It has been a while since I’ve written about Minecraft-like games, and so today I figured I’d take a moment to discuss something which seems to come up a lot in online discussions, specifically how to implement ambient occlusion in a Minecraft-like game:

Ambient occlusion was originally introduced into Minecraft as a mod, and eventually incorporated into the core Minecraft engine along with a host of other lighting improvements under the general name of “smooth lighting”. To those who are in-the-know on voxel engine development, this stuff is all pretty standard, but I haven’t yet seen it written up in an accessible format yet. So I decided to write a quick blog post on it, as well as discuss a few of the small technical issues that come up when you implement it within a system that uses greedy meshing.

## Ambient Occlusion

Ambient occlusion is a simple and effective technique for improving the quality of lighting in virtual environments. The basic idea is to approximate the amount of ambient light that is propagated through the scene towards a point from distant reflections. The basis for this idea is a heuristic or empirical argument, and can be computed by finding the amount of surface area on a hemisphere which is visible from a given point:

Adding an ambient occlusion factor to a scene can greatly improve the visual fidelity, and so a lot of thought has gone into methods for calculating and approximating ambient occlusion efficiently. Broadly speaking, there are two general approaches to accessibility computation:

**Static algorithms**: Which try to precalculate ambient occlusion for geometry up front**Dynamic algorithms**: Which try to compute accessibility from changing or dynamic data.

Perhaps the most well known of these approaches is the famous screen-space ambient occlusion algorithm:

P. Shanmugam, O. Arikan. “Hardware accelerated ambient occlusion techniques on GPUs“. SIGGRAPH 2007.

The general idea is to read out the contents of the depth buffer, and then use this geometry to approximate the accessibility of each pixel. This can then be used to shade all of the pixels on the screen:

Screen space ambient occlusion is nice in that it is really easy to integrate into an existing rendering pipeline — especially with deferred shading — (it is just a post process!) but the downside is that because the depth buffer is not a true model of the scene geometry it can introduce many weird artefacts. This link has a brief (humorous/NSFW) survey of these flaws.

## Ambient occlusion for voxels

Fortunately, in a voxel game there is a way to implement ambient occlusion which is not only faster, but also view independent. The general idea is to calculate the ambient occlusion for each vertex using only the information from the cubes which are adjacent to it. Taking this into account, there are up to symmetry 4 possible ambient occlusion values for a vertex:

Using this chart we can deduce a pattern. Let side1 and side2 be 0/1 depending on the presence of the side voxels and let corner be the opacity state of the corner voxel. Then we can compute the ambient occlusion of a vertex using the following function:

function vertexAO(side1, side2, corner) { if(side1 && side2) { return 0 } return 3 - (side1 + side2 + corner) }

## Details regarding meshing

It is actually quite easy to integrate the above ambient occlusion algorithm into a system that uses greedy meshing. The key idea is that we just need to merge facets which have the same ambient occlusion value across each of their vertices. This works because along each of the greedy edges that have length greater than 1 voxel the ambient occlusion values of the greedy mesh will be constant (exercise for reader: prove this). So, there is almost nothing to do here except modify the code that checks if two voxels should be merged.

There is a second issue here though that is a bit more subtle. Recall that to render a quad on it needs to be subdivided into two triangles. This subdivision introduces anisotropy in how non-linear values will get interpolated along a quad. For the case where the ambient occlusion values of a quad are not coplanar, this will introduce a dependence on how the quad is subdivided. To illustrate this effect, consider the following picture:

Notice that the ambient occlusion is different for the vertices on the side than it is for the vertices on the top and bottom. To fix this, we just need to pick a consistent orientation for the quads. This can be done by comparing the ambient occlusion terms for each quad and selecting an appropriate orientation. Supposing that a00, a01, a11, a01 are the ambient occlusion values for the four vertices of a quad sorted in clockwise order. Then we can correct this problem using the following rule:

if(a00 + a11 > a01 + a10) { // generate flipped quad } else { // generate normal quad }

This one simple trick easily fixes the display problem:

## Conclusion

Adding ambient occlusion to a voxel game is super easy to do and carries little cost besides a modest increase in mesh construction time. It also improves the visual quality of the results enormously, and so it is one of those no-brainer features to add. There are plenty of places to go further with this. For example, you could take the ambient occlusion of the complement space to create translucency effects in a voxel game (kind of like this idea). You would also probably want to combine this technique with other more sophisticated lighting methods to handle things like shadows and possibly reflections, but this maybe a better topic for another post.

**EDIT 1: **Embarrassingly I had the initial definition for ambient occlusion wrong. I fixed this.

**EDIT 2: **Mrmessiah, who** **is probably the true inventor of this technique commented on a reddit thread about this and said the following:

*This post caught my eye – I was the guy that wrote the original Ambient Occlusion mod for Minecraft. Minecraft’s original lighting system (I think!) had air blocks with discrete lighting levels from 0 to 15 and any block face exposed to one took its lighting level from that.*

*You sum it up how the first working version of my algorithm worked pretty well! That first version still had the “blocky” look because the underlying faces were still taking their light level from the air block touching them, but at least the AO effect softened it a bit where you had geometry nearby. edit Here’s the very first pic of it working on my test map and you can see what I mean about the “blocky light with AO” thing.*

*The smooth lighting variant came later – that worked slightly differently, by averaging light levels at vertices on a plane. Originally I had thought I would have that as an “additional” effect on top of the AO effect, and just apply it on flat surfaces. But then I realised, because the lighting level of solid blocks was 0, I could just do that averaging everywhere, and it’d give me AO for free. I suck at explaining without diagrams, unfortunately. :(*

*I should say that the lighting system currently in Minecraft was written by Jeb, he did contact me to see about using mine and I said “sure” and offered to give him my code but I think he reimplemented his own variant of it in the mean time.*

*Don’t know if I was the first person to come up with either algorithm, but it was fun working out how to do it.*

**EDIT 3: **Since posting this, I’ve learned about at least two other write ups of this idea. Here they are:

Awesome post! Thanks for going over this topic, I was just looking into ambient occlusion the other day and didn’t think about there only being 4 possible outcomes. I wonder if there is an equivalent optimization when using the Naive Surface technique you blogged about. Seeing how it produces a mesh that is similar but with averaged weights, maybe there is a way to use the value of a location for the amount of ambient occlusion to use.

-Dane

Yep! Though you have to be a bit more careful in surface nets with how you handle non-manifold facets. However, the same basic idea does work except you need to take into account the position of the vertices as well.

I was messing with this on my project and came up with the same rule after a lot of fooling around. Your treatment is much more sophisticated, as usual. And I never did realize I could just flip a quad to solve the corner problem. Thanks for that!

Here’s my writeup for anyone interested: http://www.sea-of-memes.com/LetsCode35/LetsCode35.html

Cool! It is awesome to see other people’s work in this area. It is interesting to see the thought process behind your derivation, keep up the awesome work! I’ll add a link to your post in my blog.

This is not the minecraft smooth lighting algorithm. The one used in minecraft is more complex. All blocks have a light light value assigned to them. Blocks which are directly exposed to the sky (that is, there are no other blocks above them) are assigned a light value of 15. Then adjacent neighbors to these blocks are assigned a value of 14. The light propagates like this, where the light level is lowered by 1 through each iteration. Solid blocks which are not surface blocks have a light value of 0. The light value at each vertex is then computed by taking the average of the light values of the eight blocks surrounding the vertex (or alternatively the average of the four blocks that lie on the face of the block).

Creating and removing blocks is of course considerably more complicated. However, you get things such as caves that gradually get darker and also you get a somewhat decent shadow effect for free.

More information: https://github.com/overviewer/Minecraft-Overviewer/blob/master/docs/design/designdoc.rst#lighting

Video of my implementation: https://www.youtube.com/watch?v=xSU04l4mIeU

Averaging light levels and checking occlusion are the same thing in the situation where all the non-zero light levels are equal. Of course when you add in a more complicated lighting model on top AO, then you need to do something like you describe. If you look at the edits, I have a comment from the guy who invented the original smooth lighting mod for Minecraft which basically explains the progression and he gives almost the exact same algorithm.

However, what you wrote here doesn’t quite work because of the situation where you may have a diagonal block. In that case you need to check if it is a corner and occluded by the two side blocks, or else you’ll get light leaking through cracks. But the idea is more-or-less correct.

Hi there!

Just wanted to show the anisotropy fix in action:

Before: https://twitter.com/kiwibonga/status/353578946903818241/photo/1

Buggy first attempt (flips the wrong quads): https://twitter.com/kiwibonga/status/353297183895867392/photo/1

Second attempt: https://twitter.com/kiwibonga/status/353546664985903105/photo/1

Looks MUCH better — I couldn’t possibly go back to the version without flipping now!

I do notice some jagginess near the crosshair (looks pointy) — I wonder if it’s caused by my implementation (maybe a bug), or if it’s an inevitable side effect of linear interpolation.

There was indeed an issue with the way I calculated the influence of AO that made the jaggies more noticeable. After fixing it, I fiddled around with the “curve” associated with each AO value to try and reduce interpolation artifacts:

const float AOcurve[] = float[]( 0.0, 0.25, 0.50, 0.75 );

http://i.imgur.com/fUgPYk1.png (accentuated banding)

const float AOcurve[] = float[]( 0.0, 0.2, 0.8, 1.0 );

http://i.imgur.com/IcS0S4h.png (accentuated banding)

const float AOcurve[] = float[]( 0.0, 0.6, 0.8, 1.0 );

http://i.imgur.com/39UMSMB.png (accentuated banding)

That last one is probably as good as I can get it to look without doing some sort of sine interpolation in the fragment shader…

Awesome! I am totally going to use this trick!

I’m curious as to where those values could possibly be applied – are you using that curve inside a custom fragment shader ?

To touch upon what rootdynasty pointed out, this is a bit of a naïve oversimplification of Minecraft’s smooth-lighting algorithm in that it assumes that all of the blocks in Minecraft are full cubes. In fact there are a lot of blocks to which AO is applied that are not full cubes, so one cannot make it a simple lookup based on neighboring blocks. You’d need to at least have some measure of interpolation to determine the per-vertex weights for, let’s say, a half-height block.