Fundamentals of Computer Graphics, 3rd Edition

i

i

i

i

i

i

i

i

2 5

2 5

Reflection Models

As we discussed in Chapter 20, the reflective properties of a surface can be sum-

marized using the BRDF (Nicodemus et al., 1977; Cook & Torrance, 1982). In

this chapter, we discuss some of the most visually important aspects of material

properties and a few fairly simple models that are useful in capturing these prop-

erties. There are many BRDF models in use in graphics, and the models presented

here are meant to give just an idea of non-diffuse BRDFs.

25.1 Real-World Materials

Many real materials have a visible structure at normal viewing distances. For ex-

ample, most carpets have easily visible pile that contributes to appearance. For

our purposes, such structure is not part of the material property but is, instead, part

of the geometric model. Structure whose details are invisible at normal viewing

distances, but which do determine macroscopic material appearance, are part of

the material property. For example, the fibers in paper have a complex appearance

under magnification, but they are blurred together into an homogeneous appear-

ance when viewed at arm’s length. This distinction between microstructure that

is folded into BRDF is somewhat arbitrary and depends on what one defines as

“normal” viewing distance and visual acuity, but the distinction has proven quite

useful in practice.

In this section we define some categories of materials. Later in the chapter,

we present reflection models that target each type of material. In the notes at the

end of the chapter some models that account for more exotic materials are also

discussed.

637

i

i

i

i

i

i

i

i

638 25. Reflection Models

25.1.1 Smooth Dielectrics and Metals

Dielectrics are clear materials that refract light; their basic properties were sum-

marized in Chapter 4. Metals reflect and refract light much like dielectrics, but

they absorb light very, very quickly. Thus, only very thin metal sheets are trans-

parent at all, e.g., the thin gold plating on some glass objects. For a smooth

material, there are only two important properties:

1. How much light is reflected at each incident angle and wavelength.

2. What fraction of light is absorbed as it travels through the material for a

given distance and wavelength.

Figure 25.1. The amount

of light reflected and trans-

mitted by glass varies with

the angle.

The amount of light transmitted is whatever is not reflected (a result of energy

conservation). For a metal, in practice, we can assume all the light is immediately

absorbed. For a dielectric, the fraction is determined by the constant used in

Beer’s Law as discussed in Chapter 4.

Figure 25.2. Light is re-

peatedly reflected and re-

fracted by glass, with the

fractions of energy shown.

The amount of light reflected is determined by the Fresnel equations as dis-

cussed in Chapter 4. These equations are straightforward, but cumbersome. The

main effect of the Fresnel Equations is to increase the reflectance as the incident

angle increases, particularly near grazing angles. This effect works for transmitted

light as well. These ideas are shown diagrammatically in Figure 25.1. Note that

the light is repeatedly reflected and refracted as shown in Figure 25.2. Usually

only one or two of the reflected images is easily visible.

25.1.2 Rough Surfaces

If a metal or dielectric is roughened to a small degree, but not so small that diffrac-

tion occurs, then we can think of it as a surface with microfacets (Cook & Tor-

rance, 1982). Such surfaces behave specularly at a closer distance, but viewed

at a further distance seem to spread the light out in a distribution. For a metal,

an example of this rough surface might be brushed steel, or the “cloudy” side of

most aluminum foil.

For dielectrics, such as a sheet of glass, scratches or other irregular surface

features make the glass blur the reflected and transmitted images that we can

normally see clearly. If the surface is heavily scratched, we call it translucent

rather than transparent. This is a somewhat arbitrary distinction, but it is usually

clear whether we would consider a glass translucent or transparent.