Last Saturday I received a very interesting email from Eric Sprague which was accompanied by an explanation of how he thought that movement and weapon ranges should be measured on a grid of offset squares. I thought that what he proposed was well thought out and with his permission I have reproduced it below.
Movement and Range on an Offset Square Grid
To calculate movement and range on an off-set square grid should be no different than a hex grid. I have recreated the diagrams from your book. (Figures B and D are just rotated 90 degrees.) I have added a blue line to show how you proposed calculating these. The numbers in red are how I would have calculated the same distance.
The same in hexes. These are the same as the off-set squares above to show the similarities.
Notice how I numbered in black exactly as you had above. In Figures A, B and C, in both off-set squares and hexes, the red line follows from one square or hex to the next without going astray. In Figure D the red line does not follow a distinct path but is more closely approximated by the red numbers.This makes a lot of sense, and I can see why he proposes these changes. In consequence, I thoroughly recommend anyone who wants to to use Eric's method in preference to that laid down in my book. From personal preference I will continue to use hexed and normal squared grids and avoid offset ones whenever I can ... but if I do use them at some time in the future, I will be using Eric's method of measuring weapon ranges.
Bob,
ReplyDeleteI agree this makes very good sense, and would be relatively easy to administer most of the time.
For cases like the example D, I'd suggest using a narrow stick, or a ruler held on edge, to determine through exactly how many areas fire passes.
It does seem a bit like the old school range stick, though!
Obviously, this could also be applied to land battles...
Regards,
Arthur
Arthur Harman (Arthur),
DeleteWhen I read Eric's suggestion, I had difficulty faulting his logic even though it dies not confirm to my original square-grid-derived 'up and across' method of counting distances.
Using a range stick? I've no problem with doing so, especially as it fits my Old School outlook/design philosophy.
All the best,
Bob
Ok, perhaps I missed this in your book, but why would you use the Blue lines to count distances? Of course one should use the red lines ... ???
ReplyDeleteAs we discussed before, the Blue lines correspond to what mathematically is known as the Manhattan distance: measuring distances on a street pattern resembling the lay-out of Manhattan (all strrets and avenues at orthogonal angles). It is a proper distance function, with all necessary properties for it being a distance metric, but why use it if you can somehow use Euclidean distance as well?
Phil Dutre,
DeleteHaving read Eric's suggestion, I cannot fault the logic of using a Euclidean method rather than a Manhattan one, even though in my heart-of-hearts I prefer the latter!
All the best,
Bob
I think there's nothing wrong if you want to use the Manhattan distance on a square grid, BUT then you should use it for movement as well ... mixing both types in a single game can produce some weird side-effects.
DeletePhil Dutre,
DeleteI agree. You can only use one method to measure movement and weapon ranges if you want to avoid confusion.
All the best,
Bob
My point is to find the shortest route between two squares on an offset grid. The grid is no different than a he grid. There, also, you attempt to find the shortest route.
ReplyDeleteUsing a range stick can help delineate the shortest route, but you are not counting each square (or hex) it passes though. Board wargamer's are used to doing this.
Eric
Eric Sprague (Eric),
DeleteI think that your explanation makes complete sense, but I still find grids of offset squares my least favourite type of grid. I see the idea of using a range stick or ruler to delineate the shortest spdistance between the centres of the grid squares quite appealing.
All the best,
Bob
Be careful! Using a ranged stick to determine what squares or hexes to count doesn't always work on a hexgrid. Your stick might go through hexes you don't need for counting the shortest path.
DeletePhil Dutre,
DeleteThanks for the warning. I saw using the stick or ruler as a means to help players delineate the shortest route on a grid of offset squares but not on other types of grid.
All the best,
Bob
It also doesn't always work on an offset grid. Depending on the configuration, you might count an additional square before moving to the adjacent row of squares to continue the counting.
DeletePhil Dutre,
DeleteI hadn't realised that, but I defer to your greater knowledge and understanding of the merits and limitations of the different types of grid. Thanks again for your contribution to this discussion.
All the best,
Bob
Bob,
DeleteI've sent you a little diagram by email. It's mostly a theoretical issue, I guess during actual gameplay it doesn't matter that much, since everyone is able to count the shortest path between 2 hexes or squares.
Phil Dutre,
DeleteThanks for your additional contribution to this discussion. I intend to use your diagram and note in a short blog entry that I hope to upload later today.
All the best,
Bob
What Mr Sprague is doing is to treat the off-set square system in exactly the same way as he treats a 'hex field'. He is prepared to ignore the slight dostortion of distance 'across the grain' of the array of squares.
ReplyDeleteI'm inclined to think I would adopt the same approach, just for the sake of simplicity. However, the distortion of distance 'across the grain' can be eliminated, largely, by using oblongs of side ratio 7:6 or 8:7 (or somewhere between). The long sides are parallel 'with the grain'. the short sides across it.
The is one further upside to this that might be worth bringing to mind: you can fit more oblongs across the table that way, fitting 8 where you had 7, or even 7 where you had 6, depending on their 'aspect ratio'.. That is why I recommend that the 'grain' go along the length of the table.
Archduke Piccolo,
DeleteI think that you and I have a similar understanding of Eric Sprague's suggested way of counting offset squares.
I can see why you recommend having the 'grain' of the grid of offset rectangles you use running along the length of the table. It must look aesthetically more pleasing as well as allowing you to fit more rows in.
All the best,
Bob