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I simply made up the anisotropic function out of my head. However, there's

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considerable research about how to capture BRDFs from materials, and how to

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make functions to compactly represent them. BRDFs are just the start. There's

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also the BSDF, the Beet Sugar Development Foundation. We're more interested in

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the Bi-Directional Scattering Distribution Function. This type of function

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captures both how light reflects from and transmits through material. There's

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also the BSSRDFs which stands for Bidirectional Surface Scattering Reflectance

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Distribution Function. Say that one three times fast. This function is

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important for materials like marble and milk. For these materials in

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particular, the light enters one location on the surface, bounces around inside

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the material, and comes out somewhere nearby. One other extremely important

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material that has this sort of scattering is skin. Getting skin to look good

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for interactive rendering can be quite involved. But the results are more

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convincing than using some simple reflection model. See the additional course

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materials for more information. That said, the key factor here is scale. The

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effect of subsurface scattering lessens as the viewer's distance from the

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object increases. Close up, a photon might exit at a location that's a fair

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number of pixels away from where it entered the surface. From farther away,

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they may be no change in pixel location. In fact the diffuse component for all

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non-metallic materials comes from subsurface scattering. It's just that in many

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cases this scattering is over an imperceptably small distance. Metals

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themselves are essentially all specular. Let me say that again, because all

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this time we've been living a lie. Metallic objects have no lambertian diffuse

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term. Well, not a lie, I just like being dramatic. Really, diffuse is simply an

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approximation of which we should be aware. Using it's fine, even high-quality

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applications do so. It's quick to compute and looks plausible. In reality,

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metals can indeed be given a roughened surface to give them a glossier, diffuse

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look. So, a diffuse term is fine. However, on a an atomic level, metallic

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objects have a free floating soup of electrons on the surface which absorbs and

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reemits incoming photons. If your surface represents a shiny metal, you

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probably don't want a diffuse term. Insulators have a diffuse term because the

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photons undergo subsurface scattering. Most of the time the entry and exit

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points are so close together it doesn't matter. But the direction of exit

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certainly does. Materials such as that in an unglazed clay pot, concrete, and

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even the moon itself, are rough enough that the lambertian reflection model

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doesn't capture them fully. This again turns out to be a matter of scale,

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having to do with the relationship of surface roughness with subsurface

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scattering. Admittedly, trying to capture all of these effects leads to a lot

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of work and possibly inefficient shaders. These subsurface scattering

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renderings are from 3D Studio Max and rendered offline, not at interactive

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rates. The main thing is to realize we don't have to stick with illumination

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models from the 1970's because of inertia or ignorance. Using reflection models

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based on how the real world works has a number of advantages. First and

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foremost, if everything is properly modeled, your virtual world acts like the

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real world. Change lighting conditions, and you don't have to tweak material

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settings to look good. For design software, this assurance can mean that you

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can trust what you see on the screen to have some relationship to what you

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manufacture. Physically based rendering is also a great help to virtual world

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content creators, such as game and film makers. It's a time saver to have

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predictable illumination models, as the artist does not have to learn obscure

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sliders that have no real world counterparts. It's vastly reassuring, knowing

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that materials won't show some glitch from a certain angle, and knowing that

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lighting can be changed without destroying the sense of realism. Rather than

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limit creativity, a well-designed system makes for a more productive and

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unrestrictive environment.