9 Reflection Models

This chapter defines a set of classes for describing the way that light scatters at surfaces. Recall that in Section 4.3.1 we introduced the bidirectional reflectance distribution function (BRDF) abstraction to describe light reflection at a surface, the bidirectional transmittance distribution function (BTDF) to describe transmission at a surface, and the bidirectional scattering distribution function (BSDF) to encompass both of these effects. In this chapter, we will start by defining a generic interface to these surface reflection and transmission functions.

Surface reflection models come from a number of sources:

  • Measured data: Reflection distribution properties of many real-world surfaces have been measured in laboratories. Such data may be used directly in tabular form or to compute coefficients for a set of basis functions.
  • Phenomenological models: Equations that attempt to describe the qualitative properties of real-world surfaces can be remarkably effective at mimicking them. These types of BSDFs can be particularly easy to use, since they tend to have intuitive parameters that modify their behavior (e.g., “roughness”).
  • Simulation: Sometimes, low-level information is known about the composition of a surface. For example, we might know that a paint is comprised of colored particles of some average size suspended in a medium or that a particular fabric is comprised of two types of threads with known reflectance properties. In this case, a preprocess could simulate the behavior of light within the microstructure to fit an approximate BSDF. Alternatively, simulation could occur when rendering.
  • Physical (wave) optics: Some reflection models have been derived using a detailed model of light, treating it as a wave and computing the solution to Maxwell’s equations to find how it scatters from a surface with known properties. They are mainly of use when the scene contains geometric detail at the micrometer level that makes wave-optical behavior readily apparent, such as with thin films, coatings, and periodic structures as found on digital optical data storage formats like CDs and DVDs.
  • Geometric optics: As with simulation approaches, if the surface’s low-level scattering and geometric properties are known, then closed-form reflection models can sometimes be derived directly from these descriptions. Geometric optics makes modeling light’s interaction with the surface more tractable, since complex wave effects like diffraction can be ignored.

This chapter discusses the implementation of a number of such models along with the associated theory. See also Section 14.3, which introduces a reflection model based on the simulation of light scattering in layered materials. The “Further Reading” section at the end of this chapter gives pointers to a wide variety of additional reflection models.

An important component of surface appearance is the spatial variation of reflection and transmission properties over the surface. The texture and material classes of Chapter 10 will address that problem, while the abstractions presented here will only consider scattering at a single point on a surface. Further, BRDFs and BTDFs explicitly only model scattering from light that enters and exits a surface at a single point. For surfaces that exhibit meaningful subsurface light transport, a more complete simulation of light scattering inside the material is necessary—for example, by applying the volumetric light transport algorithms of Chapter 14.

Basic Terminology

We now introduce basic terminology for describing reflection from surfaces. To compare the resulting visual appearance, we will classify reflection into the following four broad categories: diffuse, glossy specular, perfect specular, and retroreflective (Figure 9.1). Most real surfaces exhibit a mixture of these four behaviors. Diffuse surfaces scatter light equally in all directions. Although a perfectly diffuse surface is not physically realizable, examples of near-diffuse surfaces include dull chalkboards and matte paint. Glossy specular surfaces such as plastic or high-gloss paint scatter light preferentially in a set of reflected directions—they show blurry reflections of other objects. Perfect specular surfaces scatter incident light in a single outgoing direction. Mirrors and glass are examples of perfect specular surfaces. Finally, retroreflective surfaces like velvet or the Earth’s moon scatter light primarily back along the incident direction. Images throughout this chapter will show the differences between these various behaviors in rendered scenes.

Figure 9.1: Reflection from a surface can be generally categorized by the distribution of reflected light from an incident direction (heavy lines): (a) diffuse, (b) glossy specular, (c) nearly perfect specular, and (d) retroreflective distributions.

Given a particular category of reflection, the reflectance distribution function may be isotropic or anisotropic. With an isotropic material, if you choose a point on the surface and rotate it around its normal axis at that point, the distribution of light reflected at that point does not change. Diffuse materials like paper or wall paint are usually isotropic due to the directionally random arrangement of wood fibers or paint particles.

In contrast, anisotropic materials reflect different amounts of light as you rotate them in this way. Examples of anisotropic materials include hair and many types of cloth. Industrial processes such as milling, rolling, extrusion, and 3D printing also tend to produce highly anisotropic surfaces, an extreme example being brushed metal.