Adaptive Mesh Subdivision for Precomputed Radiance Transfer

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Adaptive Mesh Subdivision for Precomputed
Radiance Transfer

• Jaroslav Krivánek
• Univ. of Central Florida
• CTU Prague
• IRISA INRIA Rennes

Sumanta Pattanaik Univ. of Central Florida
Jirí Žára CTU Prague
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Goal Decrease the interpolation Error
uniform
adaptive
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Overview

• Precomputed Radiance Transfer
• Transfer Operator Sampling Density
• Subdivision algorithm
• Triangle error estimate
• Conclusion

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Precomputed Radiance Transfer (PRT)
Precompute global illumination (per-vertex)
Display GI in real-time under arbitrary lighting

• Restrictions
• Low-frequency directional lighting
• Soft shadows only
• Per-vertex precomputation
• Rigid objects only

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PRT Terminology
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PRT Terminology
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PRT Terminology
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PRT for Diffuse Surfaces

• Lp exit radiance at point p (displayed
  intensity)
• l light vector (in SH basis)
• tp source-to-exit transfer vector at p
• Computed in preprocess
• Stored per-vertex or per-texel
• Non-adaptively

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Transfer Vector

• Abrupt changes of tp
• ? Possible abrupt changes of Lp

abrupt change of tp
l1
l2
no abrupt change of tp
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Our Goal Refined

• Adaptive Sampling of tp, subject to
• visual error under any lighting is minimized,
• of samples of tp (i.e. verts) is nimimized
• Per-vertex tp ? adaptive mesh subdivision
• Subdivision in pre-process
• Along with the pre-computation of tp
• Actual lighting Lp is not known ?
• Subdivision based only on tp, not on Lp

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Adaptive Sampling Example
200 verts 246 tris
1565 verts 2548 tris
1188 verts 2828 tris
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Adaptive Sampling Example
200 verts 246 tris
1565 verts 2548 tris
1188 verts 2828 tris
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Subdivision Algorithm

• Initial mesh
• Compute tp for vertices of the initial mesh
• Compute error estimate for the triangles of the
  initial mesh
• Subdivide according to the error estimate
• Proceed recursively (priority queue), until
  triangle budget is met

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Ideal Error Estimate

• Ideal error estimate for triangle ?
• Error maximum relative deviation of the
  interpolated exit radiance from the correct exit
  radiance over all unit power lighting l and all
  triangle points x.
• Or rather one of possible ideal error
  estimates
• other possibilities
• avg instead of max ?
• smoothness of the Gouraud interpolation instead
  of deviation from the correct value ?

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Practical Error Estimate (1)

• Subdivision in preprocess ?
• Error estimate based uniquely on tp
• Triangle error Sum edge errors
• First edge error estimate (triangle edge v1-v2)
• Development of (1) from the ideal e. e. given
  in the paper

(1)
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Results with Error Estimate (1)

• Too much subdivision in shadowed areas.
• is low ? is high.

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Error Estimate (2)

• Division by promotes subdivision in
  shadowed areas.
• Solution remove the division by .
• New error estimate

(2)
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Results with Error Estimate (2)
worse
better

• Better subdivision around the box / box faces.

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Problems with Error Estimate (2)

• Works fine for flat surfaces
• Exaggerated on curved surfaces

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Rectified Error Estimate for Curved Surfaces

• Divide by the angle between the normals at v1 and
  v2.

(3)
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Conclusion

• Adaptive subdivision
• Decreased interpolation error
• Superior quality compared to uniform subdivision
• Subdivision performed in preprocess
• no dynamic subdivision in real-time
• Based on a worst error estimate

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Discussion Future Work

• Drawbacks
• Final error estimate is a pure heuristic
• Requires a lot of tweaking to get good results
• The absolute value of the error estimate is
  meaningless
• Only the ordering is ok
• Future Work
• Extend to arbitrary BRDFs
• Use textures instead of vertices
• Perceptually based