Arrow keys move, mouse looks. Try it out here Alien floating things and holes in the 'ground'

Arrow keys move, mouse looks. Try this one out here.

I've made a presentation or "slides" about the same subject, and you can check it out in video form below. It's rather slow paced because it's supposed to have a talk accompanied with it, but the visualizations might be helpful.

https://videopress.com/v/uDKGASGw

### Let's get technical -- what goes into building something like this?

The main components of the system are:

1. A coherent noise function from which we can sample a 3D field (array) of density values
2. Marching Cubes algorithm for creating surfaces at the boundaries of a chosen density value

The project's full source can be found here: https://github.com/Tsarpf/proced

Let's go through the components with a little bit more detail

### Noise functions

Noise functions in this context are basically functions that take in coordinates in some number of dimensions, and give out a single floating point value. So a 3 dimensional noise function could look something like this:

``````function(x,y,z) {
...
return a;
}``````

Now, if the return values of our noise function were completely random, say, the function's results were from a call to Math.rand, if we tried to use those values as a base for our terrain generation, we would end up with something that resembles a post modern art piece, not rolling hills or mountains.

What we need is a coherent noise function. With coherent noise functions, there's a promise that when the input values vary by a little bit, the output values vary only by a little bit as well. This means there are gradual transitions between spaces where there are solid things and where there are not.

### Surfaces from noise

At least at the moment, I use the marching cubes algorithm for creating surfaces out of noise. The algorithm has been explained way better than I can in so many places already that I'm going to just encourage you to check the wikipedia page and Paul Bourke's Polygonising a scalar field to start learning more about it.

Also feel free to copy and/or use my JS port of Paul Bourke's code.

In order for the geometry we've generated to look 3D, it needs shading. This means we need surface normals. There are two different approaches I know of for finding them.

1. A gradient for a point in a field is the direction where the field's values change the most from the current position. When surfaces are generated to go along a density level boundary, they are perpendicular to the gradients. This means the gradients are actually the same thing as normals. We can approximate a gradient for a point by sampling the density values surrounding it.

, via Wikimedia Commons" href="https://commons.wikimedia.org/wiki/File%3AGradient2.svg"> Picture from the Wikipedia article about gradients. The blue arrows show the direction of the color gradient.
here's some sample code:

``````function getNormalForVertex(x, y, z, sampler, outObj) {
outObj.x = sampler(x + dataStep.x, y, z) - sampler(x - dataStep.x, y , z);
outObj.y = sampler(x, y + dataStep.y, z) - sampler(x, y - dataStep.y , z);
outObj.z = sampler(x, y, z + dataStep.z) - sampler(x, y , z - dataStep.z);
}``````

`dataStep.x/y/z` needs to be some relatively small number. If it's too big, the normal (gradient) approximation is too coarse and is wrong for small surface details. If it's too small, it takes into accord too small changes and big surfaces can get weird normals.

I was never able to get good looking normals for both big and small features this way so I abandoned it and tried another way:

1. For each triangle, get the triangle's normal by taking the cross-product of two vectors formed from the triangle's vertices. These normals alone provide some basic shading, and the method is often called `face normals`. Since using only face normals we would have sudden changes of color at triangle borders, we want to do a bit better than that. So for each vertex, we combine it with other vertices that have the same position, and get an average normal from all the triangles it belongs to where each triangle normal is weighted by the triangle's size.

This gets us some pretty decent looking shading. IIRC it was something like 10% faster, too, but nothing drastic.

One bug or problem I haven't yet had the time to solve with shading is that the vertices are only combined within chunks (discussed below), so at chunk borders the shading still isn't smooth.

These pieces are often called "chunks" in infinite map generators. By loading the world in chunks we don't have to load everything at once, and can do tricks like prioritizing the loading of chunks closer to the player over farther away ones. Chunks also enable us to even out the CPU stress caused by loading new chunks over as many frames as we'd like.

My approach for the data structure to save these chunks to was to write a 3D circular buffer. This means old and far away chunks eventually get overwritten. You can find my implementation here and some mocha tests for it here

Further, my circular buffer, or wrapping array as I call it, uses "zones" which tell how many chunks away a given bunch of chunks is from the player, from 0 to `WorldChunkCountPerAxis / 2` (since the player is set to be at the center) An ugly 1D representation of the zone system

The zones are implemented as "zone functions" which can be set to call a specific function for every chunk that enters a given zone every time the players chunk position changes.

At the moment it also has a different function for the case where the chunks enter a zone caused by the player coming closer to them, and a different one for when the chunk enters the zone by "falling behind" or going farther away from the player. This separation could be used to unload a chunk or decrease LOD when the zone is entered backwards and load or increase LOD when entered forwards, but I'm probably removing this feature soon and instead going to use the same function for all chunks in the zone, and handling all unloading etc. when an array index gets overwritten instead.

Here's an example of setting up a zone function:

``````var size = 7; // world chunk count per axis
var zoneCount = Math.ceil(size / 2); // how many zones in the world
var wrappingArray = PROCED.wrappingArray(size); // initialize wrapping array

wrappingArray.setZoneFunction(zoneCount - 1, function (arrayCell, worldCoords) {
queue.push({
type: 'draw',
arrayCell: arrayCell,
worldCoords: worldCoords
}, 1); //priority 1 for all chunk drawings for now
}, function() {});``````

The first argument of `setZoneFunction` is the zone (represented by a single integer) we want the following functions to be used for. At the moment while the forward/backward separation is still there, the forwards function is the second argument and the third is the backwards function (which is an empty function in this case)

Now every time one of the six direction functions (x/y/z axis, +/- direction) of the wrapping array is called (f.ex triggered by the player moving in one of the directions over a chunk border), it calls the function for every chunk that entered the zone at the edge of the world (which is the zone `zoneCount - 1`) "forwards"

In my current implementation it pushes to a work queue a "draw" order for each of these chunks that newly entered the zone, where the chunk to be drawn should be placed in the cell `arrayCell` in our wrapped array (which is a 3D array flattened to 1D, see here), and the chunk drawn there should have the non-wrapped aka "world coordinates" specified by `worldCoords`.

I use Async.js's priority queue implementation to queue the processing of chunks. I use something like 1-2 workers for the queue, which means it takes 1 or 2 chunks from the queue per frame. When the processing orders come come out of the queue, the processing is delayed once more by asking for free CPU time time by calling `requestAnimationFrame`. I'm not sure if it's the best way to do it, but it seems at least to be faster than using setTimeout with zero timeout. Please leave a comment if you know more about this :)