I simply made up the anisotropic function out of my head. However, there’s considerable research about how to capture BRDFs from materials, and how to make functions to compactly represent them. BRDFs are just the start. There’s also the BSDF, the Beet Sugar Development Foundation. We’re more interested in the Bi-Directional Scattering Distribution Function. This type of function captures both how light reflects from and transmits through material. There’s also the BSSRDFs which stands for Bidirectional Surface Scattering Reflectance Distribution Function. Say that one three times fast. This function is important for materials like marble and milk. For these materials in particular, the light enters one location on the surface, bounces around inside the material, and comes out somewhere nearby. One other extremely important material that has this sort of scattering is skin. Getting skin to look good for interactive rendering can be quite involved. But the results are more convincing than using some simple reflection model. See the additional course materials for more information. That said, the key factor here is scale. The effect of subsurface scattering lessens as the viewer’s distance from the object increases. Close up, a photon might exit at a location that’s a fair number of pixels away from where it entered the surface. From farther away, they may be no change in pixel location. In fact the diffuse component for all non-metallic materials comes from subsurface scattering. It’s just that in many cases this scattering is over an imperceptably small distance. Metals themselves are essentially all specular. Let me say that again, because all this time we’ve been living a lie. Metallic objects have no lambertian diffuse term. Well, not a lie, I just like being dramatic. Really, diffuse is simply an approximation of which we should be aware. Using it’s fine, even high-quality applications do so. It’s quick to compute and looks plausible. In reality, metals can indeed be given a roughened surface to give them a glossier, diffuse look. So, a diffuse term is fine. However, on a an atomic level, metallic objects have a free floating soup of electrons on the surface which absorbs and reemits incoming photons. If your surface represents a shiny metal, you probably don’t want a diffuse term. Insulators have a diffuse term because the photons undergo subsurface scattering. Most of the time the entry and exit points are so close together it doesn’t matter. But the direction of exit certainly does. Materials such as that in an unglazed clay pot, concrete, and even the moon itself, are rough enough that the lambertian reflection model doesn’t capture them fully. This again turns out to be a matter of scale, having to do with the relationship of surface roughness with subsurface scattering. Admittedly, trying to capture all of these effects leads to a lot of work and possibly inefficient shaders. These subsurface scattering renderings are from 3D Studio Max and rendered offline, not at interactive rates. The main thing is to realize we don’t have to stick with illumination models from the 1970’s because of inertia or ignorance. Using reflection models based on how the real world works has a number of advantages. First and foremost, if everything is properly modeled, your virtual world acts like the real world. Change lighting conditions, and you don’t have to tweak material settings to look good. For design software, this assurance can mean that you can trust what you see on the screen to have some relationship to what you manufacture. Physically based rendering is also a great help to virtual world content creators, such as game and film makers. It’s a time saver to have predictable illumination models, as the artist does not have to learn obscure sliders that have no real world counterparts. It’s vastly reassuring, knowing that materials won’t show some glitch from a certain angle, and knowing that lighting can be changed without destroying the sense of realism. Rather than limit creativity, a well-designed system makes for a more productive and unrestrictive environment.