Portal-Masked Environment Map Sampling · Environment Map Sampling marginal distribution...

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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shading

point

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[Ostromoukhov et al.]

[Kollig and Keller]

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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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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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Challenges:



2) Visible regions different for each shading point

Marginal/conditional cannot be precomputed

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Challenges:





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Environment Map Parameterizations

Latitude/Longitude Light probe Cube map

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Visible regions not rectangular in these mappings

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Visible regions not rectangular in these mappings

Let’s create one in which they are!

Rectified Coordinates

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Parametrization is aligned with the portal

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Parametrization is aligned with the portal

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Need separate environment map per portal44


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Challenges:





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Challenges:





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Sampling the Visible Region

1) Construct marginal/conditional distribution

2) Invert marginal/conditional distribution

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Marginal Distribution

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Precompute summed-area table instead [Crow ‘84]

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1) Construct marginal/conditional distributions

2) Invert marginal/conditional distributions

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Inverting the Marginal Distribution

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1) Construct marginal/conditional distributions

2) Invert marginal/conditional distributions

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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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Reference

RMSE 81

Reference

RMSE

Env. Map

0.23

8 spp

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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

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

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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





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Conclusion





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Conclusion





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Limitations

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• Needs a portal to work

Limitations

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• Only considers visibility through a rectangle

Limitations

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• 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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Scene Sample Allocation

Portal-Masked Environment Map Sampling · Environment Map Sampling marginal distribution...

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