As an addition to a comment to a recent blog entry, Philip Dutré sent me the following note and diagram:
I must admit that I had not considered this possibility, but I think that it is worth sharing as it is a very useful addition to the discussion.
Dear Bob,
I've included a quick diagram below, showing a straight line on an offset grid. You can see that the distance between 2 squares is 6, but the straight line passes through 7 squares.
This happens in some particular situations, but I guess that in practice during the game, it doesn't matter.
Phil
I must admit that I had not considered this possibility, but I think that it is worth sharing as it is a very useful addition to the discussion.
Bob,
ReplyDeleteThe parts of the two squares through which the line passes, indicated by the red arrow, are vertically above/below each other, so don't - IMHO - count as two squares for horizontal movement purposes, if you see what I mean? I probably haven't expressed it very well.
In this situation I would have no hesitation in disregarding one of those squares and regarding the range as six squares. I think using some common sense in these sort of situations to disregard tiny fractions of squares/areas shouldn't be a problem - especially when playing solo!
Regards,
Arthur
Arthur Harman (Arthur),
DeleteI quite understand what you are explaining, and tend to agree with you. Using my 'up and along' method of counting, the distance is six squares.
All the best,
Bob
When I read through my copy of 'Gridded naval Wargames' (great read!), I admit I had to look twice and three times at the diagrams on p7 to figure out what was intended: count up then count across. Perhaps the addition of arrows might have helped? I don't know.
ReplyDeleteI still think my suggested rectangular cells would work and is simpler, however counter-intuitive in appearance. The reason is that the 'brick pattern' of oblongs in which the length to breadth ratio is 7:6 or 8:7 (or somewhere between) is topologically the same - for our purposes - as a field of hexagons. Ranges can then be counted simply from subject hex to object (shooter to target, say) in exactly the same way as one does with hexagons. hexagons.
Archduke Piccolo,
DeleteI'm pleased that you enjoyed reading my recent book.
In retrospect I agree that arrows would probably have made the diagrams easier to understand, but I didn't think so at the time. If I every revise the book, I'll look at changing that.
Your suggestion of a grid of rectangular cells does make sense and if it works better than offset squares, it is something that I ought to consider experimenting with.
All the best,
Bob
I think once you get past the look of the thing, you should find it works exactly the same as hexes. That is why I came up with the idea. As you yourself have observed, offset squares don't work quite the same (actually they would, if one were to ignore the slight distortion 'across' the grain).
DeleteArchduke Piccolo,
DeleteIt is an interesting concept, and I can see that it works. Persuading other people might - however - be somewhat more difficult without them seeing it in practice.
All the best,
Bob
Although this little anomaly does not matter in practice when counting distances, it might matter when determining line of sight. Rules might stipulate that line of sight can be blocked by intervening terrain in hexes/squares - and the line of sight itself might be defined by the line connecting the centres of the shooter's square and the target's square. Then you get the strange situation in which line of sight would be checked against 7 hexes, whereas the distance only is 6 hexes :-)
ReplyDeleteOn another note, there is analogy here with some algorithms used in computer graphics (this is not wargaming related :-)). When one wants to draw a sloped line on a screen that consists of square pixels, an algorithm has to decide what pixels to turn "on" to approximate the line as closely as possible. Some might think the solution is to color all the pixels that are intersected by the line, but this not the case. If you want to learn more, look up "Bresenham's line algorithm".
DeleteW.r.t line of sight: you might say "Oh, but we would only check against 6 hexes, not 7". But then the question is "what 6 hexes would you check against?". Indeed, the distance can be counted by proceeding through several different paths from starting square to target square, all ending in the same number of counted squares/hexes (in the diagram above, you can shift "lanes" at any time, still ending at the same counted number). But when checking LOS, you usually want a precise and unique path defined. The same problem might arise in a classic square grid as well.
DeleteDepending on how strict you want your rules to be (either as a ruleswriter or as a player who has to apply the rules), this might or might not be an issue.
A solution might be to consider "counting the distance" as a different procedure from "checking line of sight". Hence, the squares/hexes you use for counting the distance between shooter and target might be a different set of squares/hexes (even a different number) as those you use for checking line of sight. But I think many wargamers would consider this very counterintuitive.
DeletePhil Dutre,
DeleteWow! What a lot to think about.
Sorting out line-of-sight can be a nightmare, and one that will probably never be satisfactorily resolved. In my experience it has caused almost as many arguments across the tabletop as any other wargaming topic.
I often wondered how slopes created using pixels were generated. When looking at slopes at pixel level, the pattern of pixels used has always intrigued me.
As a wargame designer, I'd always try to avoid using any counter-intuitive game mechanisms if it is at all possible. It's difficult enough to get wargamers to do things that are obvious and logical!
All the best,
Bob
For rectangles to closely approximate to a hex grid, a ratio of 15:13 is very close to the exact solution. 7.5cm x 6.5cm might be convenient. (The required ratio of width to height is [2 divided by the square root of 3] = 1.154701 , in order for the centre of a rectangle to be equidistant to the centres of the surrounding six rectangles.)
ReplyDeleteNigel Drury,
DeleteThe 15:13 ratio is not that different from the ratio suggested by Archduke Piccolo, and seems to produce an interesting offset grid.
All the best,
Bob