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# Voxel Theory & Practice

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### #1Moehammered  Members   -  Reputation: 105

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Posted 03 November 2011 - 01:14 AM

Now I do apologise in advance if I'm repeating a topic or thread, but I've used the search function and only find people talking about detailed aspects of Voxel Theory or rendering, and I unfortunately cannot understand it clearly enough. Reason being I keep trying to think how to implement it and cannot understand it properly.

So what I do understand:
- A voxel is a 3D form of a pixel, in the sense it stores data relative to its position in the world(on screen)

Now i feel like that is wrong as well but I cannot understand implementing it. Would I make something like a voxel structure that holds position and block type or something along those lines?
I'm having trouble understanding the concept of it I guess, really am confused about this specific topic.

E.G.
struct Voxel
{
float x, y, z;
char type;
}


I'm very lost on this topic and I really am interested in it but cannot seem to grasp the concept of it firmly and confidently enough.
Also the wiki page I've read and this guys explanations I've read but he talks a lot about Raycasting more than Voxel theory.

### #2Silviu Andrei  Members   -  Reputation: 163

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Posted 03 November 2011 - 02:08 AM

Typically you would store it in a 3D texture or buffer (depends on what technology you are using) and assign a location in space for the entire volume. Usually it's not practical to store the x,y,z location for each voxel individually as it's to much waste of space.
So you would have something like:

struct VoxelVolume
{
float X, Y, Z;				//Location in world coordinates of the entire volume
float SizeX, SizeY, SizeZ;     //Size of the volume in world coordinate units
int Width, Height, Depth;     //Size of the volume in number of voxels (in each direction)
float voxelValues[Width][Height][Depth];  //The actual values of the voxels
}

This is just a basic datastructure. In order to render the volume you could cast a ray for each pixel that you draw on the screen and sample the volume at some fixed points along the ray and accumulate the value until you reach a certain threshold. There are also other volume rendering techniques, this is just an example so you can understand the basic idea.

### #3TheUnbeliever  Members   -  Reputation: 952

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Posted 03 November 2011 - 02:16 AM

A pixel is a sample of an 2D image, a voxel is a sample of a 3D (or higher) image. Representation depends on how sparse your data is, but you might just have a multi-dimensional array (at least conceptually) in the same way as you might just have a 2D array of pixels. The type of the elements depends on what your voxels are samples of - e.g. they might be bone density, or they might air quality, or colour, or anything else, or some combination of these.
[TheUnbeliever]

### #4Tachikoma  Members   -  Reputation: 544

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Posted 03 November 2011 - 03:11 AM

Voxels have an implicit representation in an array in the same way as pixels are in a 2D image. Therefore, the [x, y, z] coordinate doesn't need to be stored, you generate them and use them as a look-up index in a 3D array, and fetch the colour value from the array cell, aka. the voxel.

However, volumetric data can consume quite a lot of memory. If your volume data is sparse, you'd be wasting memory on invisible voxels. Therefore, one could represent opaque voxel data with explicit coordinates (along with colour) and discard the transparent voxels, and potentially save on memory allocation in the process. Unfortunately this approach comes at a cost, the implicit relationship of neighbouring voxel entries in the 3D array is lost, as you can no longer use a simple table lookup to fetch voxels, making table queries more expensive.
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### #5Moehammered  Members   -  Reputation: 105

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Posted 03 November 2011 - 04:50 AM

hmmm, so I've done some reading. Now I think I get it a little, would this be correct:

So say I have a 3D array of 'colours' (similar to the color values of pixels in a 2D array) and I simply want to draw a cube in 3D space using the volume data available(the 3D array) than would it be like
• Grab 8 Points in 3D space
• find the volume data using these points in space by dereferencing the 3D array with these vertex locations
• construct the vertices using these points
• assign the colors of these vertices via the data stored at those locations
I think I'm starting to grasp it a bit

### #6rouncer  Members   -  Reputation: 346

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Posted 03 November 2011 - 05:12 PM

if you split the world into chunks of 256x256x256, you only need byte values for the individual voxel positions.

What your proposing works fine, ive done it myself.

### #7Rhetorician  Members   -  Reputation: 147

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Posted 21 November 2011 - 06:24 PM

I've been working on a very long blog post about representation structures for computer graphics and simulation.
I'll let you have a taste of my draft...

1.3 Sparse Voxel Octrees and Uniform Instancing

Some brilliant graphics programmers are experimenting with an attractive new way of representing graphical data, using "sparse voxel octrees". So uh, what is that?

Before I waste my time, I recommend you do some searches on Sparse Voxel Octree technology and look at real examples, too.

Henceforth I will abbreviate the term with 'SVO'

Anyway, the most notable among these frontier programmers are Jon Olick, Cyril Crassin and Branislav Síleš, (unassociated with eachother) each who have demonstrated a variety of impressive uses and potential with the technology.

Ultimately, each of their SVO implementations are only intended to be used in hybrid applications, all of which depend on polygon meshs to represent the dynamic components within scenes, at least. The picture shown below is from Cyril Crassin, who worked on a technique which uses SVO technology to approximate triangular geometry at real-time speeds. The dynamic SVO-geometry approximation can be used to cheaply simulate ray-traced effects such as local reflection (as demonstrated in the Crysis 2 Dx11 Ultra-Upgrade) or a variety of other effects, such as fluid simulation and dynamic world path finding.

Now, I'm only sixteen, but I remember playing a lot of Super Mario World back in the 90's (yeah, I could barely talk). Many games during the time used simple tile sets for representing and visualizing levels, which was almost the only way to do anything, really.

Although an old technique, there's some very popular games of today that are still similarly based on this uniform instancing format i.e. Runescape and Minecraft. Rather than sprites, Runescape presents 3D models set about a regular planar map, while Minecraft uses textured cubes (or graphic voxels) in a "volumetric" world.

SVOs don'tuse this kind of instancing. You might rather consider voxels as instances, however.

This variety of representational techniques are all based in a strict Euclidean-space uniform format, either by square or cubic units. They're essentially beneficial from a simplified geometric aspect, giving their advantages over more arbitrary (but also more demanding) primitives. Of course however, this can be somewhat restrictive.

Before I go any further, I'll decently introduce the actual advantages that graphics programmers recognize with these geometrically uniform structures.

• Essentially, they're dedicated to the principle of instancing, making them ideal for intelligent streaming and compression.
• Planar and spacial units (i.e. squares and cubes) are analogues to linear units. When axis aligned, these primitives are incredibly fast for calculating intersections and other computations which are usually pricey to do. This enables many advanced physics and lighting effects.
• In particular, sparse voxel octrees enable volumetric data with more practical means of representation, by eliminating the need to store the nil of vacuums. Also, the nature of SVOs makes them mechanically principled for intelligent level-of-detail.
Steady advancements in SVO technology are trending to reduce natural voxel aliasing even while increasing the magnitude of content.

Edited by Reflexus, 25 June 2012 - 02:25 PM.

### #8gboxentertainment  Members   -  Reputation: 723

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Posted 11 August 2012 - 09:53 AM

I'm trying to implement the sparse voxel octree structure method described in the Crassin Gigavoxels thesis using the compute shader in dx11.
I understand that every "brick" (the lowest level voxels that store the actual color information) can be stored in a texture3d.

He mentions that the actual nodes are stored separately in a 1D gpu linear cache, which I assume would just be a simple 1-dimensional array?

In terms of storing the actual node bounds, is the standard way to store the xyz coordinates of the corners of each node?
The way I'm currently thinking of doing it is to take the minimum and maximum coordinates of a large bounding box, split it into eight boxes and storing the minimum and maximum coordinates of each of these eight boxes and recursively split and store in this manner.
Then I assume that I add each minimum and maximum coordinates to the 1D array as I recursively split, and store the stride in a separate index array, which I could then use to retrieve the data at a later stage.

Has anyone else been able to implement a sparse voxel octree structure in the gpu? How are you storing your structure?

### #9scyfris  Members   -  Reputation: 157

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Posted 11 August 2012 - 03:38 PM

So I think there may be some confusion over a voxel vs a 3D texture location.

A voxel does not nessesarily have to do anything with texels. A voxel is simply a cubical "chunk" of 3D space, usually represented by 3D coordaintes (could be corner, center of voxel, etc) and an edge length. You DON'T need 3 numbers to represent width, height, and depth for CUBICAL voxels, you only need one, the edge length. Remember, all edges in a cube are the same length. You will most likely use 3 numbers for index location though (assuming your voxel is in a grid), or X, Y, Z location of corner or center of the voxel.

3D textures is a 3-dimensional array of color samples stored in memory (most likely on the GPU). If you wanted to make your voxel data correspond to a single 3D texture data, then you would scale you voxel so that your entire voxel data lies within [0, 1] and use the transformed coordinates of each voxel corner as texture coordinates. But this doesn't have to be the case, you could scale your voxel data to span 2, 3, 1000 3D textures. The choice is yours, just don't think voxels are always the same as 3D texels, because some people don't even use voxels with color data.

I'm trying to implement the sparse voxel octree structure method described in the Crassin Gigavoxels thesis using the compute shader in dx11.

A new book came out recently entitled OpenGL Insights in which Crassin has written a chapter on how to generate the voxels on the GPU, and how to generate an SVO on the GPU. The chapter is actually in PDF form on the website as one of their sample chapters free to download! ( http://openglinsights.com/ ) look for chapter 22 PDF. It may help you in your implementation as I found it very clear and consise to read.

The way I'm currently thinking of doing it is to take the minimum and maximum coordinates of a large bounding box, split it into eight boxes and storing the minimum and maximum coordinates of each of these eight boxes and recursively split and store in this manner.

You would not store the minimum and maximum coordinates in the nodes. The span of the node is inferred implicitly from the level of the node and the position ndx of the node with relation to its parent node. I would refer you to read an excellent paper entitled Efficient Sparse Voxel Octrees by Laine and Karras in which they describe exactly how the data structure is to be implemented as well as traversed. Their method is not for the GPU , but the same ideas translate to the GPU and is referenced by Crassin in his paper as being the basis for his data structure.

Edited by scyfris, 11 August 2012 - 10:58 PM.

### #10gboxentertainment  Members   -  Reputation: 723

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Posted 11 August 2012 - 10:53 PM

Thanks scyfris - you've really clarified it for me a lot. I've actually got the OpenGL Insights chapter, and I also found the Laine/Karras source code for their paper - I just need to find their paper.

I guess I'll need to read into the fundamentals of voxels and octrees first to gain an understanding.

### #11scyfris  Members   -  Reputation: 157

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Posted 11 August 2012 - 10:59 PM

I guess I'll need to read into the fundamentals of voxels and octrees first to gain an understanding.

I really love octrees. They are used everywhere. You can also experiment with a quad-tree in 2-dimensions if you are coding one up. It may be easier to visualize the tree that way.

Also, I edited my first post. When I said you don't need 3 numbers for cubical voxels, I was referring to the numbers corresponding to voxel height, width, depth. you will still probably use three numbers to access the voxel or derive the 3-d location for the voxel (index values are fine if it is a grid).

Ooo Ooo, sorry for a TON of edits, but I also found this page which might be helpful, especially the links which are referenced:
http://gamedev.stackexchange.com/questions/17050/which-data-structure-should-be-used-to-represent-voxel-terrain

Edited by scyfris, 11 August 2012 - 11:04 PM.

### #12gboxentertainment  Members   -  Reputation: 723

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Posted 12 August 2012 - 02:19 AM

I think I understand it now:

1. The root node is just a point in 3d world space, say - (0,0,0) and the length.
2. When I subdivide by splitting along each axis plane, I just offset the centres of each children by length/2 along each axis in both positive and negative directions.
3. Then for each level I use the same function as step 2, recursively subdividing and offsetting the centres relative to their parent node.

I guess in terms of rendering the structure for visualization purposes I could do a number of things - such as rasterizing instances of boxes centred at each node position and scaled at each level. Or raycasting boxes by calculating the min and max of each box derived from the stored data.

### #13gboxentertainment  Members   -  Reputation: 723

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Posted 12 August 2012 - 04:17 AM

Now, in terms of construction of the octree structure based upon triangle data - both Laine and Crassin use the top-down method and it seems as if they test all of the triangle data at each level down from the root node. Crassin then mentions the last step is to go bottom-up to store the information.

Wouldn't it be faster to start from the bottom - voxelize all the triangles, and then build each level of resolution by combining voxels with data in them and using their bounds to create the parent nodes? I'm assuming that this method has already been tried and there must be some reason that it is not preferred - but why?

### #14scyfris  Members   -  Reputation: 157

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Posted 12 August 2012 - 11:04 AM

Wouldn't it be faster to start from the bottom

I don't remember how the Laine paper reconstructs it, but I do believe the Crassin paper does construct bottom-up. They treat the fragments produced from the graphics pipeline as leafe nodes of an octree, and then build the tree up from these leaf nodes in parallel (I think on the compute shader). Essentially the idea you mentioned.

IMHO, building bottom-up or top-down depends on a few things: 1) you use the right construction that makes sense for your application, 2) the construction method you pick is not overly-complicated for your problem 3) parallelize node construction as much as possible. (important if your on the GPU, perhaps not so much if you're on CPU, and perhaps not important at all if it is done as a preprocessing step and you don't have dynamic objects).

Obviously when using the pipeline, it is faster to construct bottom-up since you have the leaf nodes after the fragment shader (all in parallel), but if you're on a CPU or something, you may just want to construct the tree top-down since that way is generally easier.

### #15gboxentertainment  Members   -  Reputation: 723

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Posted 15 August 2012 - 08:53 AM

What would be an efficient way of being able to identify the index of a voxel based on its world space coordinates?
I.e. from a pixel location on the screen, I can use a view to world transformation to obtain the world location of a voxel corresponding to that pixel.

If I stored all voxels in a 3-dimensional array that corresponds with world space coordinates, it would be easy, but then there would be a lot of wasted memory in a sparse structure.

But if I store all voxels in a linear indexed array, how would I derive the correct voxel index from its world space coordinates?

### #16Waterlimon  Crossbones+   -  Reputation: 1699

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Posted 15 August 2012 - 09:36 AM

an array would be too slow, you would use some hierarchial structure (octree or some overly complex customized self optimizing varying node count tree?)
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### #17gboxentertainment  Members   -  Reputation: 723

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Posted 15 August 2012 - 05:01 PM

so essentially, it would be most efficient to do a lookup in the octree for a selected voxel based on its world space position? Is this done by searching each level of the octree to see which side of which axis the location of the voxel lies in from top to bottom?
Would this be fast if the operation was repeated for every pixel on the screen at every frame?

### #18gboxentertainment  Members   -  Reputation: 723

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Posted 21 August 2012 - 04:53 AM

back to voxelization for a bit.
The OpenGL Crassin paper states that he uses pretty much the same "conservative surface voxelization" method as in the Schwarz & Seidel method in their "Practical Binary Surface and Solid Voxelization with Direct3D 11" from GPU Pro 3, except Crassin uses the Geometry and Fragment Shaders in OpenGL. From the demo provided by Schwarz & Seidel, I see that their solid voxelization methods seem to be about 15% faster. What would be the disadvantages of solid voxelization?

Edited by gboxentertainment, 09 September 2012 - 12:38 AM.

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