3 ms·
On the other hand, for movement along the 8 directions the distance is 41% short, for movement along the 4 main directions, the taxicab distance is 41% longer t
by rrobukef 6y ago
On the other hand, for movement along the 8 directions the distance is 41% short, for movement along the 4 main directions, the taxicab distance is 41% longer than the actual distance.
For a hexagonal grid, the distance is approximated by counting the number of cells of the shortest path. This has <10% relative error (IIRC) from the actual distance.
- alisonkisk 6y agoIf you take diagonals to be 1.5, then distances are <10% high. The half-short-side heuristic (sqrt(aa + bb) ~= a + b/2) makes taxicab very close to correct for non-square distance as well.
- rrobukef 6y agoBut only if you move multiple cells in one turn. If movement is restricted to one cell each turn, your field distorts. The same happens when you split your movements: For example: player A moves 6 each turn; player B moves 2 thrice in a turn. Conclusion: A outruns player B at speed (4,4)/turn vs (3,3)/turn. (For A d(4,4)=6; B has d(1,1)=1.5)
- aidenn0 6y agoYes, hex grids are better when the number of cells moved per turn is very small. Handling multiple moves in a single turn is easy either by doubling the movement points you get (then N/S/E/W is 2 points, diagonal is 3), or informally by treating every other diagonal move as costing 2 points.
- aidenn0 6y agoDiagonal moves equal to horizontal/vertical moves is horrible. I don't remember which D&D suggested that, but "circles" being square is just terrible.