Path tracing is a rendering algorithm in computer graphics that simulates how light interacts with objects and participating media to generate realistic (physically plausible) images. It is based on earlier, more limited, ray tracing algorithms.
Path tracing is used to create photorealistic images for artistic purposes, and for applications such as architectural rendering and product design. It is also used to render frames for animated films, and visual effects for film and television. Because it can be very accurate and unbiased, it is commonly used to generate reference images when testing the quality of other rendering algorithms.
The technique uses the Monte Carlo method to compute estimates of global illumination and simulate the ways different materials reflect (or scatter), transmit, absorb, and emit light. It can incorporate simple modeling of the effects of aperture and lens (depth of field, and bokeh) and shutter speed (motion blur), or more realistic simulation of the optical components in a camera.
The algorithm works by describing illumination in a scene using the rendering equation, or light transport equation, and finding an approximate solution using Monte Carlo integration. An inefficient (but accurate) version of the algorithm can be very simple, and involves tracing a ray from the camera, allowing this ray to bounce in random directions as it hits different objects in the scene, and computing the amount of light transmitted along the path to the camera whenever the path encounters a light source. This process is repeated many times for each pixel (each repetition, with generated path and transmitted light, is called a sample), and the results are averaged. One main difference between this algorithm and standard ray tracing is that a single unbranching path is traced each time, while "Whitted-style" or "Cook-style" ray tracing recursively samples branching paths (e.g. when light is both reflected and refracted by a glass object).
More practical versions incorporate improvements such as quasi-Monte Carlo methods (techniques that distribute samples more evenly), importance sampling (take more samples of paths that are likely to transport more light), and next event estimation (allow a very limited form of branching, and sample additional paths that connect to the lights more directly).
Because path tracing uses random samples there is noise in the final image, which decreases as more samples are taken. Images commonly require many thousands of samples per pixel (spp) to reduce noise to an acceptable level, and denoising techniques (e.g. based on neural networks) are often used. Denoising is usually necessary when path tracing is used for real-time rendering in video games, because relatively few samples can be taken.
Many alternative algorithms for path tracing have been developed, although they do not always outperform more straightforward implementations. These include bidirectional path tracing (which traces paths forwards from the light source as well as backwards from the camera), Metropolis light transport, and ways of combining path tracing with photon mapping. Video games often use biased versions of path tracing to improve performance (e.g. limiting the number of bounces in each path). A family of techniques called ReSTIR has been developed that can help real-time path tracing by sharing data between nearby pixels and consecutive frames.
History
Like all ray tracing methods, path tracing is based on ray casting, which Arthur Appel used for computer graphics rendering in the late 1960s. In 1980, John Turner Whitted published a recursive ray tracing algorithm that allows rendering images of scenes containing mirrored surfaces and refractive transparent objects. In 1984, Cook et al. described a form of ray tracing called distributed ray tracing, which uses Monte Carlo integration to render effects such as depth of field, motion blur, reflection from rough surfaces, and area lights. The same year, the radiosity method (not a ray tracing method) was published, which was the first physically based method for rendering diffuse global illumination. In 1986, Jim Kajiya published a paper exploring how to use distributed ray tracing to render physically-based global illumination, and this paper also introduced and named the method called "path tracing". Path tracing and other distributed ray tracing techniques were further refined in the late 1980s and early 1990s by researchers such as James Arvo and Peter Shirley, and by Greg Ward in the open source Radiance software.
Despite being theoretically able to render any lighting, the original form of path tracing can sometimes be very inefficient (or noisy) for rendering light that is reflected or refracted before illuminating a visible surface, including diffuse global illumination where light enters an area through narrow gaps, because it traces paths only from the camera. To address this, variations of path tracing that trace paths from both the camera and from light sources, called bidirectional path tracing, were published in 1993 by Eric Lafortune and Yves Willems, and in 1997 by Eric Veach and Leonidas Guibas. In 1997 Veach and Guibas also published an alternative method called Metropolis light transport, which combines bidirectional path tracing with the Metropolis method. Veach's lengthy Ph.D. dissertation described both techniques, along with the theoretical background of path tracing; later, the book Physically Based Rendering (which won an Academy Award for Technical Achievement in 2014) helped to make information about path tracing more widely available.
Path tracing requires tracing a large number of paths of light in order to produce an image with a visually acceptable amount of noise. This made path tracing very slow on computers available in the 1980s and 1990s, and noise remained a problem when trying to reproduce the style of earlier computer graphics animated films. Most animated films produced until around 2010, by studios such as Pixar, used rasterization-based rendering, with ray tracing used selectively for reflections (and later for precomputed or cached global illumination). However the speed of computers rapidly increased during the 1990s. Blue Sky Studios pioneered using Monte Carlo ray tracing for global illumination in animation, including in the 1998 short film "Bunny", but they did not disclose the precise techniques used.
Path tracing gradually become more practical for film production in the early 2000s. The Arnold renderer, developed by Marcos Fajardo, was used by Sony Pictures Imageworks to produce the feature-length film Monster House, released in 2006. Pixar rewrote their RenderMan software to use path tracing, and released their first feature-length path-traced film Finding Dory in 2016. Although path tracing still had a large computational cost, animation studios discovered that less human labor was required when using it, for example because global illumination no longer needed to be faked by manually placing lights. The amount of noise present in path-traced images still caused difficulties, particularly when rendering motion blur (which was used extensively by earlier animated films) but denoising techniques were developed to address this. New techniques were also needed for rendering hair and fur, and to handle the extremely large scenes sometimes required by films.
Renderers such as Arnold, and Disney's Hyperion, originally only used CPUs for rendering, but as GPUs became more capable (and APIs such as CUDA, OpenCL, and OptiX were released) researchers and developers began adapting algorithms and implementations to use GPUs. GPUs can dramatically reduce rendering time: for example using a high-end GPU to accelerate portions of the rendering code can make it over 30 times faster than using only a high-end CPU.
Description
Kajiya's 1986 paper defined a recursive integral equation called the rendering equation, which describes a simplified form of light transport. Using Monte Carlo integration for the integral on the right side of the equation leads fairly directly to the path tracing algorithm:
This expresses , the light arriving at point from point , as the product of a geometry term, , which is 0 if there is something blocking the light between the two points and 1 otherwise, and the amount of light leaving point and traveling towards . The light leaving point is the sum of the light emitted by the surface at , and the integral of the light arriving at from all other points in the scene (the integration domain ) and being reflected towards . The factor , which calculates how much light is reflected, must take into account the angles at which the light is arriving and leaving, and characteristics of the surface material, typically expressed as a bidirectional reflectance distribution function (BRDF) or bidirectional transmission distribution function (BTDF).
The equation is often called the light transport equation (LTE), and it is frequently written using integration over directions instead of surfaces. (In Kajiya's version of the equation, the geometry term ensures that only one surface point can contribute light from any given direction.) Actual rendering also involves a related equation called the measurement equation that expresses the amount of light received by the camera along particular rays.
The version of the equation used by Kajiya assumes the light is a single wavelength (wavelength does not appear as a parameter for any of the functions). It is a simplification for geometrical optics, and does not take into account phenomena such as diffraction, polarization, and fluorescence. It integrates only over surfaces, and does not handle participating media (regions of space that scatter, absorb, and emit light). However extensions to handle such cases, and multiple wavelengths, were mentioned in the paper, and were well understood (and there is no fundamental limitation of the path tracing algorithm that prevents rendering these effects).
Kajiya described how older ray tracing methods find approximate solutions to the rendering equation. He also showed that the rendering equation is equivalent to the radiosity equation solved by the radiosity rendering method; however the radiosity method assumes surfaces are Lambertian, and using it for non-Lambertian materials gives inaccurate (biased) values. Additional bias is caused by the fact that the radiosity method uses finite element approximations of surfaces. Kajiya adapted existing distributed ray tracing methods to solve the rendering equation (i.e. to find radiance values at chosen points on surfaces for a steady state or equilibrium solution to light transport in the scene) in an unbiased way, using Monte Carlo integration.
In Whitted-style recursive ray tracing, the integral on the right side of the equation is replaced by a sum of the contributions of specific reflected and refracted rays, and the direct light arriving at the point from all light sources in the scene (lights may be point source or directional, so lighting can be evaluated easily, or some approximation may be used for other types of lights). A constant "ambient term" may be added to approximate global illumination. Distributed ray tracing introduced the use of Monte Carlo integration for rendering rough reflection, sampling multiple directions at each bounce instead of using the contribution of a single direction, but diffuse global illumination was still usually approximated using an ambient term.