pathtracing

Pathtracing is a rendering algorithm used in computer graphics to simulate global illumination by estimating the light that reaches a camera through many possible light paths. It builds images by tracing random paths from the camera into a scene, letting light bounce between surfaces, and accumulating radiance along those paths according to the scenes’ materials and light sources. The approach aims to solve the rendering equation through Monte Carlo integration, capturing effects such as soft shadows, indirect illumination, color bleeding, and caustics.

In practice, a path traced for a pixel follows a ray from the camera until it hits a surface; at each intersection a new ray direction is sampled based on the surface’s BRDF and the scene’s lighting, and the path continues up to a maximum depth or until a termination condition is met. The contribution of each path is weighted by the product of the BRDFs and cosines along the path, and by the probability density of the sampled directions. The process is repeated many times per pixel, and the results are averaged to estimate the pixel color. Russian roulette termination is commonly used to keep computation manageable.

Pathtracing is generally unbiased, meaning its expected value equals the true radiance of the scene, though it can be noisy at low sample counts. Convergence improves with more samples, but the rate is proportional to 1 over the square root of the number of samples, making high-quality images computationally intensive. It excels at handling complex lighting and caustics but can require substantial processing power for real-time use.

Historically, pathtracing grew from the rendering equation formulated by Kajiya (1986) and was developed through Monte Carlo methods by researchers such as Veach, who advanced importance sampling for light transport. Variants like bidirectional path tracing and metropolis light transport enhance sampling efficiency for difficult lighting scenarios.