Susu LI

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Rendering Foggy images

• Susu LI

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Introduction

• Goals The main focus of my final project is an
  implementation of the photon mapping method
  into
• ray tracer developed by Henrik Wann Jensen,
  and add multiple scattering of lights in
  participating media to get foggy like effect if
  possible.
• My system based on PBRT code

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Photon Mapping

• Jensen EGRW 95, 96
• Simulates the transport of individual photons
• Photons emitted from light sources
• Photons bounce off of specular surfaces
• Photons deposited on diffuse surfaces
• Held in a 3-D spatial data structure
• Surfaces need not be parameterized
• Photons collected by path tracing from eye

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Why Map Photons?

• High variance in Monte-Carlo renderings results
  in noise
• Collection of deposited photons into a photon
  map (a 3-D spatial data structure) provides a
  flux density estimate
• Flux samples filtered easier than path samples,
  resulting in error at lower frequencies
• Error is a result of bias, which decreases as the
  number of samples increase
• And, oh yeah, its a lot faster

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What is a Photon?

• A photon p is a particle of light that carries
  flux DFp(xp, wp)
• Power DFp magnitude (in Watts) and color of
  the flux it carries, stored as an RGB triple
• Position xp location of the photon
• Direction wp the incident direction wi used to
  compute irradiance
• Photons vs. rays
• Photons propogate flux
• Rays gather radiance

wp
DFp
xp
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Sources

• Point source
• Photons emitted uniformly in all directions
• Power of source (W) distributed evenly among
  photons
• Flux of each photon equal to source power divided
  by total of photons
• For example, a 60W light bulb would send out a
  total of 100K photons, each carrying a flux DF of
  0.6 mW
• Photons sent out once per simulation, not
  continuously as in radiosity

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Russian Roulette
?

• Arvo Kirk, S90
• Reflected flux only a fraction of incident flux
• After several reflections, spending a lot of time
  keeping track of very little flux
• Instead, completely absorb some photons and
  completely reflect others at full power
• Spend time tracing fewer full power photons
• Probability of reflectance is the reflectance r.
• Probability of absorption is 1 r.

r 60
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Mixed Surfaces

• Surfaces have specular and diffuse components
• rd diffuse reflectance
• rs specular reflectance
• rd rs lt 1 (conservation of energy)
• Let z be a uniform random value from 0 to 1
• If z lt rd then reflect diffuse
• Else if z lt rd rs then reflect specular
• Otherwise absorb

rd 50 rs 30
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Storing Photons

• Uses a kd-tree a sequence of axis-aligned
  partitions
• 2-D partitions are lines
• 3-D partitions are planes
• Axis of partitions alternates wrt depth of the
  tree
• Average access time is O(log n)
• Worst case O(n) when tree is severely lopsided
• Need to maintain a balanced tree, which can be
  done in O(n log n)
• Can find k nearest neighbors inO(k log n) time
  using a heap

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Reflected Radiance

• Recall the reflected radiance equation
• Convert incident radiance into incident flux
• Reflected radiance in terms of incident flux
• Numerically

DA pr2
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How Many Photons?

• How big is the disk radius r?
• Large enough that the disk surround
• s the n nearest photons.
• The number of photons used for a
• radiance estimate n is usually
• between 50 and 500.

Radiance estimate using 50 photons
Radiance estimate using 500 photons
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Filtering

• Too few photons cause blurry results
• Simple averaging produces a box filtering of
  photons
• Photons nearer to the sample should
• be weighted more heavily
• Results in a cone filtering of photons

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Participating media

• We have by far assumed that the scene is in a
  vacuum. Hence, radiance is constant along the
  ray. However, some real-world situations such as
  fog and smoke attenuate and scatter light. They
  participate in rendering.
• Natural phenomena
• Fog, smoke, fire
• Atmosphere haze
• Beam of light through
• clouds
• Subsurface scattering

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Volume scattering processes

• Absorption (conversion from light to other forms)
• Emission (contribution from luminous particles)
• Scattering (direction change of particles)
• Out-scattering
• In-scattering
• Single scattering v.s. multiple scattering
• Homogeneous v.s. inhomogeneous(heterogeneous)

emission
in-scattering
out-scattering
absorption
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Single scattering and multiple scattering
attenuation
single scattering
multiple scattering
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My implementation

• Preprocessing the scene by shooting a specified
  number of photons from light sources out into the
  scene
• Implemented new integrator works for surface and
  volume
• Implemented the ray marching method to handle
  non-homogenous media

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Problem encoutered

• Render the scene by infinite area light sources
• The caustic effect vanished

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Result

• For TT car
• Numbers of photons shooted by light 500,0k
• For spotfog
• Numbers of photons shooted by light 1.178M
• For steambath
• Numbers of photons shooted by light 178.2K

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Reference

• 1 Eric P. Lafortune, Yves D. Willems. Rendering
  participating media with bidirectional path
  tracing, Rendering Techniques '96 (Proceedings of
  the 7th Eurographics Workshop on Rendering), pp.
  92-101, 1996
• 2 Henrik Wann Jensen, Per H. Christensen,
  Efficient simulation of light transport in scenes
  with participating media using photon maps,
  Proceedings of the 25th annual conference on
  Computer graphics and interactive techniques,
  p.311-320, July 1998
• 3 Wojciech Jarosz, Craig Donner, Matthias
  Zwicker, Henrik Wann Jensen, Radiance caching for
  participating media, ACM SIGGRAPH 2007 sketches,
  August 05-09, 2007, San Diego, CA