this question rose out of interest of turn-based games, in which there mostly two type of tiling used: square-based and hexagon-based, and both have disadvantages. if you use squares, like in civ3, then moving diagonally always preferable over straight lines, if you use hexagons, like in civ5, then you cant move exactly on left-right axis or up-down. both problem would be solved if we use octagonal or dodecagonal tiling. problem: they doesn't exist in euclidean plane. so, is there any way to do that, like sacrifice straight lines and/or same sizes?
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2\$\begingroup\$ Does this answer your question? Why don't we use octogonal maps instead of hexagonal maps? \$\endgroup\$DMGregory– DMGregory ♦2022-07-15 13:21:47 +00:00Commented Jul 15, 2022 at 13:21
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There are unfortunately not many options to tile a 2-dimensional plane with regular polygons. If you want to use only one kind of tile, then you can use squares or hexagons. You can use triangles, but then you have up-facing triangles and down-facing triangles. And that's it, because any other tiling schemes require weird combinations of many different tiles with different, shapes, sizes or numbers of edges. Which is going to end in a confusing mess. So unless you want those confusing and unnatural tiling schemes be the main gimmick of your game, I would really recommend against them.
So there are really no good options besides squares or hexagons.
If you use a square grid, then you can fix the problem of diagonal moves being cheaper than orthogonal moves by making diagonal moves cost \$\sqrt2\$ (1.414) times as much. Which you can approximate pretty well while still keeping the numbers as small integers when you make orthogonal moves cost 2 points and diagonal moves cost 3 points.
And then there is of course also the out-of-the box option: Do not use tiles at all! Just let units travel arbitrary floating-point distances up to their maximum movement in any direction they want, and resolve collisions by checking for geometric collider intersection. There are not many turn-based video games which try this. The only one I can think of is the 2004 game Phantom Brave. But it is rather popular in tabletop wargames like Warhammer (both 40k and Fantasy). Some people also play Dungeons and Dragons that way.
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\$\begingroup\$ If I recall correctly, Skulls of the Shogun is another turn-based game (tactics style) that uses a continuous coordinate system. \$\endgroup\$2022-07-15 14:43:35 +00:00Commented Jul 15, 2022 at 14:43
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\$\begingroup\$ yes, i want confusing and unnatural tiling schemes. look for example at this upload.wikimedia.org/wikipedia/commons/thumb/1/11/…, this is exactly what i looking for. problem, it hyperplane, how to translate this to euclidean? i look at different projections youtube.com/watch?v=H7NKhKTjHVE , and almost all have big problem - more you move from center, more distorted it become. is there projection that looks more or less same anywhere you look? Klein-Beltrami looks good but its not plane. also apocalypses happens, now we at hunger stage \$\endgroup\$Патрик Стар– Патрик Стар2022-07-19 15:20:28 +00:00Commented Jul 19, 2022 at 15:20
