hand, the full graph description of a board as a (V,E) set is all that is required to define a game board. in the other direction, there are (V,E) sets that can't be drawn such that the only intersections drawn are those that are board points while keeping the drawing on any one topological object. these will have to be drawn on a different topological object to have this property. i'll answer your objection by noting that if you draw the board as a covering mesh, you can definitely tell whether or not it was drawn on a cylinder or a torus or a sphere. s. ____________________________________________________________________________________ Don't get soaked. Take a quick peak at the forecast with the Yahoo! Search weather shortcut. http://tools.search.yahoo.com/shortcuts/#loc_weather _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
