Hexagonal Tiles - Could this mean we get a true globe for a map?

[Oosh]

If you chuck in 12 pentagons in you can get a tessellation of the surface of a sphere. No more open cylinder or torus (i.e. donut) worlds!

This could open up new avenues of movement, but I think Ice may have to become a new obstacle type for movement penalties, and/or impassible without required tech. Submarines could go under Sea Ice, Planes (esp. Spy Planes which I'd love to see) can fly over it, etc.

Maybe even chuck its melting in there to echo real-life situations such as the opening of the Northwest Passage?

Edit: A Soccer ball is the most recognisable example of this, wiki has a pic (here) with more tiles, and you can keep increasing the number of hexagons but you only ever need 12 pentagons.

[Cashew]

I don't think any pentagons will be added to the game. It would be kind of confusing don't you think?

[avatarofentropy]

I second this notion. It would be very powerful map makers or modders to be able to choose the topology and tessellation of the world. That having been said, it would probably make the graphics, AI, and path finding much more complicated, so I don't anticipate seeing it.

[Jeffr23]

This is something I've been wanting in a CIV game since II. And pathfinding-wise it's not conceptually any harder than on a wrap-around world such as we already have seen (not that CIV AIs have ever been any great shakes at transoceanic journey-planning, but...)

It would probably make things easier if the twelve pentagonal plots were impassable and non-workable. Even if they had to make it so that none of them could ever be within 2 tiles of any settleable land (and thus never were part of any city's full radius), it'd still be worth it, although maybe not on the smallest maps...but a tiny map with spherical geometry isn't a good idea in the first place, really.

[lukeskymac]

Put the Pentagons on the poles and make them inaccessible.

[Jeffr23]

I think that they have to be evenly distributed around the sphere, alas. So one at each pole, sure, but the other ten wind up at 30 degrees N and S latitude in a pair of offset rings. If you do that kind of standard projection. A more involved map-script might apply the principles of the land-form conserving Dymaxion projection and force as many of them out to sea as possible (or generate the map around that requirement, even.), in which case the poles could be anywhere...

[Bob Ilyani]

Pentagons would kill the AI and pathfinding of the game. That being said, I'd love to see a fully spherical map, finally.

[Oosh]

I think that they have to be evenly distributed around the sphere, alas. So one at each pole, sure, but the other ten wind up at 30 degrees N and S latitude in a pair of offset rings.

That's correct.

But I don't see why 12 pentagons out of hundreds of tiles would cause much issue other than there maybe being a slight disadvantage to building your city on one.

Combinatorial Geometry is well studied and if they can't get AI to path-find around 12 pentagonal tiles on a pseudo-spherical surface in a turn-based simulation (not like it's real-time) then I'm not sure they deserve to be in the games business in 2010.

[Bigrusst]

Let's not get greedy. Hexs over squares is a great step forward. If the desginers can get a sphere to work, cool. If not, just a big ol' honkin ' huge hex maqp will suit me fine!

[Blue Oyster]

I see no reason for a few pentagons to affect the AI.

I would like to suggest that perhaps the few pentagons on a spherical map could be seen as assets to be coveted. I'm sure there are ways to exploit them to one's benefit.

[MadDjinn]

That's correct.

But I don't see why 12 pentagons out of hundreds of tiles would cause much issue other than there maybe being a slight disadvantage to building your city on one.

Combinatorial Geometry is well studied and if they can't get AI to path-find around 12 pentagonal tiles on a pseudo-spherical surface in a turn-based simulation (not like it's real-time) then I'm not sure they deserve to be in the games business in 2010.

yeah, there's too many very easily implementable pathfinding techniques for this to be an issue.

[Datames]

I second the motion that pentagonal squares would be advantageous.

Ensuring that they end up on Ocean squares (somehow) would be a fine with me. You could just make it an option:

1. Donut Map (No pentagons)

2. Spherical Map (Pentagons on ocean)

3. Spherical Map (Pentagons random)

I will also posit that worrying about the AI not being able to handle the pentagonal tiles is unnecessary.

[Bigrusst]

Well put.
As with so many of these ideas, its a matter of where they want to spend their developmental time and money. But I can't believe it would be all that big a jump from hexes to mixed hexes/pentagons to a full sphere globe.

[MadDjinn]

Can we mod the map?

[Blue Oyster]

I suspect, but cannot prove, that the 12 pentagons cannot occur with random position. (It seems to make sense if one studies a Truncated Icosahedron.) Perhaps someone knows the math to decide that one way or the other.

So anyway, if one wants pentagons in the ocean, then it's the ocean that must be put under the pentagon, and not the pentagon in the ocean.

[Oosh]

See: Post 8.

Does nobody read threads before commenting these days?

[Trias]

Actually, the pentagons do NOT have to be distributed evenly per se. You could for example put 6 pentagons at each poles and then have an arbitrary number of rows of hexagons (of 5 each) in between. This obviously lands you with a very weird type of map, since the wrap length around your "equator" will be 5. But there are plenty of other configurations each leading to a slightly different geometry.

There are at least two parameter to play with (the height and wrap length of the middle band of hexes approximately.). But I think there may be up to something like 10 parameters that fix different aspects of the geometry.

[eireksten]

Actually, the pentagons do NOT have to be distributed evenly per se. You could for example put 6 pentagons at each poles and then have an arbitrary number of rows of hexagons (of 5 each) in between. This obviously lands you with a very weird type of map, since the wrap length around your "equator" will be 5. But there are plenty of other configurations each leading to a slightly different geometry.

As I suspect people here are wanting a spherical map (true globe), and not a cigar, they are pretty stuck with where those pentagons should be placed.

There are two things that I don't like about that idea:

1) The sudden pentagon appearing on the map will be weird. It distorts the map, and you suddenly get city sites that contain less adjacent tiles. And how to easily recognize where they are?
2) The shortest path between two tiles will be unintuitive for the human player (just as the shortest flight route for planes are curved on the world map). Unless of course you zoom out to globe view and see it from there.

I don't think the benefits of having a true globe will outweigh the confusion the average player will get from this.

Now that I think of it. What exactly are the benefits of having a spherical map? Other than that "it is cool" and "that's how the real world is"? Does it add anything to the gameplay?

About the AI path finding: That's an almost trivial task that doesn't even need any form for computational geometry. Perhaps slightly more difficult when you'll want to take a longer route to avoid some enemy military or something, but that doesn't have anything to do with the pentagons. From a systems engineering point of view, the challenges related to such a change is completely different from path finding (mind, they do exist).

[Trias]

As I suspect people here are wanting a spherical map (true globe), and not a cigar, they are pretty stuck with where those pentagons should be placed.

Well, you can get anything in between as well. There is a simple two parameter family of "oblated spheres" that can reproduce anything from a cigar (all pentagons at the poles) to a regular sphere (even spaced pentagons) to a flat double disc (10 pentagons at the equator.) The earth actually is an oblated sphere with the radius at the equator larger than at the poles.
The parameters are akin to setting the height and width of a normal cylindrical map.

The geometry of the map basically determines where the pentagons appear. If you dont really care about faithfully reproducing the geometry of the sphere but are satisfied with just reproducing the topology, then you actually have quite a bit of freedom to choose where the pentagons appear.

[slowtarget]

The biggest problem with supporting a truly spherical map isn't really so much in problems with pathfinding or the "demotion" of pentagon tiles, but the fact that the map would always need to be in "globe mode". If you add those pentagons, there's no way to make a flat map that is sensical.

So, that would mean that you'd always have to do the full spherical transforms to display tiles, landforms, units, cities and so forth. CivIV optimized the local views by not doing full 3D renders of the tile and landforms on it. You'd have to give up this optimization.

Yes, I think it'd be cool to play on a real globe where I can send my troops on Great Circle routes over the poles, but you have to realize it comes at a cost, and that cost would most likely be paid in smaller maps and fewer simultaneous players, a thing many people are begging to increase.

[Trias]

The biggest problem with supporting a truly spherical map isn't really so much in problems with pathfinding or the "demotion" of pentagon tiles, but the fact that the map would always need to be in "globe mode". If you add those pentagons, there's no way to make a flat map that is sensical.

So, that would mean that you'd always have to do the full spherical transforms to display tiles, landforms, units, cities and so forth. CivIV optimized the local views by not doing full 3D renders of the tile and landforms on it. You'd have to give up this optimization.

Yes, I think it'd be cool to play on a real globe where I can send my troops on Great Circle routes over the poles, but you have to realize it comes at a cost, and that cost would most likely be paid in smaller maps and fewer simultaneous players, a thing many people are begging to increase.

Well, at least those costs don't really scale with mapsize or number of players. Moreover it is cost that should be paid mostly by the GPU, so on a machine with a sufficiently able graphics card it should not in anyway hamper the ability to run large maps/many players.

On the other hand there are a whole bunch of other optimalisations you can do that exploit the map being truly flat. For example in pathfinding routines, but also in the map data. The cost of these are generally smaller, but do consume extra CPU time/memory and also scale with mapsize/number of players.

[slowtarget]

Well, at least those costs don't really scale with mapsize or number of players. Moreover it is cost that should be paid mostly by the GPU, so on a machine with a sufficiently able graphics card it should not in anyway hamper the ability to run large maps/many players.

That's exactly the cost I'm talking about.

Remember how many people had to upgrade their machines in order to get graphics cards that ran CivIV well? CivIV didn't do full 3D renders of the world. It did 3D renders against a bumped plane with pre-rendered shadows.

Is it really worth forcing everyone to upgrade their computers yet again in order to have a "sufficiently able graphics card" that can do full 3D renders of tiles that are not only bumped, but dynamically lit and shaded, and rotated and tilted to conform to the sphere?

[Blue Oyster]

What exactly are the benefits of having a spherical map? Other than that "it is cool" and "that's how the real world is"? Does it add anything to the gameplay?

I think adding realism can add to gameplay. It's unrealistic to forbid pedestrians, missles, aircraft, and submarines from crossing the poles, and artificially reduces the range of some units.

[Oosh]

I know I kicked this off, but I freely admit I'm reaching the edge of my knowledge on the subject, so can someone tell me if the use of an Azimuthal projection around the centre of the screen (cropped down to a rectangle) would work for flattening out our globe during close-up play?

I appreciate the hexagons will increasingly deviate from being regular the further from the centre of the projection they are, but on a large enough sphere surely this could still allow the view of a reasonable amount of flat landscape, until further zooming out forced the display of curved surface?

[Ainvar]

That's exactly the cost I'm talking about.

Remember how many people had to upgrade their machines in order to get graphics cards that ran CivIV well? CivIV didn't do full 3D renders of the world. It did 3D renders against a bumped plane with pre-rendered shadows.

Is it really worth forcing everyone to upgrade their computers yet again in order to have a "sufficiently able graphics card" that can do full 3D renders of tiles that are not only bumped, but dynamically lit and shaded, and rotated and tilted to conform to the sphere?

Ya go to Best Buy and buy a gpu $30 to $60 it should play the game just fine. Upgrading a computer is not that Hard. Buy a how to book

Every few Months there something Faster something Better and your system. A system can be out dated in 2 years. If your system over 5 years old Mybe it a good idea to buy a New system. Computers are not TV where you have for 15 years with out updates.

Every few years system are 2x as faster. Right now windows xp is slowly becoming outdated.

[Leokoko]

Maybe a silly remark, but can't we have a map with "square" of hex tiles that loop at the borders to represent a "spherical" map?

This way, no tile has a preferred position.

[Procylon]

My bet is that the map will be spherical with a no-man's land at the poles. You will be able to land on the edge, but it will never be a viable route to move troops over.

The only true importance for movement in the polar region has been submarines, and we really won't be loosing a whole lot by having them go around.

And despite not having any pentagons on the entire map, if you zoom out I am quite sure that you will see a globe just as you do in Civ 4.

[Oosh]

Maybe a silly remark, but can't we have a map with "square" of hex tiles that loop at the borders to represent a "spherical" map?

This way, no tile has a preferred position.

No. What you're describing actually turns out to be a torus (i.e. donut) not a sphere.
See: http://en.wikipedia.org/wiki/File:Torus_cycles.png

You can sort of do it with mostly squares, and triangles at the top and bottom of each column, but your squares vary in width dramatically and is really just a grossly deformed cylinder.
See: http://en.wikipedia.org/wiki/File:Us...equal_area.PNG

Edit: I was just thinking you could deform a cube in to a sphere, and get greater than 6 face by sub-dividing them with squares, but it'd be a hell of mess to get your mind around traversing the surface of.

[slowtarget]

Ya go to Best Buy and buy a gpu $30 to $60 it should play the game just fine. Upgrading a computer is not that Hard. Buy a how to book

You'd almost have a point if we were talking about Starcraft II or Bad Company II. Those are games that are aimed at more hard-core gamers who are used to performing system upgrades. Much of the Civ crowd is running older retail hardware, often with onboard Intel graphics instead of a dedicated GPU. Even if we assume they are perfectly fine with spending $50 (because, let's be honest, they're buying it from Best Buy not newegg) for an nVidia 8400, cracking open their Dell to squeeze the board into the slot, they'll only get decent performance out of CivIV.

But you're not talking about CivIV. You're talking about a fully rendered CivV with obligatory graphics improvements rendered in full 3D and transformed onto a sphere.

Those 8400 owners just paid $100 for a game to look "okay", and in exchange for this, you made a small number of users happy for getting their 3D rendered globe. As a software engineer, I'd say this is a poor trade off with very little value and a decent amount of risk. Better to make a game look really good while conforming to expectations than to add eye candy that makes the game look worse for others.

[Ainvar]

We can stay in the Age of Donky Kong or pacman for the rest of our lives or Upgrade systems. To me it sounds like Programers are trying to find ways to not use new system spec. That my View.

If you think Pentium 3 should be able to run civ 5 I think it time for people to open there eyes and buy a NEW SYSTEM. I think 3 4 year old system should not have a problem with Civ 5 unless it poorly built. After 4 years it a good idea to buy a new system. It will bring down the power cost. p4 where power Hogs. The newer computers can lower there Power if People are are just surfing the web.

[Dragatus]

I don't think any pentagons will be added to the game. It would be kind of confusing don't you think?

I expect they will have one Pentagon in the game.

[Spudmiester]

Really doesn't seem too complicated, and I would love to see this

And people, stop whining about your computers, a game from 2010 is going to need new hardware. Deal with it.

And the Pentagons could always have oceans or mountains on them if the AI couldn't handle it

[M.gunnerQuist]

The subject of spherical hex maps is of tremendous interest to me. I'm a huge fan of Civilization IV. Ever since I found out that Civ V will use hexagon tiles, I have been very curious as to whether or not they will employ spherical hex maps.

From what I've learned so far, I strongly suspect that this is not the case. If they were to use spherical hex maps, they would advertise this fact in a very big way.

Maybe a silly remark, but can't we have a map with "square" of hex tiles that loop at the borders to represent a "spherical" map?

This way, no tile has a preferred position.

Yes. This is no problem. This is the way it was with square tiles in Civ IV and I expect that it will be the same with hexagonal tiles in Civ V.

I know I kicked this off, but I freely admit I'm reaching the edge of my knowledge on the subject, so can someone tell me if the use of an Azimuthal projection around the centre of the screen (cropped down to a rectangle) would work for flattening out our globe during close-up play?

I appreciate the hexagons will increasingly deviate from being regular the further from the centre of the projection they are, but on a large enough sphere surely this could still allow the view of a reasonable amount of flat landscape, until further zooming out forced the display of curved surface?

Yes, you could use Azimuthal projection for "close-up" game play on a sphere of hexagons. But I would probably recommend a simple Mercator projection.

But all this discussion of spherical hexagon maps is moot. There is a fundamental problem with this design. It's not just that there would always be 20 pentagonal tiles at each dodecahedral vertex. Hexagons at the center of the icosahedral faces would be of a different size than the ones near the dodecahedral vertices. It would look strange to have land features, roads, and cities that were larger on some parts of the globe and smaller on other parts. There is a way to construct a spherical hex map with all of the tiles of the same size but the shape of the tiles become distorted near these same dodecahedral vertices. So not only would you have the problem of dealing with pentagonal tiles but you would also have the problem of strangely-shaped tiles that surround them.

Then there is the issue of map size. Small, low-resolution hex globes would be satisfactory for typical randomly-generated Civ games. But there is a large percentage of Civ fans who enjoy playing on global Earth maps. With a spherical hex map, the problem of map distortion at the poles would be solved. But in order to get the level of detail that fans would demand (i.e. enough detail to define the boot of Italy) would require a map that would contain at least a few hundred thousand tiles.

Believe me, I've thoroughly researched the subject.

Nevertheless, the decision to make this next version of Civilization with hex maps is a good one. It goes back to the roots of tabletop war gaming.

[Marthieu du Blois]

Dodecahedron, you're totally right.

I'm happy with the cylindrical maps, and the hexes are a huge improvement in themselves. I say let it be as it is, and be grateful for the devs to have what we have.