Bidirectional path tracing

Bidirectional path tracing is a global illumination algorithm that constructs light paths by connecting vertices sampled from both the camera and the light sources, rather than tracing paths only from the camera as in standard path tracing. The method was introduced by Eric Lafortune and Yves Willems in 1993, and later refined by Eric Veach and Leonidas Guibas in 1994, who showed that the space of all possible path connections could be systematically explored and weighted using multiple importance sampling.

The core insight is that some lighting phenomena are much easier to sample from the light source than from the camera. A caustic seen through a small aperture, for instance, is unlikely to be hit by a camera-started path, but a light-started path will find it readily. Bidirectional path tracing generates paths from both ends and connects them in the middle, using a weighted combination that favors the connections most likely to contribute significantly to the image.

The algorithm is more general than path tracing but also more complex: it requires computing connection probabilities, visibility tests between arbitrary vertices, and careful weighting to avoid double-counting contributions. The payoff is that bidirectional path tracing can render scenes with difficult lighting — caustics, small light sources, strong indirect illumination — with fewer samples than unidirectional methods. The technique is the theoretical foundation of modern Light transport algorithms, though in practice, simpler methods with scene-specific optimizations often outperform it.