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2.2 Photometric image formation 55

tomography do not fit this model, but we do not deal with them in this book.) Light sources
can generally be divided into point and area light sources.
A point light source originates at a single location in space (e.g., a small light bulb),
potentially at infinity (e.g., the sun). (Note that for some applications such as modeling soft
shadows (penumbras), the sun may have to be treated as an area light source.) In addition to
its location, a point light source has an intensity and a color spectrum, i.e., a distribution over
wavelengths L(λ). The intensity of a light source falls off with the square of the distance
between the source and the object being lit, because the same light is being spread over a
larger (spherical) area. A light source may also have a directional falloff (dependence), but
we ignore this in our simplified model.
Area light sources are more complicated. A simple area light source such as a fluorescent
ceiling light fixture with a diffuser can be modeled as a finite rectangular area emitting light
equally in all directions (Cohen and Wallace 1993; Sillion and Puech 1994; Glassner 1995).
When the distribution is strongly directional, a four-dimensional lightfield can be used instead
(Ashdown 1993).
A more complex light distribution that approximates, say, the incident illumination on an
object sitting in an outdoor courtyard, can often be represented using an environment map
(Greene 1986) (originally called a reflection map (Blinn and Newell 1976)). This representa-
tion maps incident light directions ˆv to color values (or wavelengths, λ),

L(ˆv; λ), (2.80)
and is equivalent to assuming that all light sources are at infinity. Environment maps can be
represented as a collection of cubical faces (Greene 1986), as a single longitude–latitude map
(Blinn and Newell 1976), or as the image of a reflecting sphere (Watt 1995). A convenient
way to get a rough model of a real-world environment map is to take an image of a reflective
mirrored sphere and to unwrap this image onto the desired environment map (Debevec 1998).
Watt (1995) gives a nice discussion of environment mapping, including the formulas needed
to map directions to pixels for the three most commonly used representations.

2.2.2 Reflectance and shading
When light hits an object’s surface, it is scattered and reflected (Figure 2.15a). Many different
models have been developed to describe this interaction. In this section, we first describe the
most general form, the bidirectional reflectance distribution function, and then look at some
more specialized models, including the diffuse, specular, and Phong shading models. We also
discuss how these models can be used to compute the global illumination corresponding to a
scene.

The Bidirectional Reflectance Distribution Function (BRDF)

The most general model of light scattering is the bidirectional reflectance distribution func-
5
tion (BRDF). Relative to some local coordinate frame on the surface, the BRDF is a four-
dimensional function that describes how much of each wavelength arriving at an incident
5
Actually, even more general models of light transport exist, including some that model spatial variation along
the surface, sub-surface scattering, and atmospheric effects—see Section 12.7.1—(Dorsey, Rushmeier, and Sillion
2007; Weyrich, Lawrence, Lensch et al. 2008).