AllFrequency Shadows using Wavelets

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All-Frequency Shadows using Wavelets
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Pre-computed Radiative Transfer

• Hot topic at SIGGRAPH 2002
• Produces nice global illumination effects in
  real-time
• Introduced use of Spherical Harmonics

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All-Frequency?
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So what are we trying to do?

• Accurately compute the light transport
• Do it in real-time!

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Obtaining View Independence

• Consider two cases
• Geometric Relighting
• View direction can change, but assume diffuse
  reflection
• Image Relighting
• View direction is fixed, but can support
  arbitrary reflection function

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Finally
Separate incident light component and the
transport components We can now write the
exitance function as
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Pre-Computing the Transport Matrix

• Solve for columns
• Ray-trace scene as if lit by one
  (corresponding) pixel of light environment map
• Solve for rows
• Construct visibility map from corresponding
  point in the scene

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Ray-Tracing Matrix Columns
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Visibility Map Matrix Rows
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Real-Time Computation?

• Light cube map 64 64 6
• Transport Matrix 512 512 64 64 6
• Too much Computation!
• Number of multiplications in Matrix-Vector
  inner product must be reduced.

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Compression Using Wavelets

• Do 2D-Haar Transform on light map and transport
  matrix
• Results in few non-zero terms
• Sparse Matrix-Vector multiplication
• Can be handled in Real-Time!

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• A word on basis functions and the Haar Wavelets

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Wavelet Transform
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How much compression?

• We started with
• Light Map 64 64 6 24,576 terms
• We end up with
• About 100 terms (wavelets) only!
• Compression obtained
• Approximately 99 - 99.5

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So why wavelets?

• Non-linear uses dynamic set of basis functions
  depending on lighting, requires only 10 - 100
  wavelets out of a set of 24,576 to approximate
  lighting
• Compare with linear Spherical Harmonics uses
  fixed set of lower order basis functions,
  requires 25-100 coefficients.

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What's Next?

• Support arbitrary reflection function with
  arbitrary view direction
• Support non-rigid scene

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• Demo