I assume you mean draw from the center of one edge of the square, not the center of the square, itself, leaving 3/4 and 1/4 squares. If so, I really like your idea and can't believe I've never run across it before. Probably the only concern with it is that most maps are mostly square to the world, with an occasional diagonal and the shift occurs at an even square interval. That's easy enough to adjust, it just takes some thought.Final note: when using a grid, you should also draw from the middle of the square when drawing diagonals to keep the same effect. Otherwise you have a lot of unusable half-squares.
I don't see how this would solve the problem with lateral movement. It'll still be offset. I haven't actually used offset squares, but it seems like they might actually bring more of the cons for each option than the pros. You don't even get the 2/3:1/3 hex option for square lines, so you must use half spaces.Having said that, offset squares is probably the best of both worlds, hex and squares. They are virtually identical to hexes, but they are squares. Hence, they often fit quite well in square or rectangular shaped rooms (although that isn't actually a real problem with hexes, but some players could get confused).
OK. This is, in fact, true. The 3.5 templates didn't really bother me, but I'll grant that they weren't always intuitive. Firecubes suck, though.One other advantage of hexes, other than the partially diagonal movement one, is that of spells with a radius. Pick an intersection between 3 hexes and count out in all directions the radius of the effect. Squares are kind of wonky when it comes to Fireballs. This advantage also works in offset squares.
I would allow diagonal movement between enemies, but I'd be fine with a ruling that went the other way.Do other people have an issue with this? This was initiated by a player. Two PCs were diagonally adjacent, and an enemy moved up and tried to pass between them. The player declared the creature couldn't pass them diagonally. I didn't mind the the idea (and didn't want to look it up), so I let is stick. And reinforced it the next time a PC tried the same move. Now that is counts against them the other players don't like it.
How do others feel about this?
Hex grids just look so hideous if you are in a square room. all those 1/2 hex just magically unusable.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.