Measuring and Modeling Anisotropic Reflection Gregory J. Ward Lighting 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 are contained 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