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diff --git a/docs/Generator.html b/docs/Generator.html new file mode 100644 index 000000000..f6e7f1cd9 --- /dev/null +++ b/docs/Generator.html @@ -0,0 +1,319 @@ +<html> +<head> +<title>Generating terrain in MCServer</title> +</head> +<body> +<h1>Generating terrain in MCServer</h1> +<p>This article explains the principles behind the terrain generator in MCServer. It is not strictly +specific to MCServer, though, it can be viewed as a generic guide to various terrain-generating algorithms, +with specific implementation notes regarding MCServer.</p> + +<p>Contents: +<ul> +<li><a href="#preface">Preface: How it's done in real life</a></li> +<li><a href="#expectedprops">Expected properties</a></li> +<li><a href="#reversingflow">Reversing the flow</a></li> +<li><a href="#composablegen">The ComposableGenerator pipeline</a></li> +<li><a href="#coherentnoise">Using coherent noise</a></li> +<li><a href="#biomegen">Generating biomes</a></li> +<li><a href="#heightgen">Terrain height</a></li> +<li><a href="#compositiongen">Terrain composition</a></li> +<li><a href="#finishgen">Finishers</a></li> +</ul> +</p> + + +<hr /> + +<a name="preface"><h2>Preface: How it's done in real life</h2></a> +<p>The nature has many complicated geological, physical and biological processes working on all scales from +microscopic to planet-wide scale, that have shaped the terrain into what we see today. The tectonic plates +collide, push mountain ranges up and ocean trenches down. Erosion dulls the sharp shapes. Plantlife takes +over to further change the overall look of the world.</p> + +<p>Generally speaking, the processes take what's there and change it. Unlike computer generating, which +usually creates a finished terrain from scratch, or maybe with only a few iterations. It would be unfeasible +for software to emulate all the natural processes in enough detail to provide world generation for a game, +mainly because in the nature everything interacts with everything. If a mountain range rises, it changes the +way that the precipitation is carried by the wind to the lands beyond the mountains, thus changing the +erosion rate there and the vegetation type. </p> + + +<hr /> + +<a name="expectedprops"><h2>Expected properties</h2></a> +<p>For a MineCraft-like game terrain generator we need the generator to have several properties: +<ul> +<li>The generator must be able to generate terrain in small chunks. This means it must be possible to +generate each of the chunks separately, without dependencies on the neighboring chunks. Note that this +doesn't mean chunks cannot coordinate together, it means that "a tree in one chunk cannot ask if there's +a building in the neighbor chunk", simply because the neighbor chunk may not be generated yet.</li> +<li>The generated chunk needs to be the same if re-generated. This property is not exactly required, but it +makes available several techniques that wouldn't be possible otherwise.</li> +<li>The generator needs to be reasonably fast. For a server application this means at least some 20 chunks +per second for chunks close to each other, and 5 chunks per second for distant chunks. The reason for this +distinction will be discussed later.</li> +</ul> +</p> + + +<hr /> + +<a name="reversingflow"><h2>Reversing the flow</h2></a> +<p>As already mentioned, the nature works basically by generating raw terrain composition, then "applying" +erosion, vegetation and finally this leads to biomes being formed. Let's now try a somewhat inverse +approach: First generate biomes, then fit them with appropriate terrain, and finally cover in vegetation +and all the other stuff.</p> + +<p>Splitting the parts like this suddenly makes it possible to create a generator with the required +properties. We can generate a reasonable biome map chunk-wise, independently of all the other data. Once we +have the biomes, we can compose the terrain for the chunk by using the biome data for the chunk, and +possibly even for neighboring chunks. Note that we're not breaking the first property, the biomes can be +generated separately so a neighboring chunk's biome map can be generated without the need for the entire +neighboring chunk to be present. Similarly, once we have the terrain composition for a chunk, we can +generate all the vegetation and structures in it, and those can again use the terrain composition in +neighboring chunks.</p> + + +<hr /> + +<a name="composablegen"><h2>The ComposableGenerator pipeline</h2></a> +<p>This leads us directly to the main pipeline that is used for generating terrain in MCServer. For +technical reasons, the terrain composition step is further subdivided into Height generation and Composition +generation, and the structures are really called Finishers. For each chunk the generator generates, in this +sequence: +<ul> +<li>Biomes</li> +<li>Terrain height</li> +<li>Terrain composition</li> +<li>Finishers</li> +</ul> +</p> + +<img src="img/biomes.jpg" /> +<img src="img/terrainheight.jpg" /> +<img src="img/terraincomposition.jpg" /> +<img src="img/finishers.jpg" /> +<p>The beautiful thing about this is that the individual components can be changed independently. You can +have 5 biome generators and 3 height generators and you can let the users mix'n'match. +</p> + + +<hr /> + +<a name="coherentnoise"><h2>Using coherent noise for the generation</h2></a> +<p>For a great tutorial on coherent noise, see the <a href="http://libnoise.sourceforge.net/">LibNoise +documentation</a>.</p> +<p>Coherent noise is a type of noise that has three important properties that we can use to our advantage: +<ul> +<li>The noise is smooth</li> +<li>The noise is algorithmically generated, which means that the same data is generated when the same +parameters are given to the noise functions.</li> +<li>The noise can be seamlessly extended in any direction</li> +</ul></p> + +<p>We'll be mostly using Perlin noise in this article. It is the easiest one to visualise and use and is one +of the most useful kinds of coherent noises. Here's an example of a Perlin noise generated in 2 dimensions:</p> +<img src="img/perlin.jpg" /> + +<p>It comes only naturally that such a 2D noise can be used as a terrain height map directly:</p> +<img src="img/perlinheightmap.jpg" /> + +<p>However, this is not the only use for this noise, and 2 dimensions is not the limit - this noise can be +generated for any number of dimensions.</p> + + + +<hr /> + +<a name="biomegen"><h2>Generating biomes</h2></a> +<p>The easiest way to generate biomes is to not generate them at all - simply assign a single constant biome +to everywhere. And indeed there are times when this kind of "generator" is useful - for the MineCraft's Flat +world type, or for testing purposes, or for tematic maps. In MCServer, this is exactly what the Constant +biome generator does.</p> + +<p>Of course, there are more interesting test scenarios for which multiple biomes must be generated as easy +as possible. For these special needs, there's a CheckerBoard biome generator. As the name suggests, it +generates a grid of alternating biomes.</p> + +<h3>Voronoi diagram</h3> +<p>Those two generators were more of a technicality, we need to make something more interesting if we're +going for a natural look. The Voronoi generator is the first step towards such a change. Recall that a +<a href="http://en.wikipedia.org/wiki/Voronoi_diagram">Voronoi diagram</a> is a construct that creates a +set of areas where each point in an area is closer to the appropriate seed of the area than the seeds of any +other area:</p> +<img src="img/voronoi.png" /> + +<p>To generate biomes using this approach, you select random "seeds", assign a biome to each one, and then +for each "column" of the world you find the seed that is the nearest to that column, and use that seed's +biome.</p> + +<p>The overall shape of a Voronoi diagram is governed by the placement of the seeds. In extreme cases, a +seed could affect the entire diagram, which is what we don't want - we need our locality, so that we can +generate a chunk's worth of biome data. We also don't want the too much irregular diagrams that are produced +when the seeds are in small clusters. We need our seeds to come in random, yet somewhat uniform fashion.</p> + +<p>Luckily, we have just the tool: Grid with jitter. Originally used in antialiasing techniques, they can be +successfully applied as a source of the seeds for a Voronoi diagram. Simply take a regular 2D grid of seeds +with the grid distance being N, and move each seed along the X and Y axis by a random distance, usually in +the range [-N / 2, +N / 2]:</p> +<img src="img/jittergrid.jpg" /> + +<p>Such a grid is the ideal seed source for a Voronoi biome generator, because not +only are the Voronoi cells "reasonable", but the seed placement's effect on the diagram is localized - each +pixel in the diagram depends on at most 4 x 4 seeds around it. In the following picture, the seed for the +requested point (blue) must be within the indicated circle. Even the second-nearest seed, which we will need +later, is inside that circle.</p> +<img src="img/jittergridlocality.jpg" /> + +<p>Calculating the jitter for each cell can be done easily by using a 2D Perlin noise for each coord. We +calculate the noise's value at [X, Z], which gives us a number in the range [-1; 1]. We then multiply the +number by N / 2, this gives us the required range of [-N / 2, +N / 2]. Adding this number to the X coord +gives us the seed's X position. We use another Perlin noise and the same calculation for the Z coord of the +seed.</p> + +<p>Here's an example of a biome map generated using the Voronoi + jitter grid, as implemented by the Voronoi +biome generator in MCServer:</p> +<img src="img/voronoijitterbiomes.png" /> + +<h3>Distorted Voronoi</h3> +<p>The biomes are starting to look interesting, but now they have straight-line borders, which looks rather +weird and the players will most likely notice very soon. We need to somehow distort the borders to make them +look more natural. By far the easiest way to achieve that is to use a little trick: When the generator is +asked for the biome at column [X, Z], instead of calculating the Voronoi biome for column [X, Z], we first +calculate a random offset for each coord, and add it to the coordinates. So the generator actually responds +with the biome for [X + rndX, Z + rndZ].</p> + +<p>In order to keep the property that generating for the second time gives us the same result, we need the +"random offset" to be replicatable - same output for the same input. This is where we use yet another Perlin +noise - just like with the jitter for the Voronoi grid, we add a value from a separate noise to each +coordinate before sending the coordinates down to the Voronoi generator:</p> +<code> +DistortedVoronoiBiome(X, Z) := VoronoiBiome(X + PerlinX(X, Z), Z + PerlinZ(X, Z)) +</code> + +<p>The following image shows the effects of the change, as generated by MCServer's DistortedVoronoi biome +generator. It is actually using the very same Voronoi map as the previous image, the only change has been +the addition of the distortion:</p> +<img src="img/distortedvoronoibiomes.png" /> + +<p>As you can see, this already looks reasonable enough, it could be considered natural biomes, if it +weren't for several drawbacks: +<ul> +<li>There's no way to limit the neighbors. A desert biome can neighbor a tundra biome. </li> +<li>All the biomes are considered equal. There's no way to make oceans larger. A mushroom biome is +generated right next to other land biomes.</li> +</ul></p> + +<h3>Adding relativity</h3> +<p>Our next goal is to remove the first defect of the distorted Voronoi generator: unrelated biomes +generating next to each other. It is highly unlikely to find a jungle biome next to a desert biome, so we +want to have as few of those borders as possible. We could further improve on the selection of +biome-to-seed in the Voronoi generator. Or we can try a completely different idea altogether.</p> + +<p>Recall how we talked about the nature, where the biomes are formed by the specific conditions of a place. +What if we could make a similar dependency, but without the terrain? It turns out this is possible rather +easily - instead of depending on the terrain, we choose two completely artificial measures. Let's call them +Temperature and Humidity. If we knew the temperature of the place, we know what set of biomes are possible +for such temperatures - we won't place deserts in the cold and tundra in the hot anymore. Similarly, the +humidity will help us sort out the desert vs jungle issue. But how do we get a temperature and humidity? +Once again, the Perlin noise comes to the rescue. We can use a simple 2D Perlin noise as the temperature +map, and another one as the humidity map.</p> + +<p>What we need next is a decision of what biome to generate in certain temperature and humidity +combinations. The fastest way for a computer is to have a 2D array, where the temperature is one dimension +and humidity the other, and the values in the array specify the biome to generate:</p> +<img src="img/temperaturehumiditydecisionsimple.jpg" /> + +<p>We can even "misuse" the above diagram to include the hill variants of the biomes and have those hills +neighbor each other properly, simply by declaring some of the decision diagram's parts as hills:</p> +<img src="img/temperaturehumiditydecisionhills.jpg" /> + +<p>The problem with this approach is that there are biomes that should not depend on temperature or +humidity, they generate across all of their values. Biomes like Oceans, Rivers and Mushroom. We could +either add them somewhere into the decision diagram, or we can make the generator use a multi-step decision: +<ul> +<li>Decide whether the point is in the ocean, land or mushroom</li> +<li>If it's land, decide if it's real land or river.</li> +<li>If it's real land, use a TemperatureHumidity approach to generate land-biomes</li> +</ul> +</p> + +<p>This is the approach implemented in MCServer's MultiStepMap biome generator. It generates biome maps like +this:</p> +<img src="img/multistepmapbiomes.png" /> + +<p>To decide whether the point is in the ocean, land or mushroom, the generator first chooses seeds in a grid +that will be later fed to a DistortedVoronoi algorithm, the seeds get the "ocean" and "land" values. Then it +considers all the "ocean" seeds that are surrounded by 8 other "ocean" seeds and turns a random few of them +into "mushroom". This special seed processing makes the mushroom biomes mostly surrounded by ocean. The +following image shows an example seeds grid that the generator might consider, only the two framed cells are +allowed to change into mushroom. L = land, O = ocean:</p> +<img src="img/multistepmapgrid.jpg" /> + +<p>Next, the generator calculates the DistortedVoronoi for the seeds. For the areas that are calculated as +mushroom, the distance to the nearest-seed is used to further shrink the mushroom biome and then to +distinguish between mushroom and mushroom-shore (image depicts a Voronoi cell for illustration purposes, it +works similarly with DistortedVoronoi). O = ocean, M = mushroom, MS = mushroom shore:</p> +<img src="img/multistepmapdistance.jpg" /> + +<a name="perlinrivers"> +<p>The rivers are added only to the areas that have been previously marked as land. A simple 2D Perlin noise +is used as the base, where its value is between 0 and a configured threshold value, a river is created. This +creates the rivers in a closed-loop-like shapes, occasionally splitting two branches off:</p> +<img src="img/perlinrivers1.jpg" /> +<img src="img/perlinrivers2.jpg" /> +<img src="img/perlinrivers3.jpg" /> +</a> + +<p>For the leftover land biomes, the two Perlin noises, representing temperature and humidity, are used to +generate the biomes, as described earlier. Additionally, the temperature map is used to turn the Ocean biome +into FrozenOcean, and the River biome into FrozenRiver, wherever the temperature drops below a threshold.</p> + +<h3>Two-level Voronoi</h3> +<p>The 1.7 MineCraft update brought a completely new terrain generation, which has sparked renewed interest +in the biome generation. A new, potentially simpler way of generating biomes was found, the two-level +DistortedVoronoi generator.</p> + +<p>The main idea behind it all is that we create large areas of similar biomes. There are several groups of +related biomes that can be generated near each other: Desert biomes, Ice biomes, Forest biomes, Mesa biomes. +Technically, the Ocean biomes were added as yet another group, so that the oceans will generate in +approximately the size of the larger areas, too.</p> + +<p>For each column a DistortedVoronoi is used to select, which large area to use. This in turn results in +the list of biomes from which to choose. Another DistortedVoronoi, this time with a smaller grid size, is +used to select one biome out of that list. Additionally, the smaller DistortedVoronoi calculates not only +the nearest seed's distance, but also the distance to the second-nearest seed; the ratio between these two +is used as an indicator whether the column is in the "inside" or on the "outskirt" of the smaller Voronoi +cell. This allows us to give certain biomes an "edge" biome - the Mushroom biome has a MushroomShore edge, +the ExtremeHills biome have an ExtremeHillsEdge biome on the edge, etc.</p> + +<p>The images below illustrate the process with regular Voronoi diagrams, for clarity purposes. The real +generator uses distortion before querying the small areas.</p> +<img src="img/twolevellargeareas.jpg" /><br /> +<img src="img/twolevelsmallgrid.jpg" /><br /> +<img src="img/twolevelsmallareas.jpg" /><br /> + +<p>The following image shows an example output of a TwoLevel biome generator in MCServer:</p> +<img src="img/twolevelbiomes.png" /> + +<p>Note that rivers are currently not implemented in this generator in MCServer, but they could be added +using the same approach as in MultiStepMap - by using a thresholded 2D Perlin noise.</p> + + +<hr /> + +<a name="heightgen"><h2>Terrain height</h2></a> + + +<hr /> + +<a name="compositiongen"><h2>Terrain composition</h2></a> + + +<hr /> + +<a name="finishgen"><h2>Finishers</h2></a> + +</body> +</html> |