Post on 19-Aug-2020
Portal-MaskedEnvironment Map Sampling
Benedikt Bitterli 1,2 Jan Novák 2 Wojciech Jarosz 2
1 Walt Disney Animation Studios 2 Disney Research Zurich
Motivation
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Motivation
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Environment Map Sampling
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Environment Map Sampling
shading
point
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Environment Map Sampling
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Environment Map Sampling
[Ostromoukhov et al.]
[Kollig and Keller]
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Environment Map Sampling
occluded
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Problem Statement
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Visibility Caching
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Visibility Caching
[Vorba et al.]
[Georgiev et al.]
[Jensen ‘95]
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Portal Sampling
portal
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Portal Sampling
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Portal Sampling
[Arvo ‘95]
[Ureña et al.]
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Portal Sampling
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Ours
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Environment Map Sampling
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Environment Map Sampling
marginal distribution
conditional distributions
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Visible Region
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Visible Region
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Visible Region
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Portal-Masked Environment Map Sampling
Challenges:
1) Visible regions have complex shapes
Marginal/conditional decomposition difficult
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Portal-Masked Environment Map Sampling
Challenges:
1) Visible regions have complex shapes
Marginal/conditional decomposition difficult
2) Visible regions different for each shading point
Marginal/conditional cannot be precomputed
31
Portal-Masked Environment Map Sampling
Challenges:
1) Visible regions have complex shapes
Marginal/conditional decomposition difficult
2) Visible regions different for each shading point
Marginal/conditional cannot be precomputed
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Environment Map Parameterizations
Latitude/Longitude Light probe Cube map
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Environment Map Parameterizations
Latitude/Longitude Light probe Cube map
Visible regions not rectangular in these mappings
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Environment Map Parameterizations
Latitude/Longitude Light probe Cube map
Visible regions not rectangular in these mappings
Let’s create one in which they are!
Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
Parametrization is aligned with the portal
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Rectified Coordinates
Parametrization is aligned with the portal
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Rectified Coordinates
Need separate environment map per portal44
Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Rectified Coordinates
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Portal-Masked Environment Map Sampling
Challenges:
1) Visible regions have complex shapes
Marginal/conditional decomposition difficult
2) Visible regions different for each shading point
Marginal/conditional cannot be precomputed
59
Portal-Masked Environment Map Sampling
Challenges:
1) Visible regions have complex shapes
Marginal/conditional decomposition difficult
2) Visible regions different for each shading point
Marginal/conditional cannot be precomputed
60
Sampling the Visible Region
1) Construct marginal/conditional distribution
2) Invert marginal/conditional distribution
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Marginal Distribution
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Marginal Distribution
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Marginal Distribution
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Marginal Distribution
Precompute summed-area table instead [Crow ‘84]
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Sampling the Visible Region
1) Construct marginal/conditional distributions
2) Invert marginal/conditional distributions
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Precompute summed-area table instead [Crow ‘84]
Inverting the Marginal Distribution
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Inverting the Marginal Distribution
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Inverting the Marginal Distribution
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Inverting the Marginal Distribution
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Inverting the Marginal Distribution
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Inverting the Marginal Distribution
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Sampling the Visible Region
1) Construct marginal/conditional distributions
2) Invert marginal/conditional distributions
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Precompute summed-area table instead [Crow ‘84]
Use bisection algorithm for logarithmic complexity
Results
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Results
Comparison of:
a) Environment map sampling
b) Portal solid angle sampling [Ureña et al. 2013]
c) Multiple importance sampling of a) and b) [Veach 1998]
d) Ours
at equal sample count (8spp)
All methods combined with 1 BRDF sample using MIS
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77
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79
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Reference
RMSE 81
Reference
RMSE
Env. Map
0.23
8 spp
82
Reference
RMSE
Env. Map
0.23
Portal S.Angle
3.31
8 spp
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Reference
RMSE
Env. Map
0.23
Portal S.Angle
3.31
MIS
0.26
8 spp
84
Reference
RMSE
Env. Map
0.23
Portal S.Angle
3.31
MIS
0.26
8 spp
Ours
0.16 85
87
88
89
Reference
RMSE 90
Reference
RMSE
Env. Map
0.59
Portal S.Angle
0.74
8 spp
92
Reference
RMSE
Env. Map
0.59
Portal S.Angle
0.74
MIS
0.60
8 spp
93
Reference
RMSE
Env. Map
0.59
Portal S.Angle
0.74
MIS
0.60
Ours
0.34
8 spp
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More Results
Please see supplementary material
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By the numbers
Equal time:
• 33% less shadow rays than Env. Map sampling
Equal quality:
• 2x – 8x speedup w.r.t. Env. Map sampling
• 2x – 5x speedup w.r.t. Env Map/Portal MIS
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Area lights with directional profile
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Area lights with directional profile
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Uniform Solid Angle Sampling Ours
10x speedup
Conclusion
Take away from this talk:
• Can importance sample visibility x Env. Map
• Need single (precomputed) SAT per portal
• Easy to implement!
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Conclusion
Take away from this talk:
• Can importance sample visibility x Env. Map
• Need single (precomputed) SAT per portal
• Easy to implement!
101
Conclusion
Take away from this talk:
• Can importance sample visibility x Env. Map
• Need single (precomputed) SAT per portal
• Easy to implement!
102
Conclusion
Take away from this talk:
• Can importance sample visibility x Env. Map
• Need single (precomputed) SAT per portal
• Easy to implement!
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Limitations
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• Needs a portal to work
Limitations
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• Needs a portal to work
• Only considers visibility through a rectangle
Limitations
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• Needs a portal to work
• Only considers visibility through a rectangle
Future Work
Incorporate BRDF:
Combine with product sampling techniques
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[Burke et al.] [Clarberg et al.] [Cline et al.]
Thanks!
Acknowledgements: • Environment maps: Bernhard Vogl, http://openfootage.net
• Scenes: Jay Hardy, Wayne
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Bonus Slides
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Sampling multiple portals
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Sampling multiple portals
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Sampling multiple portals
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Sampling multiple portals
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Scene Sample Allocation