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Bi-directional ReflectanceDistribution Function(BRDF)

Ruigang YangCS 684

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What is BRDF

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BRDF

Depends onIncoming light directionViewing directionWave LengthPosition

),,,,,(BRDF vuooii φθφθλ

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Shift-Invariant BRDF

),,,(BRDF ooii φθφθλ

Approximation Texture mapIn CG, λ=R, G, or B

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Spherical CoordinatesCartesian Spherical

Spherical Cartesian

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Differential Solid Angles

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Solid Angle

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BRDF

The ratio of the quantity of reflected light in direction wo, to the amount of light that reaches the surface from direction wi.

Wi Wo

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Definition of BRDF

First attempt:

SourceΦsrcωi

DetectorΦdetωo

src

det

ΦΦ

=rf

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Definition of BRDF

Should fr vary with ωi?

SourceΦsrcωi

DetectorΦdetωo

YES

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Definition of BRDF

Should fr vary with ωo?

SourceΦsrcωi

DetectorΦdetωo

YES

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Definition of BRDF

What about surface area?fr must be independent of surface area

dA

SourceΦsrcωi

DetectorΦdetωo

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Definition of BRDF

SourceΦsrcωi

DetectorΦdetωo

( )EL

dAdA

src

det det =Φ

⋅Φ=

ωrf

Radiance

Irradiance

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Radiance

W/m2/sr

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Irradiance

W/m2

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Digression

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Properties of the BRDFUnit: 1/srEnergy conservation

Helmholtz reciprocity

Not always obeyed by “BRDF” models in graphics

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Isotropy A BRDF is isotropic if it stays the same when the surface is rotated around normal

3D function),,(BRDF oioi φφθθ −=

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Anisotropy

Depend on surface rotation

D. McAllister, 2002

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BRDF Representation

Physically based vs. empirical modelPhong: for glossy reflection

Torrance-Sparrow BRDF: assume surface consisting of tiny “microfacets”, with mirro-reflection off each

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Measuring BRDFs

A full BRDF is 4-dimensionalSimpler measurements often usefulStart with the simplest, andget more complex

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Measuring Reflectance

0º/45ºDiffuse Measurement

45º/45ºSpecular Measurement

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BRDF Measurements

Next step up in complexity: measure BRDF in plane of incidence (1- or 2-D)

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GonioreflectometersThree degrees of freedom spread among light source, detector, and/or sample

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Gonioreflectometers

Three degrees of freedom spread among light source, detector, and/or sample

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Gonioreflectometers

Can add fourth degree of freedom to measure anisotropic BRDFs

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Spatial Gonioreflectometer

Six degrees of freedom

D. McAllister, 2002

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Issues in BRDF Measurement

Light source: angular size, brightness, stability, speckleDetector: angular size, sensitivity, noise, resolution (if spatially varying)Positioning: accuracy, driftAcquisition time

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Image-Based BRDF Measurement

Reduce acquisition time by obtaining larger (e.g. 2-D) slices of BRDF at onceRequires mapping of angles of light to camera pixels

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Ward’s BRDF Measurement Setup

Collect reflected light with hemispherical (should be ellipsoidal) mirror [SIGGRAPH 92]

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Ward’s BRDF Measurement Setup

Result: each image captures light at all exitant angles

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Marschner’s Image-BasedBRDF Measurement

For uniform BRDF, capture 2-D slice corresponding to variations in normals

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Marschner’s Image-BasedBRDF Measurement

Any object with known geometry

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BRDF Measurement is Hard!

Result of fitting model to Ward’s measurements