279 lines
16 KiB
HTML
279 lines
16 KiB
HTML
<html>
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<head>
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<title>Generating terrain in MCServer</title>
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</head>
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<body>
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<h1>Generating terrain in MCServer</h1>
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<p>This article explains the principles behind the terrain generator in MCServer. It is not strictly
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specific to MCServer, though, it can be viewed as a generic guide to various terrain-generating algorithms,
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with specific implementation notes regarding MCServer.</p>
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<h2>Preface: How it's done in real life</h2>
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<p>The nature has many complicated geological, physical and biological processes working on all scales from
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microscopic to planet-wide scale, that have shaped the terrain into what we see today. The tectonic plates
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collide, push mountain ranges up and ocean trenches down. Erosion dulls the sharp shapes. Plantlife takes
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over to further change the overall look of the world.</p>
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<p>Generally speaking, the processes take what's there and change it. Unlike computer generating, which
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usually creates a finished terrain from scratch, or maybe with only a few iterations. It would be unfeasible
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for software to emulate all the natural processes in enough detail to provide world generation for a game,
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mainly because in the nature everything interacts with everything. If a mountain range rises, it changes the
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way that the precipitation is carried by the wind to the lands beyond the mountains, thus changing the
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erosion rate there and the vegetation type. </p>
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<h2>Expected properties</h2>
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<p>For a MineCraft-like game terrain generator we need the generator to have several properties:
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<ul>
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<li>The generator must be able to generate terrain in small chunks. This means it must be possible to
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generate each of the chunks separately, without dependencies on the neighboring chunks. Note that this
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doesn't mean chunks cannot coordinate together, it means that "a tree in one chunk cannot ask if there's
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a building in the neighbor chunk", simply because the neighbor chunk may not be generated yet.</li>
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<li>The generated chunk needs to be the same if re-generated. This property is not exactly required, but it
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makes available several techniques that wouldn't be possible otherwise.</li>
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<li>The generator needs to be reasonably fast. For a server application this means at least some 20 chunks
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per second for chunks close to each other, and 5 chunks per second for distant chunks. The reason for this
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distinction will be discussed later.</li>
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</ul>
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</p>
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<h2>Reversing the flow</h2>
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<p>As already mentioned, the nature works basically by generating raw terrain composition, then "applying"
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erosion, vegetation and finally this leads to biomes being formed. Let's now try a somewhat inverse
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approach: First generate biomes, then fit them with appropriate terrain, and finally cover in vegetation
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and all the other stuff.</p>
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<p>Splitting the parts like this suddenly makes it possible to create a generator with the required
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properties. We can generate a reasonable biome map chunk-wise, independently of all the other data. Once we
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have the biomes, we can compose the terrain for the chunk by using the biome data for the chunk, and
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possibly even for neighboring chunks. Note that we're not breaking the first property, the biomes can be
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generated separately so a neighboring chunk's biome map can be generated without the need for the entire
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neighboring chunk to be present. Similarly, once we have the terrain composition for a chunk, we can
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generate all the vegetation and structures in it, and those can again use the terrain composition in
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neighboring chunks.</p>
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<h2>The ComposableGenerator pipeline</h2>
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<p>This leads us directly to the main pipeline that is used for generating terrain in MCServer. For
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technical reasons, the terrain composition step is further subdivided into Height generation and Composition
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generation, and the structures are really called Finishers. For each chunk the generator generates, in this
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sequence:
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<ul>
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<li>Biomes</li>
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<li>Terrain height</li>
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<li>Terrain composition</li>
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<li>Finishers</li>
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</ul>
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</p>
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<img src="img/biomes.jpg" />
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<img src="img/terrainheight.jpg" />
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<img src="img/terraincomposition.jpg" />
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<img src="img/finishers.jpg" />
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<p>The beautiful thing about this is that the individual components can be changed independently. You can
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have 5 biome generators and 3 height generators and you can let the users mix'n'match.
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</p>
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<h2>Using coherent noise for the generation</h2>
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<p>For a great tutorial on coherent noise, see the <a href="http://libnoise.sourceforge.net/">LibNoise
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documentation</a>.</p>
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<p>Coherent noise is a type of noise that has three important properties that we can use to our advantage:
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<ul>
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<li>The noise is smooth</li>
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<li>The noise is algorithmically generated, which means that the same data is generated when the same
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parameters are given to the noise functions.</li>
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<li>The noise can be seamlessly extended in any direction</li>
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</ul></p>
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<p>We'll be mostly using Perlin noise in this article. It is the easiest one to visualise and use and is one
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of the most useful kinds of coherent noises. Here's an example of a Perlin noise generated in 2 dimensions:</p>
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<img src="img/perlin.jpg" />
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<p>It comes only naturally that such a 2D noise can be used as a terrain height map directly:</p>
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<img src="img/perlinheightmap.jpg" />
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<p>However, this is not the only use for this noise, and 2 dimensions is not the limit - this noise can be
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generated for any number of dimensions.</p>
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<h2>Generating biomes</h2>
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<p>The easiest way to generate biomes is to not generate them at all - simply assign a single constant biome
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to everywhere. And indeed there are times when this kind of "generator" is useful - for the MineCraft's Flat
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world type, or for testing purposes, or for tematic maps. In MCServer, this is exactly what the Constant
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biome generator does.</p>
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<p>Of course, there are more interesting test scenarios for which multiple biomes must be generated as easy
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as possible. For these special needs, there's a CheckerBoard biome generator. As the name suggests, it
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generates a grid of alternating biomes.</p>
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<h3>Voronoi diagram</h3>
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<p>Those two generators were more of a technicality, we need to make something more interesting if we're
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going for a natural look. The Voronoi generator is the first step towards such a change. Recall that a
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<a href="http://en.wikipedia.org/wiki/Voronoi_diagram">Voronoi diagram</a> is a construct that creates a
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set of areas where each point in an area is closer to the appropriate seed of the area than the seeds of any
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other area:</p>
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<img src="img/voronoi.png" />
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<p>To generate biomes using this approach, you select random "seeds", assign a biome to each one, and then
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for each "column" of the world you find the seed that is the nearest to that column, and use that seed's
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biome.</p>
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<p>The overall shape of a Voronoi diagram is governed by the placement of the seeds. In extreme cases, a
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seed could affect the entire diagram, which is what we don't want - we need our locality, so that we can
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generate a chunk's worth of biome data. We also don't want the too much irregular diagrams that are produced
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when the seeds are in small clusters. We need our seeds to come in random, yet somewhat uniform fashion.</p>
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<p>Luckily, we have just the tool: Grid with jitter. Originally used in antialiasing techniques, they can be
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successfully applied as a source of the seeds for a Voronoi diagram. Simply take a regular 2D grid of seeds
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with the grid distance being N, and move each seed along the X and Y axis by a random distance, usually in
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the range [-N / 2, +N / 2]:</p>
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<img src="img/jittergrid.jpg" />
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<p>Such a grid is the ideal seed source for a Voronoi biome generator, because not
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only are the Voronoi cells "reasonable", but the seed placement's effect on the diagram is localized - each
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pixel in the diagram depends on at most 4 x 4 seeds around it. In the following picture, the seed for the
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requested point (blue) must be within the indicated circle. Even the second-nearest seed, which we will need
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later, is inside that circle.</p>
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<img src="img/jittergridlocality.jpg" />
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<p>Calculating the jitter for each cell can be done easily by using a 2D Perlin noise for each coord. We
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calculate the noise's value at [X, Z], which gives us a number in the range [-1; 1]. We then multiply the
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number by N / 2, this gives us the required range of [-N / 2, +N / 2]. Adding this number to the X coord
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gives us the seed's X position. We use another Perlin noise and the same calculation for the Z coord of the
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seed.</p>
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<p>Here's an example of a biome map generated using the Voronoi + jitter grid, as implemented by the Voronoi
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biome generator in MCServer:</p>
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<img src="img/voronoijitterbiomes.png" />
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<h3>Distorted Voronoi</h3>
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<p>The biomes are starting to look interesting, but now they have straight-line borders, which looks rather
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weird and the players will most likely notice very soon. We need to somehow distort the borders to make them
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look more natural. By far the easiest way to achieve that is to use a little trick: When the generator is
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asked for the biome at column [X, Z], instead of calculating the Voronoi biome for column [X, Z], we first
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calculate a random offset for each coord, and add it to the coordinates. So the generator actually responds
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with the biome for [X + rndX, Z + rndZ].</p>
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<p>In order to keep the property that generating for the second time gives us the same result, we need the
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"random offset" to be replicatable - same output for the same input. This is where we use yet another Perlin
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noise - just like with the jitter for the Voronoi grid, we add a value from a separate noise to each
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coordinate before sending the coordinates down to the Voronoi generator:</p>
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<code>
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DistortedVoronoiBiome(X, Z) := VoronoiBiome(X + PerlinX(X, Z), Z + PerlinZ(X, Z))
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</code>
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<p>The following image shows the effects of the change, as generated by MCServer's DistortedVoronoi biome
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generator. It is actually using the very same Voronoi map as the previous image, the only change has been
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the addition of the distortion:</p>
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<img src="img/distortedvoronoibiomes.png" />
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<p>As you can see, this already looks reasonable enough, it could be considered natural biomes, if it
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weren't for several drawbacks:
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<ul>
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<li>There's no way to limit the neighbors. A desert biome can neighbor a tundra biome. </li>
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<li>All the biomes are considered equal. There's no way to make oceans larger. A mushroom biome is
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generated right next to other land biomes.</li>
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</ul></p>
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<h3>Adding relativity</h3>
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<p>Our next goal is to remove the first defect of the distorted voronoi generator: unrelated biomes
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generating next to each other. It is highly unlikely to find a jungle biome next to a desert biome, so we
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want to have as few of those boundaries as possible. We could further improve on the selection of
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biome-to-seed in the Voronoi generator. Or we can try a completely different idea altogether.</p>
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<p>Recall how we talked about the nature, where the biomes are formed by the specific conditions of a place.
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What if we could make a similar dependency, but without the terrain? It turns out this is possible rather
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easily - instead of depending on the terrain, we choose two completely artificial measures. Let's call them
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Temperature and Humidity. If we knew the temperature of the place, we know what set of biomes are possible
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for such temperatures - we won't place deserts in the cold and tundra in the hot anymore. Similarly, the
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humidity will help us sort out the desert vs jungle issue. But how do we get a temperature and humidity?
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Once again, the Perlin noise comes to the rescue. We can use a simple 2D Perlin noise as the temperature
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map, and another one as the humidity map.</p>
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<p>What we need next is a decision of what biome to generate in certain temperature and humidity
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combinations. The fastest way for a computer is to have a 2D array, where the temperature is one dimension
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and humidity the other, and the values in the array specify the biome to generate:</p>
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<img src="img/temperaturehumiditydecisionsimple.jpg" />
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<p>We can even "misuse" the above diagram to include the hill variants of the biomes and have those hills
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neighbor each other properly, simply by declaring some of the decision diagram's parts as hills:</p>
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<img src="img/temperaturehumiditydecisionhills.jpg" />
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<p>The problem with this approach is that there are biomes that should not depend on temperature or
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humidity, they generate across all of their values. Biomes like Oceans, Rivers and Mushroom. We could
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either add them somewhere into the decision diagram, or we can make the generator use a multi-step decision:
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<ul>
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<li>Decide whether the point is in the ocean, land or mushroom</li>
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<li>If it's land, decide if it's real land or river.</li>
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<li>If it's real land, use a TemperatureHumidity approach to generate land-biomes</li>
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</ul>
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</p>
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<p>This is the approach implemented in MCServer's MultiStepMap biome generator. It generates biome maps like
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this:</p>
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<img src="img/multistepmapbiomes.png" />
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<p>To decide whether the point is in the ocean, land or mushroom, the generator first chooses seeds in a grid
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that will be later fed to a DistortedVoronoi algorithm, the seeds get the "ocean" and "land" values. Then it
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considers all the "ocean" seeds that are surrounded by 8 other "ocean" seeds and turns a random few of them
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into "mushroom". This special seed processing makes the mushroom biomes mostly surrounded by ocean. The
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following image shows an example seeds grid that the generator might consider, only the two framed cells are
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allowed to change into mushroom. L = land, O = ocean:</p>
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<img src="img/multistepmapgrid.jpg" />
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<p>Next, the generator calculates the DistortedVoronoi for the seeds. For the areas that are calculated as
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mushroom, the distance to the nearest-seed is used to further shrink the mushroom biome and then to
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distinguish between mushroom and mushroom-shore (image depicts a Voronoi cell for illustration purposes, it
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works similarly with DistortedVoronoi). O = ocean, M = mushroom, MS = mushroom shore:</p>
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<img src="img/multistepmapdistance.jpg" />
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<p>The rivers are added only to the areas that have been previously marked as land. A simple 2D Perlin noise
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is used as the base, where its value is between 0 and a configured threshold value, a river is created. This
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creates the rivers in a closed-loop-like shapes, occasionally splitting two branches off:</p>
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<img src="img/perlinrivers.jpg" />
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<p>For the leftover land biomes, the two Perlin noises, representing temperature and humidity, are used to
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generate the biomes, as described earlier. Additionally, the temperature map is used to turn the Ocean biome
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into FrozenOcean, and the River biome into FrozenRiver, wherever the temperature drops below a threshold.</p>
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<h3>Two-level Voronoi</h3>
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<p>The 1.7 MineCraft update brought a completely new terrain generation, which has sparked renewed interest
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in the biome generation. A new, potentially simpler way of generating biomes was found, the two-level
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DistortedVoronoi generator.</p>
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<p>The main idea behind it all is that we create large areas of similar biomes. There are several groups of
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related biomes that can be generated near each other: Desert biomes, Ice biomes, Forest biomes, Mesa biomes.
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Technically, the Ocean biomes were added as yet another group, so that the oceans will generate in
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approximately the size of the larger areas, too.</p>
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<p>For each column a DistortedVoronoi is used to select, which large area to use. This in turn results in
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the list of biomes from which to choose. Another DistortedVoronoi, this time with a smaller grid size, is
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used to select one biome out of that list. Additionally, the smaller DistortedVoronoi calculates not only
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the nearest seed's distance, but also the distance to the second-nearest seed; the ratio between these two
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is used as an indicator whether the column is in the "inside" or on the "outskirt" of the smaller Voronoi
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cell. This allows us to give certain biomes an "edge" biome - the Mushroom biome has a MushroomShore edge,
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the ExtremeHills biome have an ExtremeHillsEdge biome on the edge, etc.</p>
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<p>The images below illustrate the process with regular Voronoi diagrams, for clarity purposes. The real
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generator uses distortion before querying the small areas.</p>
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<img src="img/twolevellargeareas.jpg" /><br />
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<img src="img/twolevelsmallgrid.jpg" /><br />
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<img src="img/twolevelsmallareas.jpg" /><br />
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<p>The following image shows an example output of a TwoLevel biome generator in MCServer:</p>
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<img src="img/twolevelbiomes.png" />
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<p>Note that rivers are currently not implemented in this generator in MCServer, but they could be added
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using the same approach as in MultiStepMap - by using a thresholded 2D Perlin noise.</p>
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<h2>Terrain height</h2>
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</body>
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</html>
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