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known as the Cook-Torrance BRDF model, was published in 1982 [Cook and
Torrance 82] and found widespread use in the next decades.
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A later extension to the microfacet model, developed by Xiao D. He, Torrance,
Fran¸ois X. Sillion, and Donald P. Greenberg, includes a directionally diffuse re-
flection term (the original model assumed a single diffuse term for the whole
surface) and also handles wavelength-dependent local occlusion. This model,
which is known as the He BRDF model or the He-Torrance BRDF model is con-
sidered one of the most complete analytical BRDF models for specular reflection
developed to date. Other notable microfacet-based models are the Oren-Nayar
BRDF model developed by Michael Oren and Shree Nayar [Oren and Nayar 94],
which uses diffuse microfacets, and a very general model microfacet simulation
developed by Michael Ashikhmin, Simon Premoze, and Peter Shirley [Ashikhmin
et al. 00].
8.1.5 Measured Data and BRDF Models
The Phong model has a simple formulation and is easy to apply, but it has has
some serious limitations. On the other hand, microfacet-based models are not
so practical. For example, the He-Torrance model is costly to evaluate, and the
parameters are difficult to measure directly. Most other microfacet-based mod-
els have similar issues. The model proposed in the paper “Measuring and
Modeling Anisotropic Reflection” by Greg Ward sought to balance physical accu-
racy and efficient, intuitive implementation [Ward 92]. This model is now known
as the Ward BRDF model, and has the advantage of being based on parameters
that can be determined by photographing real surfaces. Ward's model is empirical;
the measure of its utility comes in the ability to reproduce measured reflectance.
Its simplicity is also useful in Monte Carlo sampling. Moreover, the Ward model
also handles anisotropic reflection.
Surface reflectance is normally done by directing a collimated thin beam of
light onto a sample of the surface and recording the reflected radiance in another
direction using a calibrated sensor. Varying the position of the light source and
the position of the sensor captures a set of BRDF values. Of course, thousands
of measurements may be necessary to properly represent the BRDF of a particular
sample. A robotic device known as a
gonioreflectometer
automates the process.
To fit the parameters to the Ward model, a real surface is photographed with sev-
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The work with Cook was the beginning of a long-term collaboration between Ken Torrance and
the Program of Computer Graphics at Cornell University that lasted nearly 30 years. Torrance had
a significant impact on early research into physically based rendering, much of which took place
at Cornell in the 1980s. Many Cornell alumni and others who worked there credit him as a major
influence in their own careers. Sadly, Ken died at the age of 69 while this topic was in production. He
will be greatly missed.
