14 Light Transport I: Surface Reflection

This chapter brings together the ray-tracing algorithms, radiometric concepts, and Monte Carlo sampling algorithms of the previous chapters to implement two different integrators that compute scattered radiance from surfaces in the scene. Integrators are so named because they are responsible for evaluating the integral equation that describes the equilibrium distribution of radiance in an environment (the light transport equation).

Recall the scattering equation from Section 5.6.1; its value can be estimated with Monte Carlo:

StartLayout 1st Row 1st Column upper L Subscript normal o Superscript Baseline left-parenthesis normal p Subscript Baseline comma omega Subscript normal o Baseline right-parenthesis 2nd Column equals integral Underscript script upper S squared Endscripts f Subscript Baseline left-parenthesis normal p Subscript Baseline comma omega Subscript normal o Baseline comma omega Subscript normal i Baseline right-parenthesis upper L Subscript normal i Superscript Baseline left-parenthesis normal p Subscript Baseline comma omega Subscript normal i Baseline right-parenthesis StartAbsoluteValue cosine theta Subscript normal i Baseline EndAbsoluteValue normal d omega Subscript normal i Baseline 2nd Row 1st Column Blank 2nd Column almost-equals StartFraction 1 Over upper N EndFraction sigma-summation Underscript j equals 1 Overscript upper N Endscripts StartFraction f Subscript Baseline left-parenthesis normal p Subscript Baseline comma omega Subscript normal o Baseline comma omega Subscript Baseline Subscript j Baseline right-parenthesis upper L Subscript normal i Superscript Baseline left-parenthesis normal p Subscript Baseline comma omega Subscript Baseline Subscript j Baseline right-parenthesis StartAbsoluteValue cosine theta Subscript j Baseline EndAbsoluteValue Over p left-parenthesis omega Subscript Baseline Subscript j Baseline right-parenthesis EndFraction comma EndLayout

with directions omega Subscript Baseline Subscript j sampled from a distribution with respect to solid angle that has PDF p left-parenthesis omega Subscript Baseline Subscript j Baseline right-parenthesis . In practice, we’ll want to take some samples from a distribution that approximates the BSDF, some from a distribution that approximates the incident radiance from light sources, and then weight the samples with multiple importance sampling.

The next two sections derive methods for sampling from BSDFs and light sources. After these sampling methods have been defined, the DirectLightingIntegrator and the PathIntegrator will be introduced. Both find light-carrying paths starting from the camera, accounting for scattering from shapes’ surfaces. Chapter 15 will extend this approach to scattering from participating media as well, and Chapter 16 will introduce bidirectional methods for constructing light-carrying paths starting from both the camera and from light sources.