Grids and curvature of a sphere
Hal Black
For those who use a cartesian grid to represent the map of the world,
how do you reconcile the curvature of the sphere? Namely, the following
problems and their consequences: (using the geography of the earth as an
example)
1) The distance to encircle the equator is greater than that to encircle
the arctic circle.
2) The north pole has several south exits. 8')
3) When using n-s-e-w in spherical coordinates, the "squares" where a
player can stand are not square (the e-w distance is shorter nearer the
pole). This has the consequence of "squares" being either o non-uniform
size, or nonaligned.
I've thought about it a great deal and I can't really come up with any
good solutions. Any ideas?
Richard Woolcock
Do you really WANT this much accuracy? I'm quite happy to have my world
as a box 5120x5120x40, with sea level at 20 on the z-axis, and the x and
y axis wrapping around at left-right and top-bottom respectively. Its
unrealistic, but easy to implement and fun to play in. If you really
insist on realism, then maybe you should base the mud around a single
island - or perhaps have a discworld if you're using a fantasy setting?
A truely spherical mud world would be interesting, but I'm not sure if
it would really add anything to the playability of the mud. What is
your objective in creating such a world?
KaVir.
J C Lawrence
Hal Black <hab...@vt.edu> wrote:
> For those who use a cartesian grid to represent the map of the world,
> how do you reconcile the curvature of the sphere? Namely, the following
> problems and their consequences: (using the geography of the earth as an
> example)
Simply: I don't.
> 1) The distance to encircle the equator is greater than that to encircle
> the arctic circle.
> 2) The north pole has several south exits. 8')
> 3) When using n-s-e-w in spherical coordinates, the "squares" where a
> player can stand are not square (the e-w distance is shorter nearer the
> pole). This has the consequence of "squares" being either o non-uniform
> size, or nonaligned.
> I've thought about it a great deal and I can't really come up with any
> good solutions. Any ideas?
There are many possible solutions, and many fairly well known gross
simplifications. I treat the world surface as the intersection of two
perpendicular cylinders. Thus all the "squares" per se are of the
same physical dimensions over the surface.
--
J C Lawrence Internet: cl...@null.net
(Contractor) Internet: co...@ibm.net
---------(*) Internet: cl...@under.engr.sgi.com
...Honourary Member of Clan McFud -- Teamer's Avenging Monolith...
Jon A. Lambert
On Tue, 14 Apr 1998 21:26:41 +0000, Hal Black spaketh...
>
>For those who use a cartesian grid to represent the map of the world,
>how do you reconcile the curvature of the sphere? Namely, the following
>problems and their consequences: (using the geography of the earth as an
>example)
[snip]
>I've thought about it a great deal and I can't really come up with any
>good solutions. Any ideas?
Perhaps the problem lies with your use of a Cartesian system. Why not
try a Polar coordinate system instead?
--
--/*\ Jon A. Lambert - TychoMUD Email:jlsy...@nospam.ix.netcom.com /*\--
--/*\ Mud Server Developer's Page <http://www.netcom.com/~jlsysinc> /*\--
--/*\ "Everything that deceives may be said to enchant" - Plato /*\--
Hal Black
Jon A. Lambert wrote:
>
> On Tue, 14 Apr 1998 21:26:41 +0000, Hal Black spaketh...
> >
> >For those who use a cartesian grid to represent the map of the world,
> >how do you reconcile the curvature of the sphere?
>
[and unsnip]
> > 3) When using n-s-e-w in spherical coordinates, the "squares" where
> > a player can stand are not square (the e-w distance is shorter
> > nearer the pole). This has the consequence of "squares" being
> > either o non-uniform size, or nonaligned.
> Perhaps the problem lies with your use of a Cartesian system. Why not
> try a Polar coordinate system instead?
If you use polar coordinates originating at, say, the north pole, with
the radial lines as the longitudinal lines, this mapping will break down
at the equator. It breaks down because past the equator, the
longitudinal lines start getting close to eachother again, eventually
converging at the south pole. On a polar plot, however, the radial
lines contine to get farther away from eachother past the circle
corresponding to the equator. Another solution - which I admit I hadn't
thought of - would be to use 2 polar graphs: one each for the northern
and southern hemisphere. That is a bit kludgy, because exceptions would
need to be made for edge effects along the equator. It might work,
however, if one could reconcile problem 3.
When using the polar coordinate system (or its 3-dimensional analogs,
spherical and cylendrical coordinates), the third problem still holds.
The great convenience of the cartesian system lies in the fact that its
"squares" are indeed square. The first benefit of this is that all
"squares" have the same area. The second benefit is alignment: because
all sides are the same size, it is easy to stack one row upon another,
and one column beside another. In polar coordinates, both of these do
not hold. One has to make a decision between having different-sized
"squares" (actually roughly trapezoidal in shape), vs same sized
"squares" (again, roughly trapezoidal) which don't align with
eachother. Both of these approaches have serious problems.
To clarify, when I talk about "squares," I mean "rooms" as you find on
most muds. I suppose one solution would be to do away with rooms
entirely and assign everything a spherical coordinate (or worse, a
closed contour in space). But this makes building rather difficult. It
is also non-trivial numerically to map a "sphere of view" or some such
to an arbitrary position in a spherical coordinate system. Keep it up
and pretty soon you are building a 3-d engine rather than a text-based
mud.
Thank you for your response, Jon.
Any other ideas?
D. B. Brown
> Hal Black wrote:
> >
> > For those who use a cartesian grid to represent the map of the world,
> > problems and their consequences: (using the geography of the earth as an
> > example)
> >
> > the arctic circle.
> > 2) The north pole has several south exits. 8')
> > player can stand are not square (the e-w distance is shorter nearer the
> > pole). This has the consequence of "squares" being either o non-uniform
> > size, or nonaligned.
> >
> > good solutions. Any ideas?
Quick note on what we're doing on Jormundgand:
The world as mapped is a cylinder. Players can't travel into the
arcitc zones -- yes this is a bit of a cop-out, but it does solve
the problem of representing a north or south pole.
Now, what isn't really coded yet, but what we're planning on doing
to solve the curvature problem is multiplying the distance traveled
east or west by a number determined by their distance from the
equator.
This solution has a couple of problems -- while it is mostly
consistant, it isn't perfect, and we have to draw up the map for
the world as a Mercator projection.
However, we may just stick with the purely cylindrical map, as
honestly, who would care enough that the world is spherical as
opposed to cylindrical?
--
+=--=--=--=--=--=--=--=--=--=--=--=--=--=--=-+=--=--=--=--=--=--=--=-+
|Do you ever get the feeling that the story's|D. B. Brown |
|too damned real and in the present tense? |dbr...@stny.lrun.com |
| -Ian Anderson | "..." |
+=--=--=--=--=--=--=--=--=--=--=--=--=--=--=-+=--=--=--=--=--=--=--=-+
Jason Goodwin
In article <3533D491...@vt.edu>, Hal Black <hab...@vt.edu> wrote:
>For those who use a cartesian grid to represent the map of the world,
>how do you reconcile the curvature of the sphere? Namely, the following
>problems and their consequences: (using the geography of the earth as an
>example)
Well, there could be several different solutions :) Ever look at
a map that looks like someone cut a globe apart? :)
you can remove triangles from the northern and southern parts of
the grid, while mapping across the voids to the next grid space,
for instance
111111111
123456789023456789
1 * * * *
2 *** *** *** ***
3******************
4******************
5** *** *** *** *
6* * * *
The *'s represent the grid spaces, and the east exit in 3,1 would map
to 8,1. Thus, it'd be faster to go from 3,2 to 13,2, by first going
to 3,1 and then proceeding east. Not very pretty IMHO, but that's
the cost you pay. (I'm circumventing the issue all together because
_my_ world is flat ;)
A bigger problem would be how to simulate the horizon.
>I've thought about it a great deal and I can't really come up with any
>good solutions. Any ideas?
could go to a completely 3-d approach? Euler angles anyone?
Jason Goodwin
In article <353455...@dial.pipex.comNOSPAM>,
Richard Woolcock <Ka...@dial.pipex.comNOSPAM> wrote:
>Do you really WANT this much accuracy? I'm quite happy to have my world
>as a box 5120x5120x40, with sea level at 20 on the z-axis, and the x and
>y axis wrapping around at left-right and top-bottom respectively. Its
>unrealistic, but easy to implement and fun to play in. If you really
>insist on realism, then maybe you should base the mud around a single
>island - or perhaps have a discworld if you're using a fantasy setting?
Err, your world is shaped like a donut :) While keeping simplicity
in mind, perhaps you should have top and bottom wrap around to the,
er, top and bottom (top wraps to top, bottom wraps to bottom) Hmm,
it'd then still be shaped as some irregular spheriod, but what planet
is uniform anyways? :)
>A truely spherical mud world would be interesting,
Actually, the more interesting worlds IMHO wouldn't necassarily
be a sphere, Perhaps a mobius strip, or even the inside of a
sphere. (what would the horizon look like then hmm?)
Mike Davignon
There's no need to. Think about it. Most muds I have seen can be crossed
in a matter of 1-3 days (mud time, of course), depending on the size of
the mud. This would equate to a VERY small continent, or a VERY large
island. Either way, I have never encountered a mud large enough that would
need to encompass an entire planet. Even at the arctic poles, where the
circumference would be the least, it would still take at least that long
to travel completely around. When dealing with such a relatively small
area, a cartesian plane is sufficient.
D. B. Brown (dbr...@stny.lrun.com) wrote:
Cullen McGough
Hal Black (hab...@vt.edu) wrote:
: For those who use a cartesian grid to represent the map of the world,
: how do you reconcile the curvature of the sphere? Namely, the following
: problems and their consequences: (using the geography of the earth as an
: example)
<snip>
Consider the following....Most muds are set in some quazi midevil time
period. In our own little history, up untill fairly recently, a large chunk of
the population thought the world was flat, a disc, carried on the back of a
turtle and three elephants, floating in a endless ocean and so on. I'm not
saying start a discworld mud, but hey, you don't have to be a sphere.
Another option is use the 10 exit per room system (diagonals), you can get a
fairly smooth sphere that way, the larger the sphere, the smoother. (just like
real fractal geometry.)
-Cullen
darren...@hotmail.com
> Consider the following....Most muds are set in some quazi midevil time
> period. In our own little history, up untill fairly recently, a large chunk of
> the population thought the world was flat, a disc, carried on the back of a
> turtle and three elephants, floating in a endless ocean and so on. I'm not
> saying start a discworld mud, but hey, you don't have to be a sphere.
I think the key here is the people at those times believed these things. That
doesn't mean that's how the world was actually shaped or that the universe
revolved around the earth. You could create the belief in players minds that
the world is flat using good story telling but the reality of the design could
be any way you like. No amount of good coding can compensate for good
storytelling. :)
-Darren Doyle
-----== Posted via Deja News, The Leader in Internet Discussion ==-----
http://www.dejanews.com/ Now offering spam-free web-based newsreading
mor...@niuhep.physics.niu.edu
cmc...@bu.edu (Cullen McGough) writes:
>Consider the following....Most muds are set in some quazi midevil time
>period. In our own little history, up untill fairly recently, a large chunk
>of the population thought the world was flat,
You are welcome to go to soc.history.medieval and read one of the FAQ threads.
The consensus is that in medieval europe nobody who was educated thought
the world was flat, and there is no serious evidence that anybody else did
either.
Robert the killjoy
mor...@niuhep.physics.niu.edu
Somebody asked what a sphere does for the playability...
well, perhaps not playability but atmosphere... horizons, and how
they change as you gain altitude.
mdav...@pegasus.cc.ucf.edu (Mike Davignon) writes:
>
> There's no need to. Think about it. Most muds I have seen can be crossed
>in a matter of 1-3 days (mud time, of course), depending on the size of
>the mud. This would equate to a VERY small continent, or a VERY large
>island. Either way, I have never encountered a mud large enough that would
>need to encompass an entire planet.
My mud (in pre-alpha right now :) has hopes of being roughly 3000 x 3000
miles in dimension. (est. time line, another year to a 3 month 40x80 beta,
5 years to expand to final size :) That reaches from the artic
circle to the tropics.
This thread has set my mind percolating with the problems inherent with
a cartisian system.
>Even at the arctic poles, where the circumference would be the least,
>it would still take at least that long to travel completely around.
Errr, at the artic poles one can bike around the world in a matter of
single digit minutes. (just watched a member of a ice breaker crew do
just that)
>When dealing with such a relatively small
>area, a cartesian plane is sufficient.
In general true, but the mud community has a number of specifics that
don't fit in to that generality.
>D. B. Brown (dbr...@stny.lrun.com) wrote:
Richard Woolcock
Jason Goodwin wrote:
>
> In article <353455...@dial.pipex.comNOSPAM>,
> Richard Woolcock <Ka...@dial.pipex.comNOSPAM> wrote:
>
> >Do you really WANT this much accuracy? I'm quite happy to have my world
> >as a box 5120x5120x40, with sea level at 20 on the z-axis, and the x and
> >y axis wrapping around at left-right and top-bottom respectively. Its
> >unrealistic, but easy to implement and fun to play in. If you really
> >insist on realism, then maybe you should base the mud around a single
> >island - or perhaps have a discworld if you're using a fantasy setting?
>
> Err, your world is shaped like a donut :) While keeping simplicity
Hmmmm yeah I suppose it is...hadn't really thought of it like that before;)
> in mind, perhaps you should have top and bottom wrap around to the,
> er, top and bottom (top wraps to top, bottom wraps to bottom) Hmm,
> it'd then still be shaped as some irregular spheriod, but what planet
> is uniform anyways? :)
Well I want it to appear at least *fairly* realistic - besides, the
only time a z-axis wraparound would be used is if someone managed to
dig a hole through the 'bottom' of the mudworld, at which point they
would fall...and fall...and fall...
> >A truely spherical mud world would be interesting,
>
> Actually, the more interesting worlds IMHO wouldn't necassarily
> be a sphere, Perhaps a mobius strip, or even the inside of a
> sphere. (what would the horizon look like then hmm?)
I read a book somewhere (Deathgate cycle?) in which the world was
based around the inside of a sphere, with a sort of 'sun' floating
in the very centre of the sphere...wierd ;)
What would happen if you dug your way out? Would you be able to
walk around the outside of the sphere, or would you fall out into
space?
KaVir.
Joshua E Cook
Richard Woolcock wrote:
Arthur C. Clarke wrote about a world similar to this in his
_Rendevous_With_Rama_ series. The world is actually an alien spacecraft, with
a cylindrical shape, and everything of significance is on the inner surface.
A series of lights near the center turn on and off in order to simulate day
and night. There is even an 'ocean:' a wide band of water flowing around the
entire inner circumference. Imagine living in a world where you could look
upwards and see the curve of an ocean lying above you!
What happens on the outer surface of the sphere would depend on the mass
of the object, just like any other world. If it has enough gravity to hold a
body to it, then one could walk around on either the inner or outer surface.
Otherwise, you fly off into space.
This would be a very cool idea for a MU* world: A sphere with both an
inner and outer surface.
--Joshua E Cook
Hal Black
J C Lawrence wrote:
> Hal Black <hab...@vt.edu> wrote:
> > For those who use a cartesian grid to represent the map of the world,
> > how do you reconcile the curvature of the sphere? Namely, the following
> > problems and their consequences: (using the geography of the earth as an
>
> There are many possible solutions,
Would you mind mentioning a few of them or providing a reference?
> and many fairly well known gross
> simplifications. I treat the world surface as the intersection of two
> perpendicular cylinders. Thus all the "squares" per se are of the
> same physical dimensions over the surface.
That is an interesting idea. I'm not sure how you've managed to have
all the squares the same size, it seems like they will still be
pie-wedge shaped at the poles on each of the four surfaces, and
trapezoidal elswhere. I will experiment with that. Thanks for the
response.
Hal Black
D. B. Brown wrote:
>
> Hal Black wrote:
> >
> > For those who use a cartesian grid to represent the map of the world,
> > how do you reconcile the curvature of the sphere? Namely, the following
> > problems and their consequences: (using the geography of the earth as an
> > example)
>
>
> The world as mapped is a cylinder. Players can't travel into the
> arcitc zones -- yes this is a bit of a cop-out, but it does solve
> the problem of representing a north or south pole.
I don't think it's so bad of a cop-out. If you don't have players
travel to the polar regions, and the diameter of the cylinder is
sufficiently large compared to the height, you have an excellent
estimate of the equatorial band. All you have to do for your story line
is say that the arctic regions are *LARGE*, as in, taking up 80% of the
planet. Then, you can make the planet's diameter as large as you want
to make your world large, and still retain the relatively narrow band
that players can walk on. Thus, your estimate in the form of cylinder
will still hold.
[...]
> However, we may just stick with the purely cylindrical map, as
> honestly, who would care enough that the world is spherical as
> opposed to cylindrical?
Because you've already made the assumption that travel near the poles is
disallowed (which is a legitimate game decision), I would just leave it
a cylinder. It's close enough.
Thanks for the response.
Hal Black
Richard Woolcock wrote:
>
> Hal Black wrote:
> >
> > For those who use a cartesian grid to represent the map of the world,
> > how do you reconcile the curvature of the sphere? Namely, the following
> > problems and their consequences: (using the geography of the earth as an
> > example)
>
> as a box 5120x5120x40, with sea level at 20 on the z-axis, and the x and
> y axis wrapping around at left-right and top-bottom respectively. Its
> unrealistic, but easy to implement and fun to play in. If you really
> insist on realism, then maybe you should base the mud around a single
> island - or perhaps have a discworld if you're using a fantasy setting?
Of course realism isn't a neccesity for a mud. Your toroid is fine if
that is what you want to build. However, I want a sphere. 8')
> A truely spherical mud world would be interesting, but I'm not sure if
> it would really add anything to the playability of the mud. What is
> your objective in creating such a world?
My objective to be interesting 8') The fun is more in the creating of
the world than the playing of it (this is especially so for the
creator). I want a spatially oriented world for many reasons. I would
like a sphere specifically because I haven't seen it done, and would
like to try some new things, plus the sphere is the shape of all real
planets I know about. I claim it will be at least as playable and fun
and as a toroid or a flat map, and perhaps some more interesting
possibilities will arise as a result. It is beyond me to determine this
before it's implemented. (to ward off some comments, the playability of
course depends on a good implementation)
Innovation is good.
Hal Black
[I have rearranged the quoting to follow convention]
Mike Davignon wrote:
> > Hal Black wrote:
> >
> > For those who use a cartesian grid to represent the map of the world,
> > how do you reconcile the curvature of the sphere? Namely, the following
> > problems and their consequences: (using the geography of the earth as an
> > example)
>
> There's no need to. Think about it. Most muds I have seen can be crossed
> in a matter of 1-3 days (mud time, of course), depending on the size of
> the mud. This would equate to a VERY small continent, or a VERY large
> island. Either way, I have never encountered a mud large enough that would
> need to encompass an entire planet.
I am not making most muds. Most muds have already been made, so I don't
need to make them. I am making a specific mud that will be modeled
after a sphere which will certainly have more than one continent or land
mass. The idea here is to do something different, which may introduce
some new possibilities not seen before on most muds.
> Even at the arctic poles, where the
> circumference would be the least, it would still take at least that long
> to travel completely around.
No it wouldn't. If you stand one foot from the arctic pole, it will be
exactly 2*pi feet (under 7 feet) to walk west (or east) around the
planet and arrive where you started. I can travel 7 feet in a second if
I'm in a hurry. 8')
> When dealing with such a relatively small
> area, a cartesian plane is sufficient.
Again, the question I posed was not about a small area.
David Skidmore
On Thu, 16 Apr 1998, Richard Woolcock wrote:
> Jason Goodwin wrote:
> >
> > In article <353455...@dial.pipex.comNOSPAM>,
> > Richard Woolcock <Ka...@dial.pipex.comNOSPAM> wrote:
> >
> > >Do you really WANT this much accuracy? I'm quite happy to have my world
> > >as a box 5120x5120x40, with sea level at 20 on the z-axis, and the x and
> > >y axis wrapping around at left-right and top-bottom respectively. Its
> > >unrealistic, but easy to implement and fun to play in. If you really
> > >insist on realism, then maybe you should base the mud around a single
> > >island - or perhaps have a discworld if you're using a fantasy setting?
> >
> > Err, your world is shaped like a donut :) While keeping simplicity
>
> Hmmmm yeah I suppose it is...hadn't really thought of it like that before;)
>
> > in mind, perhaps you should have top and bottom wrap around to the,
> > er, top and bottom (top wraps to top, bottom wraps to bottom) Hmm,
> > it'd then still be shaped as some irregular spheriod, but what planet
> > is uniform anyways? :)
>
> Well I want it to appear at least *fairly* realistic - besides, the
> only time a z-axis wraparound would be used is if someone managed to
> dig a hole through the 'bottom' of the mudworld, at which point they
> would fall...and fall...and fall...
>
> > >A truely spherical mud world would be interesting,
> >
> > Actually, the more interesting worlds IMHO wouldn't necassarily
> > be a sphere, Perhaps a mobius strip, or even the inside of a
> > sphere. (what would the horizon look like then hmm?)
>
> I read a book somewhere (Deathgate cycle?) in which the world was
> based around the inside of a sphere, with a sort of 'sun' floating
> in the very centre of the sphere...wierd ;)
I believe these are known in Sci-Fi realms as Dyson(sp?) Spheres, and are very
interesting... The 'gravity' is generated via rotation, and if you were to
'dig through' the sphere, you would be open to the vacuum of space. However,
most seem to be man or other intelligence-created, as the outer hull is
generally metal, as far as I have seen. They even have air-locks, etc, so
spaceships can come and go.
> What would happen if you dug your way out? Would you be able to
> walk around the outside of the sphere, or would you fall out into
> space?
>
> KaVir.
Even more interesting is a series of books I read where everone lived on trees
that floated in orbit about a pair of suns. There were also giant speres of
water, etc, and there was air all the way around... I think the name was
Ring World, or something. Not sure if it'd make a good basis for a MUD
though... The trees were living, and so rooms as they grew older shrunk as
the tree grew back in on them, and each tree had a 'mouth' where our trees
have a root system, and people fed their dead to the trees. Somewhat odd, but
a neat story, as I recall.
--Raptor
Jason Goodwin
Hasn't shown up here, so I'll reply with a clarification by
using the previous post :)
On Thu, 16 Apr 1998, Richard Woolcock wrote:
> Jason Goodwin wrote:
> > Err, your world is shaped like a donut :) While keeping simplicity
> Hmmmm yeah I suppose it is...hadn't really thought of it like that before;)
>
> > in mind, perhaps you should have top and bottom wrap around to the,
> > er, top and bottom (top wraps to top, bottom wraps to bottom) Hmm,
> > it'd then still be shaped as some irregular spheriod, but what planet
> > is uniform anyways? :)
> Well I want it to appear at least *fairly* realistic - besides, the
> only time a z-axis wraparound would be used is if someone managed to
> dig a hole through the 'bottom' of the mudworld, at which point they
> would fall...and fall...and fall...
Err, here's what I meant. I'm assuming that your map would wrap
around from top to bottom and side to side like below, where the
arrows are. (I should've used north/south and east/west)
||
\/
********
********
->********<-
********
********
********
/\
||
What I meant to say, is that perhaps it should wrap like this,
where the arrows are.
______
| __ |
|| ||
\/ \/
********
********
->********<-
********
********
********
/\ /\
||__||
|____|
As in, if I go over the edge on the north, then I wrap around
by some offset, somewhere else in the north. This is one of
my pet peeves in the Final Fantasy series (and other games)
since they use the 1'st method, which means the world is a
donut :)
> I read a book somewhere (Deathgate cycle?) in which the world was
> based around the inside of a sphere, with a sort of 'sun' floating
> in the very centre of the sphere...wierd ;)
Well, there are a _lot_ of different novels involving the inside
of spheres :) In the old D&D setting, if one was to go through
the crust deep enough, they'd find that their world was hollow,
and served as a repository where the gods placed all the endangered
species/civilizations. (As a side note, at the center was a sun
which meant that it never set, so it was constantly noon.)
> What would happen if you dug your way out? Would you be able to
> walk around the outside of the sphere, or would you fall out into
> space?
Depends on the sphere. It could go on for an infinite distance :)
(Or, it could be a seperate world, completely alien to those on the
inside. In the aforementioned Hollow World setting, the poles were
really giant holes allowing access to the other side, though the slope
was so gradual no-one noticed. (in addition to the godly anti-magic
fields and unnatural fog which prevented all but the most determined))
Richard Woolcock
Hal Black wrote:
>
> Mike Davignon wrote:
[snip some stuff]
> I am not making most muds. Most muds have already been made, so I don't ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
I wish more people had this attitude!
> need to make them. I am making a specific mud that will be modeled
> after a sphere which will certainly have more than one continent or land
> mass. The idea here is to do something different, which may introduce
> some new possibilities not seen before on most muds.
Perhaps some sort of 3D coordinate-based system could work - but you would
have to drop the concept of 'rooms' if you did that. Do you want the world
to be a 3D object or a 2D plane which is spherical? Will the mud be the
entire game world, or just a single planet floating in space?
> > Even at the arctic poles, where the
> > circumference would be the least, it would still take at least that long
> > to travel completely around.
>
> No it wouldn't. If you stand one foot from the arctic pole, it will be
> exactly 2*pi feet (under 7 feet) to walk west (or east) around the
> planet and arrive where you started. I can travel 7 feet in a second if
> I'm in a hurry. 8')
Then you really will have to change movement from the typical n/s/e/w
approach - although you could still have such movement possible, eg:
]north 10
You glance at your compass.
You spin 37 degrees to your left and take 10 paces forward.
> > When dealing with such a relatively small
> > area, a cartesian plane is sufficient.
>
> Again, the question I posed was not about a small area.
Then you have a lot of work ahead! Good luck ;)
KaVir.
Richard Woolcock
Jason Goodwin wrote:
>
> On Thu, 16 Apr 1998, Richard Woolcock wrote:
>
> > Well I want it to appear at least *fairly* realistic - besides,
> > the only time a z-axis wraparound would be used is if someone
> > managed to dig a hole through the 'bottom' of the mudworld, at
> > which point they would fall...and fall...and fall...
[snip]
> What I meant to say, is that perhaps it should wrap like this,
> where the arrows are.
> ______
> | __ |
> || ||
> \/ \/
> ********
> ********
> ->********<-
> ********
> ********
> ********
> /\ /\
> ||__||
> |____|
>
> As in, if I go over the edge on the north, then I wrap around
> by some offset, somewhere else in the north. This is one of
> my pet peeves in the Final Fantasy series (and other games)
> since they use the 1'st method, which means the world is a
> donut :)
What you suggest would be a definite improvement, but it could also
prove very confusing. It's certainly worth looking into though,
thanks for the suggestion.
[snip rest]
KaVir.
Hal Black
Richard Woolcock wrote:
> Hal Black wrote:
>
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
> I wish more people had this attitude!
Heh, thanks, so do I.
> > need to make them. I am making a specific mud that will be modeled
> > after a sphere which will certainly have more than one continent or land
> > mass. The idea here is to do something different, which may introduce
> > some new possibilities not seen before on most muds.
>
> Perhaps some sort of 3D coordinate-based system could work - but you would
> have to drop the concept of 'rooms' if you did that.
I fear that you may be right about this. I would prefer to avoid
dropping the room construct because it allows for such convenient
abstraction. Without rooms, I would essentially have to build a 3d
engine. While this would be introduce some truly fascinating elements
of play, a 3d engine is not only nontrivial to implement, but also
resource-intensive to process. It is a difficult enough problem in a
Cartesian coordinate system, I suspect it would be a total nightmare in
a spherical one.
Even if there is no 3d object rasterizing involved (for display on the
screen), things like collisions and line-of-sight beg consideration.
For instance, when something happens, who witnesses it? And when
someone speaks, who hears it? With many players online at the same
time, this could consume a lot of processing power (and memory) better
used for other things.
> Do you want the world
> to be a 3D object or a 2D plane which is spherical? Will the mud be the
> entire game world, or just a single planet floating in space?
Hmm, I hadn't thought of multiple planets. I guess at this point I'd
like to keep it simple. I don't think there is much loss of generality
in defining direction relative to some point that corresponds to the
planet. A separate system could be used to deal with interplanetary
interaction. I think that having an intraplanet coordinate system would
keep things a lot simpler. For instance, it doesn't directly matter to
the player that he's moving very fast in orbit relative to the sun.
Plus it would be a royal pain to keep "absolute coordinates" of objects
on a moving planet. Then there are relativistic effects that start to
come into play. Oh, I don't even want to think about it 8')
So yes, consider the planet to be the entire game world. Of course,
the sun and perhaps some moons will exist that can be simply modeled in
a geocentric manner. This is important because those heavenly bodies
produce key atmospheric effects resulting from having a spherical
planet. I think it would be very cool to have an xearth-style display
of the sun's light on the mud planet (for my own viewing, not
necessarily for joe player). 8')
One of the things planned for the story line is a vast network of
underground caverns. Also, the world should not preclude buildings that
have more than one story. So yes, it would be a 3d model.
I was planning on worrying about the 3d portion after finding a
solution to the sphere problem. While it is true that the sphere's
surface area increases with radius, I think that the range of vertical
interest is sufficiently small to ignore this (this is analogous to the
cylindrical approximation of the sphere sufficiently close to the
equator that I spoke about in an earlier article.)
To implement height, I was thinking of using either an onion skin
model or absolute coordinates. I don't want to prematurely choose a
height solution lest it impose limitations resulting in a sub-optimal
solution to the more significant sphere problem.
> Then you really will have to change movement from the typical n/s/e/w
> approach - although you could still have such movement possible, eg:
>
> ]north 10
> You glance at your compass.
> You spin 37 degrees to your left and take 10 paces forward.
I was planning on something similar. Woe to the adventurer who loses
his compass.
> > Again, the question I posed was not about a small area.
>
> Then you have a lot of work ahead! Good luck ;)
Thanks for your response and well-wishing, Richard,
Eryi
Aye, The Big Question that I've seen posed yet is, Unless your Planning to
let the chars go above, say 70k feet (straight up), then Curvature is a moot
point.. No Player is going to notice that the farther north you go, the more
you lose 2 or 3 rooms before you end up back where you started. Standing at
any given spot on the surface will show you a "flat" horizon (Terms and
Comments are Relative to "Earth"), and if the you can see a curved horizon
on a "spherical" landmass, then its not very big :> Just some thoughts :>
Eryi
Jason Goodwin wrote in message <6h37la$5p$1...@wily-a-162.resnet.purdue.edu>...
>In article <353455...@dial.pipex.comNOSPAM>,
>Richard Woolcock <Ka...@dial.pipex.comNOSPAM> wrote:
>
>>Do you really WANT this much accuracy? I'm quite happy to have my world
>>as a box 5120x5120x40, with sea level at 20 on the z-axis, and the x and
>>y axis wrapping around at left-right and top-bottom respectively. Its
>>unrealistic, but easy to implement and fun to play in. If you really
>>insist on realism, then maybe you should base the mud around a single
>>island - or perhaps have a discworld if you're using a fantasy setting?
>
>Err, your world is shaped like a donut :) While keeping simplicity
>in mind, perhaps you should have top and bottom wrap around to the,
>er, top and bottom (top wraps to top, bottom wraps to bottom) Hmm,
>it'd then still be shaped as some irregular spheriod, but what planet
>is uniform anyways? :)
>
Eryi
Eryi
Eryi
Eryi
mor...@niuhep.physics.niu.edu
In article <6hdi6c$mg$1...@ocoee.iac.net>, "Eryi" <er...@usa.net> writes:
>Aye, The Big Question that I've seen posed yet is, Unless your Planning to
>let the chars go above, say 70k feet (straight up), then Curvature is a moot
>point..
Depends on how realistic you want to be. At 150 meters up your horizon
is roughly 10 times that of standing on the ground. This can be
approximated on a flat plane but...
As far as approximations are concerned, the tropics looks pretty much
like a cylinder, then one or two rows of decapitated isosceles triangles
(If somebody will please remind me of the proper name for these)
___
/ \
/ \
/_______\
1-3 thousand miles wide at the base, will do nicely to get you to
the artic circle (or perhaps a bit south of there).
But the artic circle itself is very ugly in cartisian coordinates.
<sigh>
Robert
mor...@niuhep.physics.niu.edu
>> I read a book somewhere (Deathgate cycle?) in which the world was
>> based around the inside of a sphere, with a sort of 'sun' floating
>> in the very centre of the sphere...wierd ;)
>
>I believe these are known in Sci-Fi realms as Dyson(sp?) Spheres, and are
>very interesting... The 'gravity' is generated via rotation,
hmmm, I never thought about that, Ringworld works, but how do you get
gravity on the "sides" of a Dyson Sphere? Anybody remember how they dealt
with it in the books set inside the moons of Jupiter?
>Even more interesting is a series of books I read where everone lived on trees
>that floated in orbit about a pair of suns. There were also giant speres of
>water, etc, and there was air all the way around... I think the name was
>Ring World,
Integral Trees
Larry Niven I think
>or something. Not sure if it'd make a good basis for a MUD
>though... The trees were living, and so rooms as they grew older shrunk as
>the tree grew back in on them, and each tree had a 'mouth' where our trees
>have a root system, and people fed their dead to the trees. Somewhat odd, but
>a neat story, as I recall.
Agreed
Robert
Threshold RPG
In article <6hgl7d$7ml$1...@ocoee.iac.net>, "Eryi" <er...@usa.net> wrote:
>Aye, The Big Question that I've seen posed yet is, Unless your Planning to
>let the chars go above, say 70k feet (straight up), then Curvature is a moot
>you lose 2 or 3 rooms before you end up back where you started. Standing at
>any given spot on the surface will show you a "flat" horizon (Terms and
>Comments are Relative to "Earth"), and if the you can see a curved horizon
>on a "spherical" landmass, then its not very big :> Just some thoughts :>
I think the real "Big Question" is how many times are you going to post this
message?
I think I have seen this exact message appear at least 4 or 5 times in this
thread.
-Aristotle@Threshold
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Alex Bertoglio
Hal Black wrote in message <3533D491...@vt.edu>...
>For those who use a cartesian grid to represent the map of the world,
>how do you reconcile the curvature of the sphere? Namely, the following
>problems and their consequences: (using the geography of the earth as an
>example)
>
The way we solved it was not to try... ;)
Take a conventional world map. It is obviously distorted from the proper
spherical representation. However, it is very easy to visualize. This
representation basically describes the world as a cylinder. This works fine
until you try to take an expedtion to the north pole. Say you start walking
North from Canada. Eventually you end up in Siberia in Russia. In our world
this is simulated by simply folding the map in the center. Therefore, when
you go north (and should fall off the turtle's back), you emerge on the
other side of the map at the top. Poor example follows:
Assume a world 10 cells by 10, with the following cells at the extreme north
edge of the map.
[1][2][3][4][5][6][7][8][9][0]
An adventurer in cell 2 goes north. He appears in cell 9 facing south. If he
goes north from cell 6 he will appear in cell 5.
Now, we fudged on cell size in our design. All main area cells in our world
(960,000 of them) are the same size. These are reasonably large chunks of
real estate into which an infinite number of conventional mud "rooms" can be
constructed. Moving across these cells depletes character resources based on
the cell's size. So if we wanted to be really realistic, we could run an
formula on the cell size based on the distance from the equator. ( Now see
what you've done, Hal...now that I see how to do it I have to implement it!)
This would build a globe which would be like a strings of pearls anchor at
both ends with a balloon inside. Inflate the balloon and (given enough pearl
strings) you would have a solid surface. The pearls at the equator would be
larger that those at the poles but the realtion ships would still be valid.
The centroid of each of those cells could be used for postional navigation.
However, the simple map actions described above would still work.
Note this is more of a macro approach. Modeling a planet with only a million
cells makes for pretty big cells.
>1) The distance to encircle the equator is greater than that to encircle
>the arctic circle.
Just take the map row that represents the artic circle and multiply cell
size times the number of cells in the world.(In our case, 1200x800) This
would mean in our model that the resource drain (distance) to circumnavigate
the equator would be much higher than the artic circle. At the extreme top
row of the map it would take a lot of lateral movement to get from one end
of asia to the other but the actual distance would be quite short. The
nature of squares works against us here. Now, if you describe the world as a
spherical space with your character a point moving along its surface....that
would be interesting.
>2) The north pole has several south exits. 8')
In my world there are 1200. There is technically no north (or south) pole
square (which in my model would be a point), because it would have to have
1200 exits...talk about making a player angry...
The model described above does not solve every problem but it does allow
(semi) realistic movement in all directions without artificial constraints
(like unpassable terrain at the north and south extremes of the map. It also
allows maps to be generated (once I figure out how, see another post on that
subject).
>3) When using n-s-e-w in spherical coordinates, the "squares" where a
>player can stand are not square (the e-w distance is shorter nearer the
>pole). This has the consequence of "squares" being either o non-uniform
>size, or nonaligned.
>
I think treating them as circles of a various diameters (my goofy pearl
analogy) could work fairly well. The other methods I can think of would lead
to math which is well beyond my skill level.
>I've thought about it a great deal and I can't really come up with any
>good solutions. Any ideas?