Computer Graphics (Spring 2003)

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Computer Graphics (Spring 2003)

• COMS 4160, Lecture 22 Global Illumination
  Ravi Ramamoorthi

http//www.cs.columbia.edu/cs4160
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Effects needed for Realism

• Global Illumination
• Diffuse Interreflections
• Color Bleeding

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Illumination Models

• So far considered mainly local illumination
• Light directly from light sources to surface
• Global Illumination multiple bounces
• Already ray tracing reflections/refractions

Some images courtesy Henrik Wann Jensen
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Global Illumination

• Diffuse interreflection (radiosity) Cornell box

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Global Illumination

• Caustics Focusing through specular surface
• Major research effort in 80s, 90s till today

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Light Transport

• Reflectance Equation
• Global Illumination
• Rendering Equation , Kajiya 86

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Rendering Equation (Kajiya 86)
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Rendering Equation

• Switch to Area param (over surfaces)
• Global Illumination tries to solve this equation
• Too hard for analytic solution
• General theory of Integral equations
• Monte Carlo (ray tracing), finite elements
  (radiosity)

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Ray Tracing History

• Appel 68
• Whitted 80 recursive ray tracing (picture)
• Landmark in computer graphics
• Lots of work on various geometric primitives
• Lots of work on accelerations
• Current Research
• Real-Time raytracing (historically, slow
  technique)
• Ray tracing architecture

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Operator Notation

• Linear System L E K L
• Will later reduce to matrices.
• Explanation of Various Algorithms
• Radiosity Finite element discretization, compute
  form factors. Reduce to matrix equation and
  solve iteratively
• Ray Tracing Monte Carlo sampling of integrals
• (I K) L E L E KE K2E
• Corresponds to sum of direct, single bounce,
  multiple bounce
• Distribution Ray Tracing, Path tracing, etc.

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Operator Notation

• Linear System L E K L
• Explanation of Various Algorithms
• Radiosity Finite element discretization,
• Ray Tracing Monte Carlo sampling of integrals
• (I K) L E L E KE K2E
• Corresponds to sum of direct, single bounce,
  multiple bounce