CS 655
Ray Tracing Optimizations
Ray Tracing Problems
• Slow

Compare every ray vs. every object
• Rays are discrete


Aliasing problems
No coherence taken advantage of
• We would like to optimize our ray tracer

Efficiency

Generality
Quality

Optimizations
• Approaches to optimizing the ray tracer:


Data structures
Numerical methods

Computational geometry
Optics
Statistical methods

Distributed computing


Ray Tracing Optimizations
• Criteria for judging acceleration techniques: (from Kirk
and Arvo)




Simplicity
Applicability
- All rays?
- All object types?
Performance
Recources
- Storage
- Multiple processors
What should we optimize
• Say intersections are 80% of the computation.
• Give an equation which describes the number of
intersections.
• What should we do?
Intersection Optimizations
• Reduce intersection computation time
• Reduce the number of intersections
• Replace individual rays with a more general entity
Ray Tracing Acceleration Summary
Acceleration Techniques
Faster
Intersections
Faster
Ray/Object
Intersections
1.
2.
Object
Bounding
Volumes
Efficient
intersectors
Fewer
Rays
Generalized
Rays
Fewer
Ray/Object
Intersections
1.
2.
3.
Bounding
Volume
Hierarchies
Space
Subdivision
Directional
Techniques
1.
2.
Adaptive
Tree Depth
Control
Statistical
Optimizations
1.
2.
3.
Beam
Tracing
Cone
Tracing
Pencil
Tracing
Ray Tracing Acceleration Summary
Acceleration Techniques
Faster
Intersections
Faster
Ray/Object
Intersections
1.
2.
Object
Bounding
Volumes
Efficient
intersectors
Fewer
Rays
Generalized
Rays
Fewer
Ray/Object
Intersections
1.
2.
3.
Bounding
Volume
Hierarchies
Space
Subdivision
Directional
Techniques
1.
2.
Adaptive
Tree Depth
Control
Statistical
Optimizations
1.
2.
3.
Beam
Tracing
Cone
Tracing
Pencil
Tracing
Bounding Volumes
• Idea:






Provide a volume that completely encloses an object, but
which has a simpler intersection calculation than the actual
object
If the ray does not intersect the bounding volume, it will not
intersect the object
Complex intersections are replaced by simpler ones
The number of intersection calculations increases, however
Want the bounding volume as near to the object as possible
Still a linear time complexity in the number of objects
Bounding Volume Example
Bounding Sphere
Bounding Volumes
• Generally, either spheres or axis-aligned bounding
volumes are used
• Simple to intersect against
• However, these may not provide close fits to the objects
being bounded
• Several different bounding volume types have been
used
• Tradoff – ease of intersection vs. object fit
Types of Bounding Volumes
Bounding
Sphere
Intersection
Of Slabs
Axis-aligned
Bounding Box
Union of
Bounding Boxes
Non-axis-aligned
Bounding Box
Intersection of
Bounding Sphere
and Bounding Box
Ray Tracing Acceleration Summary
Acceleration Techniques
Faster
Intersections
Faster
Ray/Object
Intersections
1.
2.
Object
Bounding
Volumes
Efficient
intersectors
Fewer
Rays
Generalized
Rays
Fewer
Ray/Object
Intersections
1.
2.
3.
Bounding
Volume
Hierarchies
Space
Subdivision
Directional
Techniques
1.
2.
Adaptive
Tree Depth
Control
Statistical
Optimizations
1.
2.
3.
Beam
Tracing
Cone
Tracing
Pencil
Tracing
Hierarchical Bounding Volumes
• Bounding volumes by themselves try to reduce
intersection time, but not the number of intersections
• A bounding volume hierarchy can reduce the number
of intersections
• Place each object in its own bounding volume
• Group the bounding volumes hierarchically
• Intersection computations proceed down the hierarchy
Hierarchical Bounding Volumes
Around a million triangles
Log_2(1M) = about 20
Example Bounding Volume Hierarchy
4b
4d
4a
4f
4e
3b
4c
3a
2a
2b
1
1
2a
3a
4c
2b
4b
4d
3b
4a
4e
4f
Bounding Volume Hierarchy
• Each leaf node is a single object
• Each interior node consists of a bounding volume and a
list of pointers to its children nodes
• Process:



Determine the bounding volume for each object in the scene
(usually spheres or orthogonal parallelepipeds)
Combine bounding volumes into a tree by selecting some of
them and surrounding them with another bounding volume
Repeat this process recursively until a bounding volume is
generated that surrounds the entire scene
Bounding Volume Hierarchy
• Once the tree is built, trace rays, intersecting with the
hierarchy.
• If one volume in the hierarchy is missed, you don’t
need to intersect the ray with any children of that
bounding volume
• Algorithm:
Procedure BVH_Intersect(ray, node)
Begin
if node is a leaf then
Intersect (ray, node_object)
else if Intersect_P(ray, node_bounding_volume) then
For each child of node
BVH_Intersect(ray, child)
End
Building the BVH
• Manually

Difficult
• Automatically



Simple n-ary tree
- Poor, since it doesn’t take the model into consideration
Median-cut algorithm
- Better, but still doesn’t take full advantage of scene properties
Heuristic tree search
- Good, if the heuristic is chosen well
Ray Tracing Acceleration Summary
Acceleration Techniques
Faster
Intersections
Faster
Ray/Object
Intersections
1.
2.
Object
Bounding
Volumes
Efficient
intersectors
Fewer
Rays
Generalized
Rays
Fewer
Ray/Object
Intersections
1.
2.
3.
Bounding
Volume
Hierarchies
Space
Subdivision
Directional
Techniques
1.
2.
Adaptive
Tree Depth
Control
Statistical
Optimizations
1.
2.
3.
Beam
Tracing
Cone
Tracing
Pencil
Tracing
3D Spatial Subdivision Techniques
• Start with a volume that bounds the entire environment
• Successively partition the volume into smaller pieces
• Objects are grouped based on volumes, rather than
vice-versa
• Several approaches using this idea


Uniform spatial subdivision
- Simple, doesn’t match objects well
Non-uniform spatial subdivision
- More complex, but should give a better fit to the objects
Uniform Spatial Subdivision
• Voxels are all the same size, organized into a 3D grid
• Space subdivision is independent of the objects in the
scene
• The “next voxel” calculation can be done very
efficiently
• 3DDDA can be used (three-dimensional digital
differential analyzer )
• The speedup in the 3DDDA may or may not
compensate for the loss of object locality gained in
non-uniform methods
Uniform Spatial Subdivision
• Start with a
volume enclosing
the entire scene
• Uniformly
subdivide it until
each subspace
contains less than
n objects
434243414342434
4
3
4
2
4
3
4
1
4
3
4
2
4
3
4
2
4
5
3
1
Non-uniform Spatial Subdivision
• Space is discretized into regions of varying size
• Several approaches



Octree
BSP Tree
Median Split
Octrees
• An octree is created that approximates the scene
• The octree is subdivided as necessary based on the
scene
BSP Trees
• Another non-uniform spatial subdivision technique is
Binary Space Partitioning trees
• Idea:



Split space into two subspaces (not axis aligned) based on the
objects in the subspaces
Check each subspace. If a subspace has more than n objects,
split that subspace into two smaller subspaces
Each subspace maintains a list of objects in it
BSP Trees
2a
2
4
5
3
1
1
3
2b
BSP Trees
• Divide a ray into two components – one on each side of
the partitioning plane
• Check the nearest sub-ray first

If it intersects another plane, subdivide the ray at the plane
• Intersect the nearest sub-ray against the objects in that
space
• If no intersections, move to the next sub-ray, splitting
the ray as necessary, then compute ray/object
intersections
BSP Example
Region 4
2a
• Ray is split at the 2b
plane
• Region 1 is intersected
against
• Ray is split at plane 1
Region 3
• Region 2 is intersected
against
• Ray is split at plane 2a
• Region 3 is intersected
against
• Region 4 is intersected
against
2
4
5
Region 2
3
1
1
3
Region 5
ray
Region 1
2b
Median Split BVH Technique
• An alternative method for creating a BVH is the
“Median Split” technique
• Simpler than the Goldsmith and Salmon technique
• Not as object-centric, however
• Idea:


Split space into two subspaces, based on the dimensions of the
space
Check each subspace
- If a subspace has several objects still in it, split it again
Median Split
2a
2
4
4a
1
3
8a
8b
7a
7b
6a
5a
5
3
1
5b
8c
4b
6b
2b
Median Split Pseudocode
1. Surround all of the objects in the scene in an axis-aligned
bounding box.
2. Determine the largest magnitude extent of the bounding box.
3. Subdivide the bounding box at the middle of the box, in the
coordinate direction determined by the extent from step 2.
4. If the level of subdivision is less than m (for m something like
20 or so), and the number of objects in the space is greater than
n, (n being some small number like 1 or 5 or 10 or so),
subdivide that sub-space by repeating steps 2 through 4 on the
sub-space.
5. For each subspace in the final divided space, maintain a list of
those objects associated with that sub-space.
Median Split
• With the bounding volume subspaces determined, ray
tracing proceeds:





Send out a ray
Determine which subspace is first hit
Compute intersections with all objects associated with that
subspace
If an intersection exists, report the first intersection
If no intersection, proceed to the next subspace hit by the ray
and repeat this process
Ray Tracing Acceleration Summary
Acceleration Techniques
Faster
Intersections
Faster
Ray/Object
Intersections
1.
2.
Object
Bounding
Volumes
Efficient
intersectors
Fewer
Rays
Generalized
Rays
Fewer
Ray/Object
Intersections
1.
2.
3.
Bounding
Volume
Hierarchies
Space
Subdivision
Directional
Techniques
1.
2.
Adaptive
Tree Depth
Control
Statistical
Optimizations
1.
2.
3.
Beam
Tracing
Cone
Tracing
Pencil
Tracing
Directional Techniques
• Another approach at reducing the number of ray/object
intersections is to exploit directional information
• Move processing to a higher level

i.e. rather than on a per ray basis, move computation to a
group of rays
• These techniques typically require large amounts of
storage
Direction Cube
• Axis aligned cube centered at (0, 0, 0) with edges of
length 2
• Cube is placed on the ray origin
• A ray can now be represented by a face and a (u,v)
coordinate on that face
Ray
Direction Cube
• The direction cube faces are subdivided into smaller
sub-faces

Can be either uniform or non uniform
• Each direction cell defines an infinite skewed pyramid
with its apex at the origin and its edges through cell
corners
Direction Cube
• Given the subdivided cube we can determine which cell
is pierced by each ray




Determine the dominant axis of the ray to get the intersection
face
Determine the (u, v) coordinate
Determine which cell this (u, v) point is in
Each cell keeps a list of candidate intersection objects based
on direction neighborhoods
• Is this practical for standard rays?
The Light Buffer
• Used to accelerate shadow calculations using the
directional idea
• Assumes point light sources
• Idea:




Each light source is given a uniformly subdivided direction
cube.
Prior to ray tracing, each object is projected onto each
direction cube.
Each cell contains a list of all objects that project to that cell.
For shadow computations, determine which cell is intersected
by the shadow ray, and only intersect objects in that cell’s list
The Light Buffer
• Find where ray intersects light buffer
• Intersect against objects in that cell’s list
Light Buffer
Shadow Ray
Point light source
Incoming Ray
Ray Tracing Acceleration Summary
Acceleration Techniques
Faster
Intersections
Faster
Ray/Object
Intersections
1.
2.
Object
Bounding
Volumes
Efficient
intersectors
Fewer
Rays
Generalized
Rays
Fewer
Ray/Object
Intersections
1.
2.
3.
Bounding
Volume
Hierarchies
Space
Subdivision
Directional
Techniques
1.
2.
Adaptive
Tree Depth
Control
Statistical
Optimizations
1.
2.
3.
Beam
Tracing
Cone
Tracing
Pencil
Tracing
Beam Tracing
Funkhouser et al., “A Beam Tracing method for interactive architectural acoustics” in J. of Acoust. Soc. of Am. 115(2) 2004