13 maj 2012

Making caves from simplex noise


In Ephenation, we want underground caves. The requirements on these caves, and their construction, are:

  1. Any sub underground region shall be possible to create without knowledge of neighbour regions.
  2. The caves shall be long and winding.
  3. They shall split and join randomly, sometimes ending in a dead end.
  4. Most of them shall be of a size to allow a player to pass through.
  5. The algorithm shall be based on 3D simplex noise.
The description below is not really depending on OpenGL. Anyway, path finding algorithms are out of the question. The first problem is the simplex noise. I use simplex algorithms defined by Stefan Gustavsson, normalized to the interval 0 to 1. Using a 3D simplex noise produces a density function. The the underground is created as empty space where this density is below a certain threshold, and you will get some kind of caves. But the simplex noise is spherical in nature, and not at all long and winding.

To demonstrate the result, I show pictures of inverted caves. That is, ground where the space should be, and vice versa. This makes it easier to visualize.
density > 0.85
These caves are not very nice. They are too round, and most of them are not connected to each other. One reason for this is the limit set on the density. With a lower density limit, the caves (that is the floating blobs in the picture) will grow, and start to connect.
density > 0.7
This is better. But the caves are starting to dominate the world. That is, there are caves almost everywhere. And they are very wide and spacey, with no feeling of a cramped cave. The question then is if another algorithm than simplex noise should be used.

There is a way to continue, based on this. The principle is that an intersection between two planes is a line. If the planes have a certain thickness, then the line will get a height and width. Thus, the next step is to change the above into curved planes instead of massive objects. An easy way to do this is to have the condition "make stone if density > 0.7 and less than 0.8". That will make most of them hollow. The inside will have no opening to the outside, making it difficult to visualize. But using the Ephenation X-ray view, it will look as follows:
density > 0.7 && density < 0.8
This is now curved planes, sometimes looping around into spheres. If used inverted as caves, you would run around inside these walls, which can be adjusted to an appropriate size. But they are still rather unnatural caves. The trick is to make two such worlds, based on different random seed. That will make two worlds, each looking a little like a bottle full of soap bubbles with thick membranes. Now create a third world as stone, but with the condition for every coordinate to be air if both the first and second world is air. That will be an intersection, looking as follows.
dens1 > 0.7 && dens1 < 0.8 && dens2 > 0.7 && dens2 < 0.8
It is easy to adjust how long the caves shall be. In my example, I am using the interval 0.7 to 0.8. Changing this to 0.45 to 0.55 increases the chance to make tunnels, while still remaining of the approximately same size, and gives the following, based on the same view.
dens1 > 0.45 && dens1 < 0.55 && dens2 > 0.45 && dens2 < 0.55
I should mention that I scale the y argument (the height) to the simplex function a factor of 2 compared to the x and z. That way, the caves get more elongated in horizontal level.

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