Non flat maps (use pentagons and septagons on maps)

Non flat maps (use pentagons and septagons on maps)

[Jakob Ilves]

Hello!

The orbiter is back, and in this email I'm considering to take a trip to the moon...  And you are
welcome to join me on the ride...

One thing I've been tinkering with on paper and in Java for approx 10-12 years is to let strategy
games take place not only on a flat hexagon playfield but upon a playfield where you have
occasional pentagons and septagons thrown in.

For instance, there were a few strategy games written in the 80s (Task force games' "Cerberus" and
Game Designers Workshop's "Traveller") which uses hexagonal maps of planets where a few hexes were
replaced with pentagons, resulting in a playfield which topologically was a icosokaeder (20 sided
die).  That would be cool to use in Xconq (or any other computer strategy game as well).

Imagine the 32 patches making up a leather football to be a playfield for Xconq.  Ok, it would be
a heck of a small map but still.

Actually, by using septagons (7-sided "hexes") in clever ways it's possible to create a playfield
with "tubes" protubing out of or into playfield surfaces.  One can have a few large ikosaeders
tied together with bridging tubes.

Imagine such a playfield where you have various terrains laid out... wow!  Imagine the nightmare
of displaying the thing in a GUI.... ouch!  It's the latter part which I've been scratching my
head with.

In the nordic mythology, the world consists of one huge tree, the ash named "Yggdrasil".  With
such a playfields with pentagons, hexagons and septagons, "yggdrasil" can be played upon in Xconq
:-).

As I said, this was a trip to the moon.  Stay tuned.  I'll create some docs and images for you to
view with this.

Best regards

/IlvJa, about to be lost in space


=====
(Jakob Ilves) <illvilja@yahoo.com>
{http://www.geocities.com/illvilja}

Höstrusk och grå moln - köp en resa till solen på Yahoo! Resor på adressen http://se.docs.yahoo.com/travel/index.html

Re: Non flat maps (use pentagons and septagons on maps)

[Emmanuel Fritsch]

Jakob Ilves a écrit :
> 
> Hello!
> 
> The orbiter is back, and in this email I'm considering to take a 
> trip to the moon...  And you are welcome to join me on the ride...
> [..]
> Imagine the 32 patches making up a leather football to be a 
> playfield for Xconq.  Ok, it would be a heck of a small map but still.

You may enlarge it 
- each pentagone of your leather football is an inaceesible area. 
- each hexagone is divided into as many hexagone as you want. 
You may produce a simily spheric map.  


> Actually, by using septagons (7-sided "hexes") in clever 
> ways it's possible to create a playfield with "tubes" 
> protubing out of or into playfield surfaces.  One can 
> have a few large ikosaeders tied together with bridging tubes.
> 
> Imagine such a playfield where you have various terrains 
> laid out... wow!  Imagine the nightmare

More simple : juste plug the north of the map with the south, 
and you will have a cool toric univers. For multi player mode, 
it would warant more balnaced initial position, since with the 
present ice border, all position are not equivalent. 

a+
  manu

PS : 
septagons = heptagon ?
ikosaeders = ikosaeder ?

Re: Non flat maps (use pentagons and septagons on maps)

[Eric McDonald]

Hi Emmanuel, Jakob,

On Thu, 20 Nov 2003, Emmanuel Fritsch wrote:

> and you will have a cool toric univers. For multi player mode, 

> PS : 
> septagons = heptagon ?
> ikosaeders = ikosaeder ?

American lexicon:
  football = soccer ball
  ikosaeder = icosahedron
  toric = toroidal

Eric

RE: Non flat maps (use pentagons and septagons on maps)

[Brandon J. Van Every]

Emmanuel Fritsch
>
> More simple : juste plug the north of the map with the south,
> and you will have a cool toric univers. For multi player mode,
> it would warant more balnaced initial position, since with the
> present ice border, all position are not equivalent.

Yes, torus topologies aka "wraparound maps" are far easier, real world
doable solutions.  Forget true spheres.  They're big trouble.


Cheers,                     www.indiegamedesign.com
Brandon Van Every           Seattle, WA

Taking risk where others will not.

RE: Non flat maps (use pentagons and septagons on maps)

[Eric McDonald]

> Emmanuel Fritsch
> >
> > More simple : juste plug the north of the map with the south,
> > and you will have a cool toric univers. For multi player mode,
> > it would warant more balnaced initial position, since with the
> > present ice border, all position are not equivalent.

Xconq already supports east-west tori. If you join north and south 
as well, then you can get a sphere (depending on what type of 
folding you use). A sphere, while preventing someone from 
starting in a corner, can be a mess to deal with.

  Regards,
   Eric

RE: Non flat maps (use pentagons and septagons on maps)

[Brandon J. Van Every]

Eric McDonald wrote:
>
> Xconq already supports east-west tori. If you join north and south
> as well, then you can get a sphere (depending on what type of
> folding you use). A sphere, while preventing someone from
> starting in a corner, can be a mess to deal with.

Are you sure you don't mean that Xconq supports east-west cylinders, and
north-south-east-west torii?  A NSEW wraparound map is not a sphere, it
is a torus.


Cheers,                         www.indiegamedesign.com
Brandon Van Every               Seattle, WA

20% of the world is real.
80% is gobbledygook we make up inside our own heads.

RE: Non flat maps (use pentagons and septagons on maps)

[Eric McDonald]

> > Xconq already supports east-west tori. If you join north and south
> 
> Are you sure you don't mean that Xconq supports east-west cylinders, and

Yes. I had the correct topological space in my head but wrote 
the wrong word. A torus requires an additional aligned folding 
to create. And a sphere takes two anti-aligned foldings to 
create.

Eric

RE: Non flat maps (use pentagons and septagons on maps)

[Brandon J. Van Every]

Jakob Ilves wrote:
>
> For instance, there were a few strategy games written in the
> 80s (Task force games' "Cerberus" and
> Game Designers Workshop's "Traveller") which uses hexagonal
> maps of planets where a few hexes were
> replaced with pentagons, resulting in a playfield which
> topologically was a icosokaeder (20 sided
> die).  That would be cool to use in Xconq (or any other
> computer strategy game as well).

Oh fuck.  Dude, don't take this personally, but I want to seriously save
you from yourself now.  The primary reason I'm all but bankrupt is
because my 4X TBS game "Ocean Mars" is based on exactly such a hexified
icosahedron.  I thought with 11 years of 3D graphics experience it
wouldn't be any big deal to build such a thing, and it was.  YOU DO NOT
KNOW OF WHAT YOU SPEAK.  TURN BACK NOW.  Seriously, you can lose the
roof over your head going down this primrose path.  I've got $60K+ worth
of credit card debt to prove it.

The whole reason I went looking for other people's projects was to find
a more doable, interim prototyping effort to test some game design
ideas, before getting back to Ocean Mars sometime next year.

Now granted, it might have been more doable if I had adopted a very
coarse hex scale, instead of trying to model Mars at 10 km/hex scale.  I
was shooting for a map of 1.6 million hexes.  Much much smaller maps
actually run ok with unoptimized code.  But there are still decidedly
nontrivial issues of geometry projection, terrain texture mapping, and
stitching the mathematics together so that AIs can navigate the faces.
Realize that when traversing the topology of a real sphere, it's easy to
get lost!  Many directions are indeterminate, no matter how you hexify /
pentify them.

> Actually, by using septagons (7-sided "hexes") in clever ways
> it's possible to create a playfield
> with "tubes" protubing out of or into playfield surfaces.
> One can have a few large ikosaeders
> tied together with bridging tubes.

With such topologies, you're talking about a general nodal graph
implementation.  From an efficiency standpoint, you will need to
restrict the size of your map because each arbitrarily flexible node is
going to cost a lot more bytes than it would in an array.  Also search
algorithms have to be general purpose, they can't be optimized for the
special cases of rectangular or hexagonal arrays.  As long as you're
willing to settle for modest topologies, it's viable.  For instance,
Europa Universalis uses a freeform territory approach, and even though
it's fairly coarse the map of Earth feels huge.  One spends a lot of
time zooming in and out in that game, changing from the Eurpoean to the
New World theaters.

> Imagine such a playfield where you have various terrains laid
> out... wow!  Imagine the nightmare
> of displaying the thing in a GUI.... ouch!  It's the latter
> part which I've been scratching my head with.

Please... stop scratching your head.  You are wasting your time.  You
could spend weeks just *designing* this thing, on paper.  And you will
never, ever finish what you started.  You won't even make a dent in it.
I have Been There, Done That, the entireity of the past year.  And I
mean full time, not as a hobby project.  I know exactly how much labor
it's going to cost you.


Cheers,                     www.indiegamedesign.com
Brandon Van Every           Seattle, WA

Taking risk where others will not.

Re: Non flat maps (use pentagons and septagons on maps)

[Eric McDonald]

On Thu, 20 Nov 2003, Jakob Ilves wrote:

> In the nordic mythology, the world consists of one huge tree, the ash named "Yggdrasil".  With
> such a playfields with pentagons, hexagons and septagons, "yggdrasil" can be played upon in Xconq
> :-).
> 
> As I said, this was a trip to the moon.  Stay tuned.  I'll create some docs and images for you to
> view with this.
> 
> Best regards
> 
> /IlvJa, about to be lost in space

I think you should return to Midgard soon. :-)

Xconq, in terms of direction finding and the way maps are laid out 
in memory, is rather tied to hexes.

Interesting ideas though.

  Best regards,
   Eric

Re: Non flat maps (use pentagons and septagons on maps)

[Eric McDonald]

On Thu, 20 Nov 2003, Eric McDonald wrote:

> Xconq, in terms of direction finding and the way maps are laid out 
> in memory, is rather tied to hexes.

Actually, the memory layout is not a big issue. I was thinking of 
something else. Sorry.

Eric

Re: Non flat maps (use pentagons and septagons on maps)

[Stan Shebs]

Jakob Ilves wrote:

>Hello!
>
>The orbiter is back, and in this email I'm considering to take a trip to the moon...  And you are
>welcome to join me on the ride...
>
>One thing I've been tinkering with on paper and in Java for approx 10-12 years is to let strategy
>games take place not only on a flat hexagon playfield but upon a playfield where you have
>occasional pentagons and septagons thrown in.
>
Heh, not to be discouraging or anything, but I used up a bunch of dead
trees sketching out hex sphere algorithms around 1995, finally gave up.
Executive summary is that it's messy for geometry calculations (how
units are nearby?), messy for graphics (although 3D hw changes the
difficulty), and messy for AI. I then decided it was intrinsically
out of scope for Xconq, and went on to the next knotty problem. :-)

Ironically, the most plausible model was a pair of hemispheres; while
things are weird all along the seam, at least they're consistently
weird, and the player can plan for it.

Stan

Re: Non flat maps (use pentagons and septagons on maps)

[Jakob Ilves]

Hello!

(back in orbit! Back to the moon!)

--- Stan Shebs <shebs@apple.com> skrev:

> Jakob Ilves wrote:
> 
> >Hello!
> >
> >The orbiter is back, and in this email I'm considering to take a trip to the moon...  And you
> are
> >welcome to join me on the ride...
> >
> >One thing I've been tinkering with on paper and in Java for approx 10-12 years is to let
> strategy
> >games take place not only on a flat hexagon playfield but upon a playfield where you have
> >occasional pentagons and septagons thrown in.
> >
> Heh, not to be discouraging or anything, but I used up a bunch of dead
> trees sketching out hex sphere algorithms around 1995, finally gave up.
> Executive summary is that it's messy for geometry calculations (how
> units are nearby?), messy for graphics (although 3D hw changes the
> difficulty), and messy for AI. I then decided it was intrinsically
> out of scope for Xconq, and went on to the next knotty problem. :-)

Actually, I did not intend to use this pentahexahepta (PHH) world for Xconq, even if I think the
icosaeder (I checked the spelling ;-) would make sense with it's tradition in strategy boardgames.
 I've a dream of an empire/xconq like play by mail game where I would like to have these PHH
worlds in from the VERY start.  Not at an extreme granularity considering hexes, but still.

3D rendering actually not necessarely solve rendering the entire world.  It's easy to create PHH
worlds were the sectors (let's just call all hexes, pentagons and heptagons for "sectors") are
tied together in a topologically consistent way but still the entire world would be impossible to
render in a 3D model.  One could of course decide to only look at parts of the world and then let
the player put together a mental map himself.

Considering the 3d rendering of these things, if you attach a "tube" to a flat hex surface, is
that tube then going inwards (a tunnel) or outwards (a pillar) from the surface?  Topologically
they are equivalent, from a 3d rendering perspective they are not.  (and game mechanics as I see
itright now ONLY considers the 2d topology of things...)

But yes, as also Brandon pointed out there are tons of nasty obstacles (potential nightmares):
* AI would be a challenge (that's why I aim at PBM, there all players are human, hence no AI
needed.  Easy cop out for me ;-).
* How to render?  My plan right now is to let the player focus on the current sectors and then the
sectors within a certain radii is displayed as well, possibly distorted as needed.
* How to render the whole world?  Ouch!  Do I have to do that :-).  Seriously, I might "cut down"
the topological info for the whole world display, limiting the visibility of individual sectors. 
Or, I can use a flattened out, cut up map of the world.
* Economics of data storage.  Yes, it's a pain and my current prototype uses one Java object per
hex, per vertice and per edge, including links to all neighbor objects.  Lots of bytes per sector.
 But computer performance is getting cheaper and cheaper and so is memory...  Given my development
pace and Moores law, this memory usegae is not an issue ;-).

Why even do this?  I don't do it because it's hard.  I do it becaues it's darn impossible. (Ok,
that's a travesty of a quote I found on the NASA web site, I admit).  Mostly I want to create it
because I want to play it and it's too hard of a problem to expect anyone else create it for me.

(Brandon, I sincerely hope you get out of debt.  I also hope you manage to get together Ocean Mars
because it sounds like a very cool game!  Good luck with both!)

> Ironically, the most plausible model was a pair of hemispheres; while
> things are weird all along the seam, at least they're consistently
> weird, and the player can plan for it.
> 
> Stan

/IllvilJa, @ the moon 


=====
(Jakob Ilves) <illvilja@yahoo.com>
{http://www.geocities.com/illvilja}

Höstrusk och grå moln - köp en resa till solen på Yahoo! Resor på adressen http://se.docs.yahoo.com/travel/index.html

RE: Non flat maps (use pentagons and septagons on maps)

[Elijah Meeks]

"Xconq already supports east-west tori. If you join
north and south as well, then you can get a sphere
(depending on what type of folding you use). A sphere,
while preventing someone from starting in a corner,
can be a mess to deal with."

I assumed there was same way to do this in Xconq, but
I can't seem to find out how.  What's the procedure
for setting up a map up like this?

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RE: Non flat maps (use pentagons and septagons on maps)

[Eric McDonald]

On Fri, 21 Nov 2003, Elijah Meeks wrote:

> I assumed there was same way to do this in Xconq, but
> I can't seem to find out how.  What's the procedure
> for setting up a map up like this?

Make the width of the world area greater than its circumference.

  Hope that helps,
    Eric