Two Methods for Fast Ray-Cast
Ambient Occlusion
Samuli Laine and Tero Karras
NVIDIA Research
Ambient Occlusion in Theory

Occlusion of incoming ambient light
Light from these directions
does not reach the surface
Light from these
directions reaches
the surface
What It Looks Like
Ambient Occlusion in Practice


Use limited range for occlusion

Otherwise everything would be occluded in indoor scenes

Also faster to calculate because of finite radius

Use falloff function to smooth the transition
Do not solve analytically

Theoretically doable, but would be ridiculously expensive

Solution: Monte Carlo sampling

256 – 1024 samples is usually enough
Ray Casts for Ambient Occlusion

Cast a number of rays from the point to be shaded

Determine occlusion distance, apply falloff, sum

In reality use a fancy low-discrepancy sampling pattern
Using Shadow Rays

Shadow rays are usually faster than ordinary rays


Enough to detect any intersection, not necessarily closest one
Can do if we bake falloff function into the rays
Our Contributions

Two methods for calculating ambient occlusion faster

One for rasterization-based renderers

One for ray tracing -based renderers

No approximations as in screen-space methods

Up to ~10–15x speedup over state-of-the-art ray caster
Common Part: Occlusion Masks

Both methods keep occlusion status in bit masks


Utilize precalculated look-up tables for fast update of
these masks


Occlusion of all rays from one point = one bit mask
Update occlusion of all rays at once!
Resembles LUTs of hemispherical rasterization paper
by Kautz et al. 2004, but more versatile
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion Look-up Table

Store binary plane vs. ray occlusion

Plane normal & distance from origin  3D table

Clever parameterization to avoid singularity at the
center
Occlusion of a Triangle

Combination of four occlusion masks
Using Pre-Calculated Masks

1283 look-up table is sufficiently accurate

To calculate occlusion of one triangle vs. all occlusion
rays from a single receiver point

Transform triangle into coordinate space of receiver point

Calculate triangle plane and edge planes (trivial)

Fetch occlusion masks for all planes

Combine fetched masks together (binary AND)

Combine with current occlusion status (binary OR)
Method 1: Rasterization

First render depth and normal buffers

For each occluding triangle, rasterize bounds for region
of influence

For each fragment inside the region of influence,
calculate triangle vs. point occlusion and accumulate in
frame buffer


Use logic op blending into occlusion bits in frame buffer
Bounding the region of influence similar to ambient
occlusion volumes by McGuire 2010
Rasterization
Bounding the Region of Influence

Two choices for bounding volume

If triangle is large, construct hexagonal prism

If triangle is small, construct hemispherical billboard
Large triangle
Small triangle
Level of Detail Optimization

Far away occlusion doesn’t care about small details in
the occluding surface

Therefore, we could use simplified geometry for larger
occlusion distances

Nearby occlusion always has to be done using original geometry!

Split occlusion distance to various ranges, apply
progressively more and more aggressive simplification
as the distance grows

Can yield 30–140% speedup with tolerable error,
depending on the scene
Level of Detail Example
Method 2: BVH Traversal

Assume that BVH for scene triangles is available

Find occluding triangles by traversing the BVH around
the neighborhood of the receiver point

Similarities to packet traversal of Wald et al. 2007.
BVH Traversal Algorithm

Maintain cumulative occlusion mask for all AO rays
during traversal

When making traversal decision, estimate the occlusion
potential of current node’s children

Occlusion potential = Number of currently non-blocked rays that
are blocked by the bounds of the node

If occlusion potential is zero, don’t go there

If both children are eligible, first process the one with
greater potential

Try to build up occlusion quickly to be able to cull remaining nodes
Calculating Node Occlusion Mask

Tried out two kinds of node bounds

Boxes



Find silhouette edges, use same mask LUT as for triangles

Tight bounds, but expensive to compute (6 lookups)
Spheres

Determine direction and apex angle

Needs a separate 3D LUT for finding the occlusion mask

Conservative bounds, but cheap to compute (1–2 lookups)
Found out that spheres gave best overall performance
Results

Compared against our previous GPU ray caster
[Aila and Laine 2009]

Added optimizations for shadow rays

Performance measured in Mrays/second

Used various ambient occlusion radii
Results
Results: Scalability
Results: Correctness
Future Work

Soft shadows from area light sources
Thank You

Questions