Last Time

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Last Time

• Ray-tracing implementation
• Recall the light paths that ray-tracing captures
• Technically, we are talking about eye ray
  tracing, which traces rays originating at the
  eye
• Some people use the terms forward or backward
  ray-tracing, but there is no agreement in which
  direction is forward!

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Which paths are present? Which paths are missing?
Ray-traced Cornell box, due to Henrik
Jensen, http//www.gk.dtu.dk/hwj
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Today

• Rendering algorithms that capture other light
  paths
• Distribution ray-tracing
• Radiosity
• Bi-directional ray tracing

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Ray-Tracing and Sampling

• Basic ray-tracing casts one ray through each
  pixel, sends one ray for each reflection, one ray
  for each point light, etc
• This represents a single sample for each point,
  and for an animation, a single sample for each
  frame
• Many important effects require more samples
• Motion blur A photograph of a moving object
  smears the object across the film (longer
  exposure, more motion blur)
• Depth of Field Objects not located at the focal
  distance appear blurred when viewed through a
  real lens system
• Rough reflections Reflections in a rough surface
  appear blurred

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Distribution Raytracing

• Distribution raytracing casts more than one ray
  for each sample
• Originally called distributed raytracing, but the
  names confusing
• How would you sample to get motion blur?
• How would you sample to get rough reflections?
• How would you sample to get depth of field?

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Distribution Raytracing
Depth of Field
From Alan Watt, 3D Computer Graphics
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Missing Paths

• Basic recursive raytracing cannot do
• LSDE Light bouncing off a shiny surface like a
  mirror and illuminating a diffuse surface
• LDE Light bouncing off one diffuse surface to
  illuminate others
• Basic problem The raytracer doesnt know where
  to send rays out of the diffuse surface to
  capture the incoming light
• Also a problem for rough specular reflection
• Fuzzy reflections in rough shiny objects

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Bi-directional Raytracing

• Cast rays from the light sources out into the
  scene
• When a ray hits a diffuse surface, accumulate
  some light there
• Surfaces record the amount of light that hits
  them
• Store the light in texture maps
• Store the light in quadtrees
• Store the light in photon maps
• Cast rays from the eye out into the scene
• When a ray hits a diffuse surface, look up the
  amount of light that hit it in the light-ray
  phase
• What paths does it capture?
• What sort of visual effects do you see?

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Caustics
Standard raytracer Diffuse table and blue ball,
mirrors left, right and back, transparent red ball
Bi-directional raytracer
More rays in the light pass
Note the LSDSE paths
From Alan Watt, 3D Computer Graphics
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Refraction caustic
Henrik wann Jensen, http//www.gk.dtu.dk/hwj
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Refraction caustics
Henrik wann Jensen, http//www.gk.dtu.dk/hwj
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Still Missing

• LDE paths Diffuse-diffuse transport
• Formulated and solved with radiosity methods
• L(SD)E paths
• Solved with Monte-Carlo renderers very very
  inefficient
• Also solvable with multi-pass methods, but also
  very very inefficient, and subject to aliasing
• An unsolved (unsolvable?) problem

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Real World LDE Paths
From Alan Watt, 3D Computer Graphics
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Radiosity Assumptions

• All surfaces are perfectly diffuse
• Means that is doesnt matter which way light hits
  or leaves a surface
• Illumination is constant over a patch
• Can break the world up into a discrete number of
  pieces
• Problems at sharp illumination boundaries -
  shadows
• Ways around these problems, but less efficient
  and less able to manage scene complexity
• Assumptions allow us to solve for LDE paths

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Radiosity Equation

• Derived from the global illumination equation
  using radiosity assumptions
• Bi is the radiosity (brightness) of patch i
• ?i is the diffuse reflection coefficient
• Fij is the form factor, which quantifies how much
  light patch j contributes to patch i
• The brightness of each patch depends on how much
  light it gets from all the others, and its
  diffuse reflection

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Solving the Radiosity Eqn

• Radiosity algorithms use one of several methods
  to solve the radiosity equation
• Basically a very large linear system, so
  techniques can all be mapped onto linear system
  solvers
• A large part of the computation is in finding
  form factors
• Describe how much light gets from each patch to
  every other patch
• Geometric in nature - do not depend on the
  illumination, just the layout of the scene
• Another key factor is finding good meshing
  strategies - ways of laying out the patches

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Radiosity Example

• Color bleeding is extreme in this example
• Textures are applied after solving for
  illumination
• Some meshing artifacts are visible - note the
  banding around the pictures on the wall

From Alan Watt, 3D Computer Graphics
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Radiosity Meshing

• Each patch is colored with its illumination
• Note the discrete nature of the solution
• The previous image was obtained by pushing color
  to vertices and then Gourand shading

From Alan Watt, 3D Computer Graphics