'Hexes', hexagons, and tessellation patterns.


Pathfinder Online

Goblinworks Executive Founder

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I figured from the description of how territory would be divided that the territory control areas would be tiled as regular hexagons, with a settlement hex taking up exactly the same amount of room as a POI hex or any other hex. I just now challenged that assumption; there is no need for every unit of territorial control to have the same shape and area, not even in the abstract math.

For example, a 3-4-6-4 semi-regular tessellation could cover the entire world, with the hexagons being settlement, escalation, or theme park locations and the squares and triangles being POI, wilderness, or other lesser locations. Or a 4-6-12 SRT could be used, if the lack of a border between the triangles and the largest areas was deemed a problem.

In terms of gameplay, the difference is subtle, and mostly comes down to the fact that the lesser areas are arranged such that more than one 'settlement' location has equally good claims on it based on location, instead of each settlement having a number of 'natural' areas closer to it than to any other settlement site and relatively few 'contested' locations.

Either tiling can be adapted to an existing hex tessellation, by arranging and resizing such that each vertex of a hex of the original map corresponds 1-1 with the center of a square in the new map. Roads can exist on the 'lesser' regions and be straight for long sections.

With some math work, a tessellation could be made that did not conform to the mathematical definition of 'regular' that met additional gameplay requirements; among the possibilities is that expanding the map when map expansion is desired need not continue the pattern used previously, although the border between one pattern and a different one would probably be strange and very irregular.

Goblin Squad Member

I would wish it were less regular. If we could come up with a useful algorithm that would accommodate shifts in tessellation, perhaps depending on terrain type, then the world might appear more natural and adaptable to the realistic terrain depicted in the reveal of generated landscapes of the Making Movies blog.

Goblin Squad Member

triangle grid inside the hex

Goblinworks Executive Founder

The terrain is not determined by the political boundaries; the political lines will appear only in the political view.

Goblin Squad Member

Presuming that the curvature of Golarion is not sufficient to make substantial positional inaccuracies due to map projection, I believe there is an issue with the regular auto-generation of expansion hexes as the playable area of PFO expands. I seem to remember one of the devs concerns is the time required to generate detailed additional territory as EE expands into OE and beyond. Having multiple geometries for area mapping may be an example of diminishing returns. Xaer's suggestion of a triangular grid inside a hex makes an alternative map area pattern possible. However I think that there are practical problems of having six 60 degree angles at each vertices rather than the three 120 degree angles when calculating into which area characters enter when crossing from one area to the next.

Goblinworks Executive Founder

I somewhat dislike having two areas which touch only at the corners, which rules out any uniform triangular tessellation. I'm not strictly opposed to using irregular polygons, but I don't think concave areas are a good idea.

Goblin Squad Member

DeciusBrutus wrote:
The terrain is not determined by the political boundaries; the political lines will appear only in the political view.

Terrain often dictates political boundaries.

I understand 'diminishing returns' is an effective objection to my preference.

Goblin Squad Member

example of triangle grid

Goblinworks Executive Founder

Xaer: What would be the practical effect of the triangle grid subdivision?

Being: I would love it if there were natural-seeming features that also served as political boundaries but were also balanced in the metagame.

What I'm suggesting is a way to have a typical settlement border 12 locations that they have a claim to by proximity, but on average can only hold 5 of them due to competition with an equally good location.

This arose from looking at various possible embodiements of a PFO map and realizing that there was little territory that didn't obviously 'belong' to one settlement or another.

Goblin Squad Member

I am still holding out for more information. Estimates of distribution of settlement and PoI hex locations based on blog posts will be subject to change I'm sure. I would like to see PoI that are separate from settlement hexes so we could build a lone fort as a bastion against armies and hordes.

Goblin Squad Member

DeciusBrutus wrote:
Xaer: What would be the practical effect of the triangle grid subdivision?

I feel sure it is too late in development to change this core mechanic, but the hex system (as I understand it) is using "ownership as one big settlement structure in the middle of the central area. The footprint is already there (as seen in the flyover video), and the settlement footprints are pretty regular. Xaer's diagram link makes the hex more granular so either ownership could be shared, fought over or partial for some other reason.

It could be also that outlying hexes having a Point of Interest could have that PoI placed in other than a center location just for the sake of visual variety. Much more pleasing on the eye to see some irregularity as you move from one settle area to the next.

Goblin Squad Member

Hardin Steele wrote:
It could be also that outlying hexes having a Point of Interest could have that PoI placed in other than a center location just for the sake of visual variety.

I agree entirely. The POI is the most important thing, not the hex boundary itself and its location should make sense given local conditions, not be forced into the centre of a hex. Which leads me on to my next point...

Is there any reason why political boundaries need to match hex boundaries? As long as the POI is within the area covered wouldn't it be expedient to give up a few yards of hex to say that the river/stream/path/whatever is the edge of your territory, if that would make the boundary obvious to all (I am assuming no loading screen here - that may be a big assumption). I'd also like the ability to stick up sign posts, flags or skulls on sticks etc to warn people that they are now entering the territory of X. Imagine a trip to Golgotha that starts at their border with a gibbet displaying the remains of "the last recipient of Golgothan justice"!

Goblin Squad Member

OFF THE WALL
The concept ot hex boundaries grow out of board gaming practices, just as d20 grows out of RPG simplifications. As GW moved from d20 to 3 d100 rolls. Consider, there may be need to move to other than hexes. THis is not a minimum deliverable. Start with hexes, but consider the argument below.

C0onsider that a lords (knight or baron) demesne consisted of farm, grazing, orchards, woods and forest lands. Often the forest was kings domain, but license was held but foresters and woodcrafters for specific harvest to maintain health forest (reducing boars/high carnivores; reducing dead wood). This is lower level of abstraction than GW seeks, but it informs what a higher level domain looks like. An Earl may oversee many barons, but their domains are largely plain/grassland/orchard/woods. They do not extend into forests, but other holders (forester) may be responsible for those.

Areas of control are not driven by hexes but but geography. For OE, I would like to see that.

Hexes are a start. But later I would like to seek domains defined by multiple triangles, based upon geography; say 18 sub triangles per hex with 15 to 36 triangles (or more) per settlement depending upon extended patrol/ control. Not only is "size of settlement dependent on "Influence" but physical size and number of buildings is based upon land controlled.

I understand this is extension beyond what GW is thinking. Pushing further, I would like to see companies to control. be responsible for expansion triangles (like a baron).

I would like to see real feudal responsibility support in design. "We control this land and must supply a knight, squire, and archer unit for that control. It return we get protection.

Lam

Goblin Squad Member

The shape of a 'region' only really matters if we are talking about rather large area. Given a sufficiently small unit by which land is divided, borders can become very organic given any regular tessellation.

Goblin Squad Member

EE can only do large areas. EE may not be much better. The finer grain I describe may note happen with this generation MMO. As compute power and network through put increase, smaller domains my happen. While wild concept may tackle my concept, it is not yet (2013) affordable.

Still, drop a bone for some to reach for?

Lam, seems I am a dreamer, not a cleric from the north west,

Goblin Squad Member

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DeciusBrutus wrote:

I figured from the description of how territory would be divided that the territory control areas would be tiled as regular hexagons, with a settlement hex taking up exactly the same amount of room as a POI hex or any other hex. I just now challenged that assumption; there is no need for every unit of territorial control to have the same shape and area, not even in the abstract math.

interesting thoughts and tesselations. The good ole' honeycomb still has some strong points though.

-can place settlement sites in 'irregular' patterns. ie not only every second hex, some places maybe 2-3-4 hexes deep border. Distribution of resources is irregular anyway so another 'imbalancing' parameter may be just fine.
-If a higher resolution is wanted, scale so that settlement site span 7 hexes (1 central, 6 peripheral) and use 4-5 deep borders between sites.
-no point borders anywhere
-every border is potentially equally important. While I like how the tesselations split "two front" and "three front" boundaries, it feels artificial once a settlement starts gobbling up the neigbouring territories. The "high resolution honeycomb" offers equivalent strategy opportunities while remaining adaptable.

all that said, it is not turn based strategy and battles will be for structures, not for moving lines in the sand.

Goblinworks Executive Founder

I feel that if equal-sized hexes are small enough that there are four or five of them between neighboring settlements, then either the POIs are too close together and things get crowded, or the settlements are too far apart. It's possible for both to be true.

In the game-theoretic perfectly balanced world, there would be bi- or trifold symmetry around the portion of each POI that is fought over. In a reasonably balanced implementation, it is only necessary that no settlement site had a significant positional advantage over many more POIs than any other settlement, OR that settlements with advantageous positions were more likely to be taken over by hostile players.

Goblin Squad Member

DeciusBrutus wrote:
In the game-theoretic perfectly balanced world, there would be bi- or trifold symmetry around the portion of each POI that is fought over. In a reasonably balanced implementation, it is only necessary that no settlement site had a significant positional advantage over many more POIs than any other settlement, OR that settlements with advantageous positions were more likely to be taken over by hostile players.

I'm not convinced that having a balanced world is necessary or even desired. Less than random resource distribution (so no settlement has access to all resources - thereby forcing trade) might be a more important part of the world generation.

The worst settlement sites can be expected to have 6 bordering hexes where POIs can be placed. More advantaged sites will have additional claimable hexes beyond that, but they still have to be cleared before claiming (with an Influence cost). Any alliance of companies that tries to take an advantaged site and doesn't have the strength to capitalize on the extra hexes... well, they'll be a target for someone else.

The smallest settlement sites might have some inherent weakness, but their companies won't be tying up all their Influence in land claims - which means they might develop strong positions through other means.

Scarab Sages Goblin Squad Member

I like the idea of getting away from pure hexes. I've always felt that hexes force a very strange, non-intuitive sense of "directionality" on a map. People are used to thinking in terms of forward, back, left and right (or at least I am). Turn 90 degrees on a square-based map, or some of the complex tesselation maps, and you can still easily go forward. Turn 90 degrees on a hex map, and you're suddenly tacking against the wind, moving forward-left then forward-right. It's less noticeable on a large scale map than on a 5- or 10-foot pattern, but to me, hexes still produce unsettling "preferred" directions of travel.

(Side Note: Pure squares have their own problem, making diagonal distances cumbersome to calculate. Unfortunately, octagons require a complex tesselation or leave gaps in the map. Hexes, as far as I can tell, are a compromise, more detailed than squares, but still regular and equal-area. Ruler-based movement on a grid-less map produces the free-est movement, but it's more cumbersome than counting polygons.)

I also like the idea of breaking the world into small enough grains that edges can follow terrain. A mountain space could extend in odd directions away from the summit. Rivers, hills and lowlands could form the boundaries of plains spaces. It would be pretty neat to explore a map without easily-predicted boundaries, discovering the extent of your new holdings as the jagged lines are revealed on the map. It would be less novel after the area has been mapped, but having odd control boundaries could lend itself to really unusual military actions.

Squares and hexes reduce complex terrain to an abstraction that's easy for people to manage. Computers don't necessarily need the same degree of aabstraction. EE probably wouldn't be the best time to start with complex, irregular polygons, but terrain that started as hexes could theoretically be subdivided later on.

Goblinworks Executive Founder

Urman wrote:
DeciusBrutus wrote:
In the game-theoretic perfectly balanced world, there would be bi- or trifold symmetry around the portion of each POI that is fought over. In a reasonably balanced implementation, it is only necessary that no settlement site had a significant positional advantage over many more POIs than any other settlement, OR that settlements with advantageous positions were more likely to be taken over by hostile players.
I'm not convinced that having a balanced world is necessary or even desired. Less than random resource distribution (so no settlement has access to all resources - thereby forcing trade) might be a more important part of the world generation.

Perfectly random isn't nearly even enough. There should be little or no random element in the placement of anything:

In the days when Sussman was a novice, Minsky once came to him as he sat hacking at the PDP-6.

“What are you doing?”, asked Minsky.

“I am training a randomly wired neural net to play Tic-Tac-Toe” Sussman replied.

“Why is the net wired randomly?”, asked Minsky.

“I do not want it to have any preconceptions of how to play”, Sussman said.

Minsky then shut his eyes.

“Why do you close your eyes?”, Sussman asked his teacher.

“So that the room will be empty.”

At that moment, Sussman was enlightened.

Scarab Sages Goblin Squad Member

Ommmmmmm. 10 goto 10. Ommmmmmmm.

Goblin Squad Member

Those egs in the OP look like magic eye/pain in the eye unfortunately to me, let alone comprehending their geometry.

Simple usually works best for containers if these hexes are a combination of: (1) Design (eg spatial management and scaling), (2) information containers on all sorts of things (resources) and (3) technological load balancing and art assets existing etc.

Maybe someone can correct me if I'm wrong on that, but my gut feeling is I think simple = most useful to stack/scale containers? Is that the principle with hexes/boxes?

I think the designers will have to shape the land according to "what is a natural land at least in mmo proportions eg hills = mountains, a 2 dozen buildings = a town and some random trees clustered = forest etc, but where the hex lines are they maybe need to think about those borders and making the borders align with the natural visuals with a view to tactical consideration eg

- marching paths/road construction
- blockable features that make natural borders
- seemless transition and variety between "related hexes" of major biome type etc.

=

I'm wondering if hexes are so flexible that the devs can tinker with the map in the future adding/removing/altering hexes to whatever future unforeseen purpose also as the game plays out and things arise that could be detrimental in terms of the relationship between hexes eg unforeseen bottle-kneck that Ryan says wishes to avoid by comparison with EVE?

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