CS 655

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CS 655

• Ray Tracing Optimizations

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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

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Optimizations

• Approaches to optimizing the ray tracer
• Data structures
• Numerical methods
• Computational geometry
• Optics
• Statistical methods
• Distributed computing

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Ray Tracing Optimizations

• Criteria for judging acceleration techniques
  (from Kirk and Arvo)
• Simplicity
• Applicability
• All rays?
• All object types?
• Performance
• Recources
• Storage
• Multiple processors

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Intersection Optimizations

• Reduce intersection computation time
• Reduce the number of intersections
• Replace individual rays with a more general entity

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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

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Bounding Volume Example
Bounding Sphere
Bounding Sphere hit, object missed
Bounding Sphere hit, object hit
Bounding Sphere missed, object missed
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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

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Types of Bounding Volumes
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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

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Example Bounding Volume Hierarchy
4b
4d
4a
4f
4e
3b
4c
3a
2a
2b
1
1
2a
2b
3a
4d
3b
4a
4c
4b
4f
4e
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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

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Bounding Volume Hierarchy

• Once the tree is built, trace rays, intersecting
  with the hierarchy.
• If one volume in the hierarchy is missed, you
  dont 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

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Building the BVH

• Manually
• Difficult
• Automatically
• Simple n-ary tree
• Poor, since it doesnt take the model into
  consideration
• Median-cut algorithm
• Better, but still doesnt take full advantage of
  scene properties
• Heuristic tree search
• Good, if the heuristic is chosen well

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Goldsmith and Salmon approach

• Observations
• Must be able to handle many objects (hundreds of
  thousands)
• Checking all possible nodes will be too slow
• Limit the search to a small portion of the nodes
• This may (probably does) produce a sub-optimal
  tree
• This is okay, as long as it still works
  better/faster than other techniques
• Heuristic
• Search only the subtree of a node that would give
  the smallest increase in surface area to the node
  if the new node were to be inserted as a child of
  it.

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Goldsmith and Salmon Algorithm

• Create root node
• For each object x do
• Insert node x as a child of the root node
• Compute the increase in surface area
• For the original root node, it is the sum of the
  surface areas of all children
• For other nodes, it is the surface area of the
  enclosing bounding volume
• Insert node x as a child of each node i that is a
  child of the root.
• If node i is currently a leaf node
• Create a new node j.
• Insert nodes i and x as children nodes of node j
• Compute increase in surface area caused by the
  new node j
• Select the location which produces the smallest
  increase in surface area
• If that location is the root node, insert the new
  node as a child of the root node
• Otherwise, repeate steps 2a-g with the candidate
  node as the root node

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Goldsmith and Salmon example
Scene before creating the hierarchy Each object
is surrounded by its bounding volume The black
rectangle is the entire scene
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1st Iteration
Current Tree
Possibilities
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2nd Iteration
Current Tree
Possibilities
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3rd Iteration
Current Tree
Possibilities
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4th Iteration
Current Tree
Possibilities
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5th Iteration
Current Tree
Possibilities
4
5
5
5
5
1
3
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5th Iteration Recursive
Current Tree
5
Possibilities
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Goldsmith and Salmon Technique

• The order in which the objects are inserted has a
  huge influence on how good the tree is
• They experimented with
• User supplied order
• Shuffled
• Sorted by line

Number of intersection Calculations per Ray
User supplied or shuffled generally best
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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, doesnt match objects well
• Non-uniform spatial subdivision
• More complex, but should give a better fit to the
  objects

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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
• The speedup in the 3DDDA may or may not
  compensate for the loss of object locality gained
  in non-uniform methods

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From Stephen Ward
Biplane 300 x 300 No 3DDDA No Anti-Aliasing 115
minutes
Biplane 300 x 300 3DDDA Anti-Aliasing 50 minutes
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Skull 300 x 300 No 3DDDA No Anti-Aliasing 95
minutes
Skull 300 x 300 3DDDA Anti-Aliasing 8 minutes
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Spheres 300 x 300 No 3DDDA No Anti-Aliasing 1.5
minutes
Spheres 300 x 300 3DDDA Anti-Aliasing 1.5
minutes
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Uniform Spatial Subdivision

• Start with a volume enclosing the entire scene
• Uniformly subdivide it until each subspace
  contains less than n objects

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Non-uniform Spatial Subdivision

• Space is discretized into regions of varying size
• Several approaches
• Octree
• BSP Tree
• Median Split

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Octrees

• An octree is created that approximates the scene
• The octree is subdivided as necessary based on
  the scene

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Octree Spatial Subdivision

• Each voxel has a list of objects whose surfaces
  penetrate the volume
• When a ray penetrates a voxel, the list of
  objects for that voxel is used for possible
  intersections
• Objects are tested for intersection with the 6
  voxel faces
• If no intersection occurs, a point on the object
  is tested for being inside the voxel
• Start with a box which contains all objects
• Recursively subdivide the box until each voxel
  contains fewer than n objects in its list

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Octree Subdivision

• (shown in the 2-D case here)

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Octree Algorithm

• Locate the voxel which contains the ray origin
• Perform intersection calculations
• Determine the next voxel
• compute ray/box intersection with the current
  voxel
• move slightly beyond that point
• Intersections near edges and vertices can cause
  problems

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Octree Algorithm

• Procedure Octree-intersect(ray)
• Begin
• Q ray.origin
• Repeat
• Locate the voxel containing Q
• For each object associated with that voxel do
• Intersect (ray, object)
• If no intersection has been found then
• Q the point in the next voxel pierced by the
  ray
• Until an intersection is found, or Q is outside
  the bounding box of the environment

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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

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BSP Trees
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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

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BSP Example
Region 4
2a

• Ray is split at the 2b plane
• Region 1 is intersected against
• Ray is split at plane 1
• Region 2 is intersected against
• Ray is split at plane 2a
• Region 3 is intersected against
• Region 4 is intersected against

Region 3
Region 2
1
Region 5
2b
Region 1
ray
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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

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Median Split
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Median Split Pseudocode

• Surround all of the objects in the scene in an
  axis-aligned bounding box.
• Determine the largest magnitude extent of the
  bounding box.
• Subdivide the bounding box at the middle of the
  box, in the coordinate direction determined by
  the extent from step 2.
• 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.
• For each subspace in the final divided space,
  maintain a list of those objects associated with
  that sub-space.

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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

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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

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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
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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

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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?

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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 cells list

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The Light Buffer

• Find where ray intersects light buffer
• Intersect against objects in that cells list

Light Buffer
Shadow Ray
Point light source
Incoming Ray
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Ray Tracing Acceleration Summary
Acceleration Techniques
Faster Intersections
Fewer Rays
Generalized Rays
Faster Ray/Object Intersections
Fewer Ray/Object Intersections

• Object
• Bounding
• Volumes
• Efficient
• intersectors

• Bounding
• Volume
• Hierarchies
• Space
• Subdivision
• Directional
• Techniques

• Adaptive
• Tree Depth
• Control
• Statistical
• Optimizations

• Beam
• Tracing
• Cone
• Tracing
• Pencil
• Tracing