Adaptive Mesh Subdivision for Precomputed Radiance Transfer

1
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 ára CTU Prague
2
Goal Decrease the interpolation Error
uniform
adaptive
3
Overview

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

4
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

5
PRT Terminology
6
PRT Terminology
7
PRT Terminology
8
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

9
Transfer Vector

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

abrupt change of tp
l1
l2
no abrupt change of tp
10
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

11
Adaptive Sampling Example
200 verts 246 tris
1565 verts 2548 tris
1188 verts 2828 tris
12
Adaptive Sampling Example
200 verts 246 tris
1565 verts 2548 tris
1188 verts 2828 tris
13
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

14
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 ?

15
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)
16
Results with Error Estimate (1)

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

17
Error Estimate (2)

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

(2)
18
Results with Error Estimate (2)
worse
better

• Better subdivision around the box / box faces.

19
Problems with Error Estimate (2)

• Works fine for flat surfaces
• Exaggerated on curved surfaces

20
Rectified Error Estimate for Curved Surfaces

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

(3)
21
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

22
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