CS 655 Computer Graphics

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CS 655 Computer Graphics

• Photon Mapping

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Photon Mapping

• Photon mapping is a a technique for simulating
  global illumination.
• There are combined radiosity/ray tracing
  approaches to global illumination, as well as
  stochastic techniques (e.g. path tracing)
• Ray tracing extended with Monte Carlo techniques
• Very time consuming.
• Noisy results.
• Radiosity extended with directional capabilities
• Requires too much storage.
• Doesnt handle specular reflections correctly.

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Photon Mapping

• Idea
• Photons are emitted from light sources.
• Each photon is traced through the scene using
  path tracing.
• Every time a photon hits a surface it is stored
  in the photon map.
• Photons are either absorbed or reflected.
• Reflected photon directions are computed using
  the BRDF of the surface.
• After the photon map is created, the scene is ray
  traced.
• The photon map information is used by the ray
  tracer.

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Photon Mapping

• Constructing the Photon Map
• The photon map is created in the first pass.
• Two photon maps are kept the caustics photon
  map and the global photon map.
• The Caustics Photon Map
• Used to store photons corresponding to caustics.
• Created by emitting photons toward specular
  objects and storing these as they hit diffuse
  surfaces.
• Requires a high density of photons.

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Photon Mapping

• The Global Photon Map
• Created by emitting photons towards all objects.
• Doesnt require as much precision as caustics
  map.
• Shadow photons are created by tracing rays from
  the light source through the scene, and keeping
  track of shadow information.
• The shadow photons are later used to reduce
  shadow rays.
• Photons are stored in a balanced kd-tree. This
  provides efficiency (O(M log2 N) to locate M
  photons in a tree with N photons).
• Each photon is represented with 20 bytes.

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Photon Mapping

• Pass 2 Rendering
• Rendering is done using Monte Carlo ray tracing.
• Pixel intensities are the average of the sample
  rays sent through the pixel.
• The radiance returned by each ray is computed at
  the first surface intersected, and is equal to
  Ls(x,Yr), the surface radiance leaving point x in
  the direction of the ray Yr.

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Photon Mapping

• Pass 2 Rendering (cont)
• Ls(x,Yr) is computed using the rendering
  equation
• where
• Le is the radiance emitted by the surface and is
  taken directly from the surface definition.
• Li is the incoming radiance in the direction Yi.
• fr is the BRDF.
• Lr is the integral portion of the equation.

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Photon Mapping

• Pass 2 Rendering (cont)
• The value of the integral, Lr, can be solved
  using path tracing, but this is expensive.
  Instead, the photon map is used.
• Lr is split into several components
• where
• Li,1 represents contributions from the light
  sources.
• Li,c represents contributions from the light
  sources via specular reflection (caustics).
• Li,d represents light which has been reflected
  diffusely at least once (indirect soft
  illumination).
• Li Li,1 Li,c Li,d .

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Photon Mapping

• Pass 2 Rendering (cont)
• The BRDF is separated into diffuse and specular
  components
• fr,s represents the specular component of the
  BRDF.
• fr,d represents the diffuse component of the
  BRDF.
• fr fr,s fr,d .
• The integral is computed in two different ways
• Accurate computation used
• When the surface is seen directly by the eye.
• Within a few specular reflections.
• When the distance between the ray origin and
  intersection point is small.
• Approximate evaluation used
• When the ray has been reflected diffusely.
• If the weight of the ray is low.

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Photon Mapping

• Pass 2 Rendering (cont)
• The pieces of the equation
• The contribution via direct illumination by the
  light sources.
• Computed by using the shadow information in the
  shadow map.
• The radiance reflected off specular surfaces.
• Computed using standard Monte Carlo ray
  tracing.
• Caustics on diffuse surfaces.
• Computed using the caustic photon map.

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Photon Mapping

• Pass 2 Rendering (cont)
• The pieces of the equation (cont)
• Incoming light which has been reflected diffusely
  at least once.
• Computed using the global photon map.

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Photon Mapping

• Pass 2 Rendering (cont)
• Estimating Radiance using the Photon Map
• The photon map can be used to compute the
  radiance leaving a surface in a given direction.
• Works well with diffuse to slightly glossy
  surfaces.
• For highly glossy surfaces, lots of photons would
  be needed.
• To compute the radiance, Lr, leaving an
  intersection point x at a surface with BRDF fr
• Find the N photons with the shortest distance to
  x.
• Each photon p represents flux DFp arriving at x
  from direction Yi,p.
• Putting this into the rendering equation we
  get
• Center a sphere at x and expand until it contains
  N photons and has radius r. The area is then
  approximated with pr2.

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Photon Mapping

• Data structure
• Struct photon long energy // packed
  energy (RGB) float position3 // photon
  position float theta, phi // photon
  direction char normal3 // surface normal
  char key // kd-tree parameter struct
  photon left, right // rest of kd-tree

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Photon Mapping

• Advantages of Photon Mapping
• Can be implemented into traditional ray tracers
  by adding an additional module to the existing
  code.
• Photon maps are geometry independent.
  Calculation time for the maps is generally low,
  allowing an efficient method to recalculate maps
  during animated scenes.
• Results are comparable to or better than
  combination radiosity/ray tracing methods, and it
  is much more efficient.
• Photon mapping also reduces shadow ray
  computation by marking shadow photons.
• Caustics can be realized directly by using a
  separate photon map with higher density.

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Photon Mapping
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Photon Mapping

• An example
• Museum
• 5000 polygons and spheres.
• 1 procedural object.
• Two small spherical area light sources.
• 390,000 caustic photons.
• 165,000 global photons (9 MB).
• 298 seconds for 1st pass, 51 minutes for 2nd.
• Contains
• Caustics from glass onto rough surface.
• Caustics from cylinder to wall.
• Color bleeding between walls.

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Photon Mapping
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Photon Mapping
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Photon Mapping
 
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Photon Mapping
 
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Photon Mapping