I think we should unify some terms and definitions first (otherwise we end up fighting cause we don't understand the other one):
Here's what I suggest:
direction = Each way, a train (and all the other vehicles) can run.
basic direction = The most trivial directions supported by the grid. There are four in rectangular grid and six in triangular or hexagonal grid.
axis = like basic direction, but back and forth is considered as one axis
grid = a pattern of points and connecting lines (rectangular or triangular)
tile = the basic shape formed by the grid (rectangular or triangular or hexagonal)
Your OK with these definitions or shoud we change something?
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ChrisCF wrote:It is, because if you can't build in the two fundamental directions of 2-dimenional geometry, you're already making people's lives difficult. [...]
In most cases, 2-dimensional geometry also means, that you have a rectangular grid (just think of paper, even without lines on it, there is a rectangular grid indicated by the edges of the paper). In computer environment you dont have any edges or indicators. If the complete system is based on triangels, than you'll never miss the 90° angle. Have you played "The Settlers"? In there, the whole world is based on triangles, and you really don't miss the rectangles. I think, that peaple will learn pretty fast to think in triangular grid.
At this point it depends ones personal preferences.
ChrisCF wrote:With the range of motion you suggested with nine directions, it's impossible to build straight along one of the axes of the two-dimensional region - generating a track to run vaguely along that axis in three-dimenional space just doesn't bear thinking about.
See above. I think you won't miss it.
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ChrisCF wrote:I really don't think that beeing stuck to increments of π/6 is that bad and I also don't consider the "intermediate points at π/4" "all-important". please post some arguments, why these directions are imortant for you.
Tell you what, how about *you* demonstrate why they are *unimportant*?
For this reason, I posted the two photos of Munich, two demonstrate, that
rectangular grid is not obvious in reality, at least not for traffic lines (roads and railtrack) at a scale similar to the one used in games like TT (second picture).
The other argument is, that rectangular grid is question of what's more common, but not a natural law. So there's no need to do, what everyone does. But I think, that most players will grow familiar with the triangles very fast.
ChrisCF wrote:Remember that we're not only dealing with railway tracks here - roads have to fit the bill too, and it should be patently obvious why right-angled junctions make sense, and therefore have to be supported.
Look at the Photos again. Right-angled junctions are obvious in small scale, but in TT-like scale and for interurban streets there are not many right angles.
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Now for the technical stuff.
First of, I'm learning all this geometry stuff in my math classes (and I'm not bad in it), so please don't hesitate bombarding me with technical terms.
ChrisCF wrote:Two perpendicular axes are rather easier to deal with than three non-perpendicular axes.
Agree.
ChrisCF wrote:Ignore height for a moment.
NSure. For the following we'll look at a 2-dimensional area (the ground where the grid is).
ChrisCF wrote:With three axes, as you'd get with triangles, you have three unit vectors along the sides of the triangle, (1,0,0), (0,1,0) and (1,0,0).
What are you doing there??? We have only two dimensions, and your vectors have three.
ChrisCF wrote:Since you have to satisfy both linear independence and vector space span to form a basis, the triangular model doesn't provide a basis for measuring your terrain.
Three vectors are never ever able to make up a basis for a 2-dimensional area. So no wonder about that. But your conclusion is not true.
I'm afraid to tell you, but you've lost yourself in the geometry.
You only need two vectors to form a basis (cause three vectors will never be linear independent in two dimensions). You're totally free in choosing these vectors (but they have to be linear independent). So you choose two of the three axis provided by the grid (for the ease of use).
See the picture below (VectorBasis.png) for two examples of suitable basic vectors.
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ChrisCF wrote:Ultimately, if it's more understandable, then it will be within the ability of more people to contribute to it. No point having a beautifully complex model if few of the other coders can get their head around it when you mysteriously disappear. In terms of the code, maintainability has to be placed before complexity, because it is something which will be around longer. Before you answer, how do you know that you won't disappear?
Certainly right. I'm here to explain, and I hope, I'll be able to make my suggestion fully understandable for pretty much everybody. There is no sense in trying to master a system that noone really understands (That's why I've no comprehension of capitalists and/or bankers). For the contributors, it should be no problem to provide converters for models, cause transferring vectordata from one basis to another is a totally common operation in computer grafics.
mysteriously disappearance might be possible
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but is not planned
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ChrisCF wrote:»» It's as simple: Using triangular grid will result in shorter detours.
You're quoting numbers and not proving them.
Right. Here you are:
Take a look at the picture below (Diagonal.png) to see what I meant with "the minimal way of basic directions to connect two diagonally placed points in triangular and rectangular grid"
Start and
End are positioned "worst case".
In the triangular grid, the bee-line is 6 * 1/2 sqrt(3) = 5.196... long, the way following only the basic directions is 6 * 1 = 6 long, ca. 15,5% longer than bee-line.
In the rectangular grid, the bee-line is 3 * sqrt(2) = 4.242... long, the way following only the basic directions is 6 * 1 = 6 long, ca. 41,4% longer than bee-line.
So the detour will be 22.5% longer in rectangular grid.
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ChrisCF wrote:Then you can rather handily work along the diagonals, which provides the eight you need.
The point is, that diagonals do not equal the basic directions. You have to use different technics for Junctions, hills, bridges, overhead electrical wire, signals and so on. Will be rather confusing IMHO.
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eis_os wrote:About the city shots, I see more square-ich houses
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As I do. But do you really see one House in the second picture? They are extreamly small.
In a game one should see houses somwhat larger, but I don't think that building single houses and placeing them on the grid is the way to go. I suggest building whole districts (manually or by a algorithm) of urban area with buildings, small streats and narrow alleys, gardens, trees and so on which are not snaped to the overall grid, but the district itself should be placed into the grid.
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Steve wrote:We keep the range of straight peices, shown in layout4d.
We allow the wider curves so things are just straight, any making things look A LOT prettier. Kinda like Loco does it.
The one doesn't work without the other. Either Layout4 or Layout8.
Steve wrote:We have the 6 points around the triangle that things can join to.. could we add one in the middle? Then we'd have a pretty square grid, with the traingle cells.
Don't understand what you mean.
Steve wrote:I'm not sure about landscapes made by the tiles [...]
tiles should be smothed in any way. Just start out small and make it more sophisticated later. (I already have some ideas for that, but this would confuse the discussion - there are enough ways to do a great landscape)
BTW: Can someone tell me, why I've allways posted 2 pictures with each post
BTW2: Hope to write shorter posts next time
Fixed your [color] tags. ~Hellfire