How do you store voxel data?

Question

I've been looking online and I'm impressed by the capabilities of using voxel data, especially for terrain building and manipulation. The problem is that voxels are never clearly explained on any site that i visited or how to use/implement them. All i find is that voxels are volumetric data. Please provide a more complete answer; what is volumetric data. It may seem like a simple question but I'm still unsure.

Also, how would you implement voxel data? (I aim to implement this into a c++ program.) What sort of data type would you use to store the voxel data to enable me to modify the contents at run time as fast as possible. I have looked online and i couldn't find anything which explained how to store the data. Lists of objects, arrays, ect...

How do you use voxels?

EDIT: Since I'm just beginning with voxels, I'll probably start by using it to only model simple objects but I will eventually be using it for rendering terrain and world objects.

Answer 1

Voxels are just 3D pixels, i.e. 3D space regularly subdivided into blocks.

How do you use them? It really depends on what you are trying to do. A ray casting terrain game engine? A medical volume renderer? Something completely different?

Plain 3D arrays might be the best for you, but it is memory intensive. As BWG pointed out, octree is another popular alternative. Search for Sparse Voxel Octrees for a more recent approach.

Answer 2

In essence, voxels are a three-dimensional extension of pixels ("volumetric pixels"), and they can indeed be used to represent volumetric data.

What is volumetric data

Mathematically, volumetric data can be seen as a three-dimensional function F(x,y,z). In many applications this function is a scalar function, i.e., it has one scalar value at each point (x,y,z) in space. For instance, in medical applications this could be the density of certain tissues. To represent this digitally, one common approach is to simply make slices of the data: imagine images in the (X,Y)-plane, and shifting the z-value to have a number of images. If the slices are close to eachother, the images can be displayed in a video sequence as for instance seen on the wiki-page for MRI-scans (https://upload.wikimedia.org/wikipedia/commons/transcoded/4/44/Structural_MRI_animation.ogv/Structural_MRI_animation.ogv.360p.webm). As you can see, each point in space has one scalar value which is represented as a grayscale.

Instead of slices or a video, one can also represent this data using voxels. Instead of dividing a 2D plane in a regular grid of pixels, we now divide a 3D area in a regular grid of voxels. Again, a scalar value can be given to each voxel. However, visualizing this is not as trivial: whereas we could just give a gray value to pixels, this does not work for voxels (we would only see the colors of the box itself, not of its interior). In fact, this problem is caused by the fact that we live in a 3D world: we can look at a 2D image from a third dimension and completely observe it; but we cannot look at a 3D voxel space and observe it completely as we have no 4th dimension to look from (unless you count time as a 4th dimension, i.e., creating a video).

So we can only look at parts of the data. One way, as indicated above, is to make slices. Another way is to look at so-called "iso-surfaces": we create surfaces in the 3D space for which each point has the same scalar value. For a medical scan, this allows to extract for instance the brain-part from the volumetric data (not just as a slice, but as a 3D model).

Finally, note that surfaces (meshes, terrains, ...) are not volumetric, they are 2D-shapes bent, twisted, stretched and deformed to be embedded in the 3D space. Ideally they represent the border of a volumetric object, but not necessarily (e.g., terrain data will probably not be a closed mesh). A way to represent surfaces using volumetric data, is by making sure the surface is again an iso-surface of some function. As an example: F(x,y,z) = x^2 + y^2 + z^2 - R^2 can represent a sphere with radius R, centered around the origin. For all points (x',y',z') of the sphere, F(x',y',z') = 0. Even more, for points inside the sphere, F < 0, and for points outside of the sphere, F > 0.

A way to "construct" such a function is by creating a distance map, i.e., creating volumetric data such that every point F(x,y,z) indicates the distance to the surface. Of course, the surface is the collection of all the points for which the distance is 0 (so, again, the iso-surface with value 0 just as with the sphere above).

How to implement

As mentioned by others, this indeed depends on the usage. In essence, the data can be given in a 3D matrix. However, this is huge! If you want the resolution doubled, you need 8x as much storage, so in general this is not an efficient solution. This will work for smaller examples, but does not scale very well.

An octree structure is, afaik, the most common structure to store this. Many implementations and optimizations for octrees exist, so have a look at what can be (re)used. As pointed out by Andreas Kahler, sparse voxel octrees are a recent approach.

Octrees allow easier navigating to neighbouring cells, parent cells, child cells, ... (I am assuming now that the concept of octrees (or quadtrees in 2D) are known?) However, if many leaf cells are located at the finest resolutions, this data structure will come with a huge overhead! So, is this better than a 3D array: it somewhat depends on what volumetric data you want to work with, and what operations you want to perform.

If the data is used to represent surfaces, octrees will in general be much better: as stated before, surfaces are not really volumetric, hence will not require many voxels to have relevant data (hence: "sparse" octrees). Refering back to the distance maps, the only relevant data are the points having value 0. The other points can also have any value, but these do not matter (in some cases, the sign is still considered, to denote "interior" and "exterior", but the value itself is not required if only the surface is needed).

How to use

If by "use", you are wondering how to render them, then you can have a look at "marching cubes" and its optimizations. MC will create a triangle mesh from volumetric data, to be rendered in any classical way. Instead of translating to triangles, you can also look at volume rendering to render a "3D sampled data set" (i.e., voxels) as such (https://en.wikipedia.org/wiki/Volume_rendering). I have to admit that I am not that familiar with volume rendering, so I'll leave it at just the wiki-link for now.

Answer 3

In popular usage during the 90's and 00's, 'voxel' could mean somewhat different things, which is probably one reason you have been finding it hard to find consistent information. In technical imaging literature, it means 3D volume element. Oftentimes, though, it is used to describe what is somewhat-more-clearly termed a high-detail raycasting engine (as opposed to the low-detail raycasting engine in Doom or Wolfenstein). A popular multi-part tutorial lives in the Flipcode archives. Also check out this brief one by Jacco.

There are many old demos you can find out there that should run under emulation. They are good for inspiration and dissection, but tend to use a lot of assembly code.

You should think carefully about what you want to support with your engine: car-racing, flying, 3D objects, planets, etc., as these constraints can change the implementation of your engine. Oftentimes, there is not a data structure, per se, but the terrain heightfield is represented procedurally by functions. Otherwise, you can use an image as a heightfield. For performance, when rendering to the screen, think about level-of-detail, in other words, how many actual pixels will be taken up by the rendered element. This will determine how much sampling you do of the heightfield. Once you get something working, you can think about ways you can blend pixels over time and screen space to make them look better, while doing as little rendering as possible.