THE RENDERING EQUATION
📜 Abstract
We present an integral equation which generalizes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient new technique for a wide variety of monte carlo procedures. The resulting rendering algorithm extends the range of optical phenomena which can be effectively simulated.
✨ Summary
Contribution. The paper introduces a general surface light-transport integral equation that unifies several rendering approaches, including classical shading, ray tracing, distributed ray tracing, and radiosity. It develops a Monte Carlo solution based on sampling light-transport paths through a scene and proposes hierarchical sampling techniques for reducing integration variance. The paper also demonstrates phenomena such as indirect illumination, caustics, and color bleeding that are not captured by conventional Whitted-style ray tracing.
Influence. Subsequent physically based rendering literature identifies Kajiya’s work as the paper that introduced path tracing together with the light transport equation. Path tracing became a foundational unbiased Monte Carlo technique for global illumination and is treated as a central algorithm in modern physically based rendering systems and research. (doi.org)