08/23/2025
Introduction
For image synthesis we need to have some model of light. The prevalent models of light are geometric optics and physical optics. Geometric optics models light propagation in terms of rays that travel in straight lines and their paths are described through a series of reflections and refractions. Physical optics treats light propagation as a wave phenomenon where effects of polarization, interference and diffraction can be modeled.
Classical raytracing, an application of geometric optics, point samples the incoming radiance from a scene by tracing rays from the eye through the scene to the lights. The images generated by an implementation of the classical raytracing algorithm can look wonderful but also unrealistic and often times suffer from severe aliasing problems. The problem is that the algorithm severely undersamples the domains for the integral equations that describe the complex optical interations of light.
Distribution raytracing, originally called distributed raytracing, extends classical raytracing by incorporating Monte Carlo techniques. Instead of sampling with one ray it distributes multiple rays to sample the integrals over the pixel area, lens area, time, and the hemispheres for reflection and refraction. This simple extension is much more computationally expensive but as a point sampling process it is necessary to render cool effects such as soft shadows, depth of field, motion blur, glossy and translucent surfaces. Although distribution raytracing is a huge improvement it does not solve the complete problem.
Cornell Box - Direct Lighting
16 samples were used per pixel, shadows and reflections.
For realistic image synthesis we also need to solve the rendering integrals for the light paths that account for global illumination and caustics. However, these integrals can be deeply nested and seemingly impossible to solve. Using Monte Carlo techniques we have the facilities for approximating these integrals. The basic idea behind Monte Carlo techniques is to approximate a function by randomly sampling it within some domain. Hopefully, the samples give some insight on what the functions look like.
Path tracing was developed as a solution to the complete rendering equation and is heavily based on Monte Carlo techniques. It completely samples the entire domain while distribution raytracing only samples portions of it. Path tracing renders a scene by tracing rays from the eye back to the light sources. Each of these ray paths is a non-branching path where at each ray-surface interaction the new direction for the path is determined probabilistically. For the solution to converge to the correct result many rays are needed. The main problem with path tracing is that the variance in the solution shows up as noise. Fortunately, there are ways to alleviate this noise such as using Photon Mapping to handle caustics.
In the following sections I will discuss the rendering equation, distribution raytracing, and will briefly touch upon path tracing. This write-up reflects my understanding of these topics and there may be errors. If there are any please let me know.