Computer Animation

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Computer Graphics Global Illumination Photon
Mapping, Participating Media Lecture
12 Taku Komura
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last lecture

• Monte-Carlo Ray Tracing
• Path Tracing
• Bidirectional Path Tracing
• Photon Mapping

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Today

• Methods to accelerate the accuracy of photon
  mapping
• Rendering Participating Media

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Accelerating the accuracy of photon mapping

• Combine with ray tracing to visualize the
  specular light visible from the camera
• Shoot more photons towards directions where more
  samples are needed
• Caustics photon map
• Tracing photons only towards specular surfaces

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A Practical Two-Pass Algorithm

• Building photon maps by photon tracing
• Separate the photon paths into different
  categories according to the reflectance
• Rendering
• Combining the radiance of difference light paths

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Light Transport Notation

• L Lightsource
• E Eye
• S Specular reflection
• D Diffuse reflection
• (k) one or more k events
• (k) zero or more of k events
• (k)? zero or one k event
• (kk) a k or k event

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Photon Tracing

• Create two photon maps
• Global photon map (the usual photon map)?
• All Photons with property L(SD)D are stored.
• Caustics photon map
• Created by tracing photons that hit the specular
  surfaces
• Cast the photons only toward specular objects
• LSD

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Rendering

• Separate the irradiance into four groups
• Direct illumination (by ray tracing or global
  photon map)? LD
• Diffuse indirect illumination (by global photon
  map) LD(SD)D
• Specular reflection (by ray tracing) L(SD)S
• Caustics (by caustics photon map)? LSD

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Caustics Photon Map

• Caustics require high resolution
• Need to cast more photons towards surfaces that
  generates caustics
• Projection Map

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Projection map

• A map of the geometry seen from the light source
• Made of many cells which is on if there is a
  geometry in that direction, and off if not
• For a point light, it is a spherical projection
• For directional light, a planar projection
• Use a bounding sphere to represent the objects

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Direct Indirect Specular
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(No Transcript)
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Why is photon mapping efficient?

• It is a stochastic approach that estimates the
  radiance from a few number of samples
• Kernel density estimation
• Can actively distribute samples to important
  areas
• Caustics photon map

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Today

• Methods to accelerate the accuracy of photon
  mapping
• Rendering Participating Media

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Participating Media

• Dusty air, clouds, silky water
• Translucent materials such as marble, skin, and
  plants
• Photon mapping is good in handling participating
  media
• In participating media, the light is scattered to
  different directions

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Single / Multiple scattering
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The brightness of a point

• Is decided by
• Out scattering
• Absorption
• In scattering

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Light out-scattering

• The change in radiance, L, in the direction ?,
  due to out scattering is given by
• The change in radiance due to absorption is

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In-scattering

• The change due to inscattering
• where the incident radiance, Li, is integrated
  over all directions
• p is called the phase function describing the
  distribution of the scattered light

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Phase function

• Isotropic scattering
• Scattered in any random direction
• Henyey-Greenstein Phase Function
• Scattered in the direction more towards the front
• Dust, stone, clouds

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Phase function
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Examples

• Cornell Box scene isotropic, homogeneous
  participating medium.
• 200,000 photons used with 65,000 in the volume
  map. Radiance
• estimate used 100 photons.

Cornell Box scene anisotropic, homogeneous
participating medium. 200,000 photons used with
65,000 in the volume map. Radiance estimate used
50 photons.
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Ray marching and single scattering

• Now we compute how the light will be accumulated
  along a ray
• This is called ray marching
• where N is the number of light sources and Li is
• the radiance from each light source
• The last term is the light entering from behind,
  which is attenuated by proceeding ?x

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Ray marching through a finite size medium
(Single Scattering)
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Multiple scattering

• For multiple scattering, it is necessary to
  integrate all the in-scattered radiance at every
  segment
• Here S sample rays are used to estimate the
  in-scattered light

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Photon mapping participating media

• Photon mapping can efficiently handle multiple
  scattering
• The photons interact with the media and are
  scattered / absorbed
• The average distance the photon proceeds after
  each interaction is
• Here S sample rays are used to estimate the
  in-scattered light

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Photon Scattering

• The photon is either absorbed or scattered
• The probability of scattering is
• Deciding what happens by Russian Roulette
• Once the photon interacts with the media, it is
  stored in a volume photon map

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Volume Radiance Estimate

• Same as we did for surface radiance estimate,
  locate n nearest photons and estimate the radiance

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Rendering Participating Media

• By ray tracing
• If a ray enters a participating media, we use ray
  marching to integrate the illumination.

Single scattering term
multiple scattering term
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Examples

• single scattering multiple scattering

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Subsurface Scattering

• In computer graphics, reflections of non-metallic
  materials are usually approximated by diffuse
  reflections.
• Light leaving from the same location where it
  enters the object
• For translucent materials such as marble, skin
  and milk, this is a bad approximation
• The light leaves from different locations

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Single scattering

• Direct single scattering
• Compute the distance the light has traveled and
  attenuate according to the distance
• Indirect Multiple scattering
• Photon maps

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Subsurface Scattering by Photon Mapping

• Photon tracing as explained before
• Rendering Ray marching

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BSSRDF

• Bidirectional Scattering Surface Reflectance
  Distribution Function (BSSRDF)
• Relates the differential reflected radiance dLr,
  at x in the direction ?, to the differential
  incident flux, dF, at x from direction ?.
• We can capture/model the BSSRDF and use it for
  rendering

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Rendering using BSSRDF

• (a) sampling a BRDF (b) sampling a BSSRDF
• Collect samples of incoming rays over an area

http//graphics.ucsd.edu/henrik/animations/BSSRDF
-SIGGRAPH-ET2001.avi
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Rendering by BSSRDF

• Human skin reflectance simulated by
• BRDF BSSRDF

• Readings Realistic Image Synthesis Using Photon
  Mapping by Henrik Wann Jensen, AK Peters Chapter
  9, 10