3.1 Lighting and Materials

The traditional ``Whitted-style'' illumination model has many variations, but for one light the following formula is representative:   where the vector quantities are shown in Figure 7, and L is the radiance (color) being computed, s is a shadow term that is either zero or one depending on whether the point luminaire is visible, k_d is the diffuse reflectance, l_a is the ambient illumination, l_e is the luminaire color, k_h is the Phong highlight reflectance, k_s is the specular reflectance, L_s is the radiance coming from the specular direction, k_t is the specular transmittance, and L_t is the radiance coming from the transmitted direction. Although this basic formula serves us well, we believe some alterations can improve performance and appearance. In particular, we are careful in allowing k_s and k_t to change with incident angle, we modify the ambient component l_a to be a very crude approximation to global illumination (Section 3.1.1), and we allow soft shadowing by making s vary continuously between zero and one (Section 3.2). Finally, we break the materials into several classes to compute only non-zero coefficients for efficiency.

  

Figure 7: The directional quantities associated with Equation 1.

One well-known problem with Equation 1 is that the specular terms do not change with incident angle. This is different from the behavior of materials in the real world [14]. In a conventional ray tracer the values of k_d, k_s and k_t can be hand-tuned to depend on viewpoint but in an interactive setting this does not work well. Instead, we first break down materials into a few distinct subjective categories suggested in [31]: diffuse , dielectric , metal , and polished . The modifications for these materials is described below:

Diffuse. For diffuse surfaces we use Equation 1 with k_h = k_s = k_t = 0. This is the same as a conventional ray tracer.

Metal. Metal has a reflectance that varies with incident angle [6]. We are currently ignoring this effect, and other effects of real metal, and using traditional Whitted-style lighting. We use Equation 1 with k_d = k_t = 0, and k_h = k_s.

Dielectric. Dielectrics, such as glass and water, have reflectances that depend on viewing angle. These reflectances are modeled by the Fresnel Equations, which for the unpolarized case can be approximated by a polynomial developed by Schlick [28]:

and k_t is determined by conservation of energy:

The internal attenuation of intensity I is the standard exponential decay with distance t according to extinction coefficient :

To approximate the specular reflection of an area light source we add a Phong term to dielectrics as well.

Polished. We use the coupled model presented in [30]. This model allows the k_s to vary with incident angle, and allows the diffuse appearance to decrease with angle. As originally presented, it is a BRDF, but it is modified here to be appropriate for a clamped RGB lighting model with an ambient component:

where the first term assumes the ambient component arises from directionally uniform illumination.