Measuring and Modeling Anisotropic Reflection

Gregory J. WardLighting Systems Research Group

Lawrence Berkeley Laboratory

Outline

Definition of the BRDF A typical Gonioreflectometer An Imaging Gonioretlectometer Modeling Anisotropic Reflectance Rendering

Definition of the BRDF

Wavelength and polarization arecontained implicitly in the function

A typical Gonioreflectometer

Designed by Murray – Coleman and Smith

An Imaging Gonioretlectometer

Key elements A half–silvered hemisphere A sample target holder A CCD camera with fisheye lens

Measuring step Light reflect off the sample surface The mirror collect it Then reflect back into the lens and CCD array

An Imaging Gonioretlectometer (Side view)

An Imaging Gonioretlectometer (Front View)

Imaging Gonioretlectometer geometry

Recovering the reflected angles

Two step First Determine mapping function from pixel

location to lens incident direction Second compute reflection angles from

camera incident angles A captured image

Measurement Limitations

Limited to measure the reflectance function near grazing angles

Limited to measure more polished surface with sharp specular peaks

Modeling Anisotropic Reflectance

Directly using the data or using series approximation impractical

Some model published for anisotropic case may not fit measured data

Use Gaussian Model

The Isotropic Gaussian Model

The Anisotropic Gaussian Model

Data and model comparison

Rendering

An unbiased and low variance approximation of rendering equation required but

Either unbiased and high variance Or low variance and biased

Hybrid can be used! deterministic solution for source contributions stochastic sampling for indirect contributions

Rendering

Deterministic without sampling

solely on stochastic sampling

hybrid method.

Rendering

photograph Deterministic and isotropic Gaussian model

Hybrid and anisotropic Gaussian model

rendering