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I want to to develop a game like Populous: The Beginning with my friend. But we could not find out what type of geometry they have used for the world.

We know that - all tiles have the same size - all tiles are squares

So.. It cannot be a Icosahedron, because there are triangles, nor cant it be a standard sphere geometry, because not all tiles have the same size.

Can someone help me?

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Since the guys at Uber are now creating the game of my dreams called "Planetary Annihilation", they also shared their thoughts and techniques of how they solved the problems. This blog post of Mavor really is genious: mavorsrants.com/2013/02/planetary-annihilation-engine.html –  FlashFan Jun 12 '13 at 10:05
    
This is not a direct answer to your question, but you may be able to find some useful information here: gamedev.stackexchange.com/questions/56231/… –  DaleyPaley Jun 13 '13 at 5:31
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2 Answers

up vote 6 down vote accepted

Triangles you are seeing are likely just a product of the rendering system -- everything, in the end, has to be broken down into triangles for rendering.

I suggest you do this: search google (images) for "sphere tessellation". You will get an idea of the many, many ways of doing this. Your game does not need to be tessellated in exactly the same way as Populous: The Beginning (which, by the way, is a great game which I love). Meaning you don't even need to use square tiles, if you don't want to; you could use any hexagons, triangles, pentagons, arbitrary quadrilaterals like kites, or even voronoi tessellation (irregular, non-repeated polygons).

What's important in any tessellation used for game logic is connectivity, i.e. the fact that your "grid" forms a (somewhat) connected graph for movement purposes.

EDIT: Probably what they've done is something a little like StarControl's melee -- they actually have a wrapping 2D grid (modulo in x and y). Then, when you view the sphere, you can only see one hemisphere at once, which makes it possible to map the tiles without too much noticeable distortion. And at a closer zoom, all would look perfect.

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The problem with non-square tiles is texturing. It´s really hard to create a texture image and then calculate the UVs for it to map it on the world. If I had squares, it would be as simple as possible. Using A*, pathfinding is easy with every sort of tiles, I know. –  FlashFan Aug 23 '11 at 9:11
    
The problem with a 2d perspective project of a sphere (as used on Earth's world maps) is that while you do get square tiles, you also get warping: increasingly small tiles toward the poles. What's more important to you, dealing with the difficulties of UV mapping easily, or ensuring your tiles are well-distributed for game logic purposes? If you do find out what P:TB uses I'd be interested to know. –  Nick Wiggill Aug 23 '11 at 9:20
    
I think both ways are not possible for me... There is a Map editor for P:TB where you can enable the grid. There are definately used squares as tiles. But the strange thing on P:TB is that you can either see the complete planet, or see a part of it. There is nothing between. I think they could have faked it, so that it only looks like a Sphere in the end. But I´m not sure... –  FlashFan Aug 23 '11 at 9:27
    
I was just thinking that. Probably what they've done is something a little like StarControl's melee -- they actually have a wrapping 2D grid (modulo in x and y). Then, when you view the sphere, you can only see one hemisphere at once, which makes it possible to map the tiles without too much noticeable distortion. And at a closer zoom, all would look perfect. –  Nick Wiggill Aug 23 '11 at 9:33
    
^^ ok, then I think it´s really a fake. The fact, that the planet is completely round (no hills) when watching at the full planet, indicates that there is used a normal sphere geometry for it. We can see it here: s.uvlist.net/l/y2008/09/53528.jpg –  FlashFan Aug 23 '11 at 9:43
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The problem here is that Populous maps are not spheres at all. They're a Real Projective plane, more analogous to a flat torus manipulated on screen to look like a sphere than an actual sphere.

For example:

  • Populous maps are squares when viewed outside of the populous engine
  • Populous maps ingame are visibly warped to show/hide the curvature by moving from the normal to the close up/overhead view
  • When viewing the overhead globe, the terrain is visibly warped to ensure a spherical appearance
  • One can navigate around the world using non-euclidian geometry

The game is played from a 3D third person perspective with the camera at a variable height and capable of rotating 360°, enabling the player to quickly move across the planet's terrain, which is actually a real projective plane rather than a usual sphere; on maps where there is no fog of war, players can see what opponents are doing at any time. Extensive support for 3D acceleration enables the player to view the game in 16-bit or 32-bit colour.[10] The landscape and real-time structure building and follower movement are also shown.

Also, notice here:

enter image description here

If the overview is of half the planet, as it the minimap, why does the minimap show so much more water? And why does the water texture not reflect the true proportions of a sphere by showing an almost side on view at the edges?

Instead, for a modern game I would advise tessellating an icosahedron. You'll find many questions on SO on how to do that in a programming language of your choosing

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