CS 655 Computer Graphics

1
CS 655 Computer Graphics

• Final Exam Review

2
Ray Tracing Basics

• General idea
• Forward vs. Backward ray tracing
• Primary rays
• Intersection calculations
• sphere
• plane
• polygon
• even/odd rule
• box
• quadric

3
Ray Tracing Basics II

• Reflection rays
• Transmission rays
• Indices of refraction
• Shadow rays
• The Ray Tree
• Computing a pixel color

4
Ray Tracing Improvements - Antialiasing

• Why does aliasing occur?
• Antialiasing approaches
• Supersampling
• Send multiple rays per pixel
• Average the results for the sub-pixels
• Adaptive Sampling
• Supersample near object edges
• Leave non-aliased areas at lower sampling
  resolution
• Cone Tracing
• Rather than sending a ray, send a cone
• Makes computation difficult, but gives nice
  results
• Beam Tracing
• Similar to cone tracing, but a pyramidal beam is
  sent instead
• Pencil Tracing
• Send out an axial ray and a group of paraxial rays

5
Disributed Ray Tracing

• Idea Introduce noise into the ray traced scene
  to reduce aliasing, perfect reflections, etc.
• Rays (primary or secondary) are stochastically
  jittered from their original direction

6
Disributed Ray Tracing II

• Distribute rays over
• Space
• Antialiases the image
• Send jittered rays through subpixels
• Reflection angle
• Gives glossy reflections
• Transmission angle
• Gives translucency
• Shadow Ray
• Gives soft shadows
• Lens Area
• To simulate depth of field
• Time
• For motion blur

7
Ray Tracing Optimizations

• Attempt to improve the ray tracer in some
  fashion
• Reduce intersection time
• Reduce the number of intersections performed
• Use general entities rather than single discrete
  rays

8
Bounding Volumes

• Replace expensive intersection computations with
  cheaper ones
• Increases the total number of intersection
  computations
• Hopefully reduces the overall time required for
  intersection calculation
• Various objects can be used for the bounding
  volume
• Sphere
• Axis aligned box
• Non-axis aligned box
• Union of bounding boxes
• Intersection of slabs

9
Bounding Volume Hierarchies

• Surround each object in a bounding volume
• Group the volumes into a hierarchy
• Perform intersection tests against nodes in the
  hierarchy
• If the ray misses a node, you dont need to
  intersect against objects down that branch

10
Bounding Volume Hierarchies

• Goldsmith and Salmon algorithm
• 3D Spatial Subdivision approaches
• Uniform Spatial Subdivision
• Use 3DDDA to traverse
• Simple computation, but the structure may not fit
  the data well
• Non-Uniform Spatial Subdivision
• Octree
• BSP Tree
• Median Split
• Direction Cube
• Shadow buffer

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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

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The Rendering Equation
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The Rendering Equation II

• How well do various rendering techniques fit into
  the rendering equation?

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Path Tracing

• Send a ray through a pixel
• Trace the ray to its first intersected object
• From the intersected object, send out
• One ray to each light source
• One additional ray
• a diffusely reflected ray,
• a specularly reflected ray, or
• a transmissive ray
• Trace the ray and recursively follow it, as above
• Produces a ray path not a ray tree

15
Radiosity

• An attempt to deal with diffuse interactions in
  an environment
• Assume a closed environment
• Determine how much light is transmitted between
  all pairs of patches in the environment

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The Radiosity Solution
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Substructuring

• Idea
• Divide areas of large change into smaller
  elements
• Compute patch radiosities
• Compute element radiosities assuming that all
  other patches remain undivided
• To compute this, we must first compute
  element-to-patch form factors and patch
  radiosities

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Substructuring Summary

• Compute element-to-patch
• form factors

• Compute patch-to-patch
• form factors

• Solve for patch radiosities

• Compute element
• radiosities

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Progressive Refinement Radiosity

• Rearrange the radiosity equation so that at each
  iteration you shoot all energy from one patch to
  all other patches, rather than gathering all
  energy from all patches to one patch

Standard Radiosity
Progressive Refinement
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Progressive Refinement with Ambient

• Progressive refinement images will be too dark in
  the early stages
• We can add some ambient light into the
  environment, then reduce it as we get closer to
  the actual solution

21
Radiosity Terminology

• Gathering
• Standard radiosity at each iteration, one
  patchs radiosity is updated by accounting for
  contributions from all other patches
• Shooting
• the technique used in progressive refinement in
  which at each iteration, one patch shoots its
  energy and all patches that receive energy from
  that one are updated
• Shooting and ambient
• An ambient term is introduced to lessen the
  variation in the image from iteration to
  iteration. As the solution converges, the
  ambient term goes away

22
Form Factor Computation

• Form Factor the fraction of energy leaving one
  patch that arrives at another patch
• Expensive to compute
• Analytic solutions
• Too difficult
• Numeric solutions
• Hemicube
• Hemisphere
• Single plane
• Monte Carlo methods
• Hierarchic methods

23
Global Illumination

• How do we get both specular and diffuse
  interactions?
• What strengths and weaknesses to our current
  rendering approaches have?
• Rushmeier and Torrance two pass method
• Diffuse transmission
• Specular transmission
• Specular reflection
• Sillion and Puechs approach

24
Photon Mapping

• What is it?
• Photon maps
• Caustic photon map
• Global photon map
• Rendering with photon maps

25
Image Based Modeling and Rendering

• What it is
• Why is it interesting
• Using images to create 3D models, or to render an
  environment
• Each of the papers covered in class

26
IBMR Papers

• QuickTime VR
• View Interpolation for Image Synthesis
• Plenoptic Modeling
• Plenoptic Stitching
• Modeling and Rendering Architecture from
  Photographs
• View Morphing
• Rendering with Concentric Mosaics
• Multiple Center-of-Projection Images
• Video Mosaics for Virtual Environments
• The Lumigraph
• Light Field Rendering
• Layered Depth Images
• LDI Trees
• Tour Into The Picture

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Metropolis Light Transport

• Statistical approach to global illumination
• Uses the idea of detailed balance
• Follow paths of light through the scene
• The path to follow is determined based on
  mutations and probability distribution of the
  light
• Implicit and explicit light paths
• Evaluating light paths
• Mutation strategies
• Bidirectional path tracing

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Volume Modeling and Rendering

• Data storage considerations
• Contours
• Isosurface rendering
• Marching Cubes
• Edge intersection table
• Normal calculation
• Volume rendering
• Cast ray through volume accumulating as you go
• Efficient processing of rays
• Computing next cell intersected

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Non Photorealistic Rendering

• Pen and Ink Illustration
• Strokes
• Texture
• Tone
• Outline
• Painterly Rendering
• Physical simulation
• Automatic painting
• Cartoons
• Using graftals
• Technical Illustrations
• Scientific Visualization