Hex Grid vs. Square Grid

[halfeye]

Huh? How is that relevant to what I was talking about? I am not talking about rotating in place if that is what you thought. Form a triangle with 3 coins. Moving the triangle to the right 1 step is equivalent to 5ft of movement. Now by moving only 1 coin, leaving the other two where they are, invert the triangle and move it slightly to the right. How much movement does that cost? (the coin moves right 1 hex + up&right 1 hex or right 1 hex + downright 1 hex depending on the facing of the original triangle) I called it rotation because it is equivalent to a 60 degree pivot centered on/holding 1 hex constant.

I don't know whether it's relevant to your issues, however it is geometically true. From a hex of six triangles it's trivial to make a triangle of nine lesser triangles, or one from a partial hex of four triangles. If you can see your circles as hexes divisible into triangles, then you can do this, if not then you have to use the circles as the bases for triangles and build hexes, if you want to, from there.

[OldTrees1]

I don't know whether it's relevant to your issues, however it is geometically true. From a hex of six triangles it's trivial to make a triangle of nine lesser triangles, or one from a partial hex of four triangles. If you can see your circles as hexes divisible into triangles, then you can do this, if not then you have to use the circles as the bases for triangles and build hexes, if you want to, from there.

Ah, so you were talking about "a 3 hex triangle is defined as the 3 hexes that join at a shared vertex" which was assumed background information for anyone reading my post. I was talking beyond that about the consequence of a gray area in the movement rules when introducing a 3 fold symmetry space into a movement system that uses 6 fold symmetry. That gray area being the movement cost of a pivot to invert the triangle when maneuvering.

[halfeye]

Ah, so you were talking about "a 3 hex triangle is defined as the 3 hexes that join at a shared vertex" which was assumed background information for anyone reading my post. I was talking beyond that about the consequence of a gray area in the movement rules when introducing a 3 fold symmetry space into a movement system that uses 6 fold symmetry. That gray area being the movement cost of a pivot to invert the triangle when maneuvering.

I don't know what you're talking about here really, but it sounds as if what I was thinking of would translate into suggesting you pick the three or six fold symetry on the fly, depending on which makes movement easier to calculate.

[OldTrees1]

I don't know what you're talking about here really, but it sounds as if what I was thinking of would translate into suggesting you pick the three or six fold symetry on the fly, depending on which makes movement easier to calculate.

Look at the brown hexs. The 3 hexs represent a large creature and has 3 fold rotational symmetry (I will presume you will look up "rotational symmetry" if you are unfamiliar). The 7 hexes represent a huge creature and has 6 fold rotational symmetry. Everything I talk about from here on only applies to the 3 hex large creatures and is a direct result of their 3 fold rotational symmetry while living on a hex grid.

Now look at the red creatures. If the red creature moved from the left location to the right location that would be 5 hexes of movement (all 3 hexes moved 5 spaces )and thus 25ft.

But if we look at the green creatures we notice the 3 green hexes don't all move the same distance. One of those green hexes only moved 4 spaces unlike the other 2 green hexes that moved 5 spaces. At some point in the path the green creature pivoted 60 degrees around one of its hexes. How much movement would it cost total (20? 25? 3050?)?

Finally look at the blue and purple creatures. Consider the various step & pivot combinations they could use to negotiate the turn in the corridor.

This is a uniquely Large creature on hex grid result.

Now, where should I be clearer?

[Aotrs Commander]

Dungeon floor plans and combat on a square grid (because I have to draw it (and not just the actual map, the grid itself - I have only once draw a hex grid and it's not something I have time to care to repeat), plus the size issues and the fact that they map to square dungeons better).

Large scale mapping - no grid at all. Any distance the PCs are going to be travelling will be pre-calculated (if they decide to wander of in a random directionn, there will be larger problems with the game than mapping) and if it's my own games, the map is a digital CAD image where I can measure the distances as accurately as I need to, and local details are generally unecessary to map anyway outside of actual combat areas.

[Chronos]

You use digital CAD images, and yet you still draw all of your graph paper by hand?

[Aotrs Commander]

You use digital CAD images, and yet you still draw all of your graph paper by hand?

Who said anything about graph paper?

Nah, the DM's maps are CAD, but I draw the maps for the actual combats on what is essentially a A1 plastic wallet containing (various colours of) hand-drawn square grid.

(Strangely enough, I don't have room for an A1 printer in the house, or it would be even easier...)

Best idea I ever had, far better than any other solution were ever had.

[Lvl 2 Expert]

If you really want to mess with your players you could always pull an Escher-y disguise over the grid.





Instant confusion.

[OldTrees1]

If you really want to mess with your players you could always pull an Escher-y disguise over the grid.

Instant confusion.

That last one is a tessellation of irregular pentagons. Specifically is a square grid with some diagonal steps disabled.

[Lvl 2 Expert]

That last one is a tessellation of irregular pentagons. Specifically is a square grid with some diagonal steps disabled.

Jup. To be fair, it does still look pretty weird without the humans.

[OldTrees1]

Jup. To be fair, it does still look pretty weird without the humans.

It does indeed.

Now with the clear image, I can see how the conversion from 45 degree rotated square grid to pentagons resulted in 2 hex grids with 90 degree offset.

This is fun. The first one is a triangle grid with the triangles trisected into kites. This forms both the 4 corner intersections where 2 triangles meet side-to-side and the 3 corner intersections in the middle of each triangle. (Alternatively you could view this one as a hex grid with each hex divided into 6 kites.)

The second one has pentagons with 4 3corners and 1 6corner. Is that a hex grid with the inner hex of every 7 removed? I think so.

[Lvl 2 Expert]

The second one has pentagons with 4 3corners and 1 6corner. Is that a hex grid with the inner hex of every 7 removed? I think so.

I'm not sure. It might be. I can see it's (also) a triangle grid with each triangle split into three butterflies. The edges of the full triangles are ragged but rotationally symmetrical. Butterfly/color wise the "pointing left" and "pointing right" triangles are rotated versions of each other, not mirror images, and if you follow the pointing left ones up or the pointing right ones down the butterflies move one step clockwise with every step.

It's probably one of the more confusing examples of this kind of art I've seen. The pattern is pretty well hidden.

EDIT: O right, I haz the Gipmz.



This is it I think. Dividing lines starting from the middle of the triangles, shifted away from being perpendicular to the line they end up on, creating a windmill pattern.

Not the best grid for gaming perhaps. Although I do suddenly feel an urge to get myself one of those fancy tiled hallways.

EDIT again:

This is pretty much just the same thing as the shark, isn't it? Only those lines joined in the middle of the triangles. But same hexagon-triangle stuff going on.

Ah well, at least I can pretty.

[Asmodean_]

Well if you end up adventuring in a four-dimensional hypercube for some reason then square grids clearly have their advantages.

[halfeye]

Look at the brown hexs. The 3 hexs represent a large creature and has 3 fold rotational symmetry (I will presume you will look up "rotational symmetry" if you are unfamiliar). The 7 hexes represent a huge creature and has 6 fold rotational symmetry. Everything I talk about from here on only applies to the 3 hex large creatures and is a direct result of their 3 fold rotational symmetry while living on a hex grid.

What I was saying was that the grid could be thought of as like the hex in the middle of the seven hex "creature". As such, you'd probably give everything twice the moves, and have them move on the triangles, which are half the length (because 1/2 * 2 = 1)

Now look at the red creatures. If the red creature moved from the left location to the right location that would be 5 hexes of movement (all 3 hexes moved 5 spaces )and thus 25ft.

But if we look at the green creatures we notice the 3 green hexes don't all move the same distance. One of those green hexes only moved 4 spaces unlike the other 2 green hexes that moved 5 spaces. At some point in the path the green creature pivoted 60 degrees around one of its hexes. How much movement would it cost total (20? 25? 3050?)?

Finally look at the blue and purple creatures. Consider the various step & pivot combinations they could use to negotiate the turn in the corridor.

This is a uniquely Large creature on hex grid result.

Now, where should I be clearer?

I suspect we are entirely missing each other's points all the way along, no harm done and fun while it lasted, but probably no common point of reference either.

Well if you end up adventuring in a four-dimensional hypercube for some reason then square grids clearly have their advantages.

Sure, squares are also very good on a torus, but for a sphere you want hexes (and some pentagons that turn into irregular triangles on which you can draw irregular hexes).