Last Time

1
Last Time

• An introduction to global illumination
• We cant solve the general case, so we look to
  special cases
• Light paths as a way of classifying rendering
  algorithms L(SD)E
• Raytracing
• Captures LDSE paths Start at the eye, any
  number of specular bounces before ending at a
  diffuse surface and going to the light
• Can also do LSE and LE if light source is not a
  point

2
Today

• A bit more on ray-tracing
• Bi-directional ray-tracing
• Radiosity
• Take home point What algorithms do what sort of
  light paths, and what assumptions do they make

3
Mapping Techniques

• Raytracing provides a wealth of information about
  the visible surface point
• Position, normal, texture coordinates,
  illuminants, color
• Raytracing also has great flexibility
• Every point is computed independently, so effects
  can easily be applied on a per-pixel basis
• Reflection and transmission and shadow rays can
  be manipulated for various effects
• Even the intersection point can be modified

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Bump Mapping Examples
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Displacement Mapping

• Bump mapping changes only the normal, not the
  intersection point
• Silhouettes will not show bumps, even though
  shading does
• Displacement mapping actually shifts the
  intersection point according to a map
• Gives bump map effects and also correct
  silhouettes and self shadowing, if implemented
  fully

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From RmanNotes http//www.cgrg.ohio-state.edu/sma
y/RManNotes/index.html
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Soft Shadows

• Light sources that extend over an area (area
  light sources) should cast soft-edged shadows
• Some points see all the light - fully illuminated
• Some points see none of the light source - the
  umbra
• Some points see part of the light source - the
  penumbra
• To ray-trace area light sources, cast multiple
  shadow rays
• Each one to a different point on the light source
• Weigh illumination by the number that get through

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Soft Shadows
Umbra
Penumbra
Penumbra
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Soft Shadows
All shadow rays go through
No shadow rays go through
Some shadow rays go through
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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

• Multiple rays for each pixel, distributed in
  time, gives you motion blur
• Object positions have to vary continuously over
  time
• Casting multiple reflection rays at a reflective
  surface and averaging the results gives you
  rough, blurry reflections
• Simulating multiple paths through the camera lens
  system gives you depth of field

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Motion Blur
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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 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 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