**In this reprinted #altdevblogaday opinion piece, game programmer Simon Yeung shares the results from his implementations of angle-based SSAO, or Screen Space Ambient Occlusion.**
SSAO (Screen space ambient occlusion) is a common post processing effect that approximates how much light is occluded in a given surface by the surrounding objects.

In this year's SIGGRAPH, there were a few slides in

"The Technology behind the Unreal Engine 4 Elemental Demo" about how Epic implements SSAO. Their technique can either use only the depth buffer or with the addition of per-pixel normal.

I tried to implement both versions with a slight modification:

# Using only the depth buffer

The definition of

ambient occlusion is to calculate the visibility integral over the hemisphere of a given surface:

To approximate this in screen space, we design our sampling pattern as paired samples:

paired sample pattern
So for each pair of samples, we can approximate how much the shading point is occluded in 2D instead of integrating over the hemisphere:

The AO term for each given pair of samples will be min( (θ

left + θ

right)/π, 1). Then by averaging the AO terms of all the sample pairs (in my case, there are 6 pairs), we achieve the following result:

# Dealing with large depth differences

As seen in the above screen shot, there are dark halos around the knight. But the knight should not contribute AO to the castle, as he is too far away. So to deal with the large depth differences, I adopted the approach used in

Toy Story 3.

If one of the paired samples is too far away from the shading point, say the red point in the following figure, it will be replace by the pink point, which is on the same plane as the other valid paired sample:

So we can interpolate between the red point and the pink point for dealing with the large depth difference. Now the dark halo is gone:

The above treatment only happens if one of the paired samples is far away from shading point. What if both of the samples have large depth differences?

dark halo artifact is shown around the sword
AO strength of this pic is increased to high light the artifact
In this case, it will result in the dark halo around the sword in the above screenshot. Remember we are averaging all the paired samples to compute the final AO value. So to deal with this artifact, we just assign a weight to each paired sample and then re-normalize the final result.

Say, for each paired sample, if both of the samples are within a small depth difference, that sample pair will have a weight of 1. If only 1 sample is far away, that pair will have a weight of 0.5. And finally if both of the samples are far away, the weight will be 0. This can eliminate most (but not all) of the artifacts:

# Approximating arc-cos function

In this approach, the AO is calculated by using the angle between the paired samples, which needs to evaluate the arc-cos function, which is a bit expensive. We can approximate acos(x) with a linear function: π(1-x)/2.

And the resulting AO looks much darker with this approximation:

computed with the arc-cos function
computed with the linear approximation
Note that the maximum error between the two functions is around 18.946 degrees.

This may affect the AO for the area of a curved surface with low tessellation. You might either need to increase the bias angle threshold or switch to a more accurate function. So my second attempt is to approximate it with a quadratic function: π(1- sign(x) * x * x)/2.

And this approximation shows a very similar result to the one using the arc-cos function.

computed with the arc-cos function
computed with the quadratic approximation
And the maximum error of this function is around 9.473 degrees.

# Using per-pixel normal

We can enhance the details of AO by making use of the per-pixel normal. The per-pixel normal is used for further restricting the angle to compute the AO where the angle θ

left, θ

right are clamped to the tangent plane:

And here is the final result:

# Conclusion

The result of this AO is pleasant by takinga total of 12 samples per pixel and with 16 rotation in 4×4 pixel block at half resolution. I did not apply bilateral blur to the AO result, but applying the blur may give a softer AO look. Also, approximating the arc-cos function with a linear function is not accurate, but it gives a good enough result for me.

Finally, more time is needed to spend on generating the sampling pattern in the future, where the pattern I currently used is nearly uniform distributed (with some jittering).

**References**
[1]

The Technology behind the Unreal Engine 4 Elemental Demo
[2]

Rendering techniques in Toy Story 3
[3]

Image-Space Horizon-Based Ambient Occlusion
[4]

Wolfram Alpha
[5] The models are exported from UDK and extracted from

*Infinity Blade* using umodel.exe

*[This piece was reprinted from #AltDevBlogADay, a shared blog initiative started by @mike_acton devoted to giving game developers of all disciplines a place to motivate each other to write regularly about their personal game development passions.]*