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Parameterization of Tabulated BRDFsIan Mallett (me), Cem Yuksel

University of Utah, USA

Background / Motivation

● BRDFs describelight scattering

● Extremely importantto realism

● Measured data is realistic– e.g. Matusik et al. 2003

Background / Motivation

BRDF Data TableBRDF

Parameterization

● What parameterization (mapping of data to BRDF's angle space) should we use?

θin

φin

θout

Background / Motivation

● Literature lacks general methods to compare and generate parameterizations!

Contributions

1. Framework to generate and evaluate parameterizations

2. Provide example parameterization and analysis

3. Discuss related technical and theoretical issues

Mathematical Framework

● Want parameterization to importance-sample BRDF:

γ is angle state vector (θin,φin,θout,φout)s is parameter vector (s inθ ,s inφ ,s outθ ,s outφ )

● We describe how to formulate this in the paper

d γ

d s∝BRDF (γ)

d γ

d s∝ BRDF (γ)

Example Parameterization

● Fit a quadratic Bézier curve for each table axis

P1

P0

P2

Effect on BRDF data spacing:Higher density near specular plane (green/blue axes)

Example Parameterization

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0.1

0.2

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Uniform

Identity

Example Parameterization

● More examples in paper . . .

Higher-OrderReconstruction Filtering

● Important for measured data

● We suggest cubic B-spline– Good results

– Efficient GPU implementation (Sigg and Hadwiger 2005)

Higher-OrderReconstruction Filtering

Linear Filter Higher-Order Filter(Cubic B-spline)

Conclusion

● Propose new mathematical framework to generate and analyze parameterizations

● Validate our approach by generating and analyzing an example parameterization

● Discuss higher-order filtering for measured BRDFs

Questions

External Image Sources

● BRDF picture: Derived from https://en.wikipedia.org/wiki/Bidirectional_scattering_distribution_function#/media/File:BSDF05_800.png

● BRDF diagram: remade from http://cybertron.cg.tu-berlin.de/rapid_prototyping_11ws/rp_brdf/img/reflection_t.png

● University of Utah and CGI images adapted from respective websites