Path tracing
Path tracing is a algorithm for image synthesis , the simulation of the global lighting allows.
Path tracing is based on the knowledge that the simulation of global lighting corresponds to the solution of the so-called rendering equation , which specifies the radiation density of any light beam emanating from a certain point.
Path tracing uses rigorous mathematical techniques derived from the field of mathematical statistics . The algorithm uses a so-called Monte Carlo integration to solve the rendering equation approximately. Path tracing is therefore also known as Monte Carlo ray tracing, just like advanced algorithms based on it such as Metropolis Light Transport or Bidirectional Path Tracing .
With path tracing, every ray that is shot into the scene is reflected , refracted or absorbed when it hits surfaces , with at least one random ray being generated each time (except in the case of absorption) that approximates the integral of the rendering equation. The initial ray seeks its way ( path ) through the scene. The more initial rays you use, the closer you get to the ideal image. The errors in the approximation are expressed as variance , which corresponds to image noise. Techniques like Importance Sampling help reduce variance.
The difference to diffuse ray tracing is that with path tracing the complete rendering equation is solved by means of randomly generated rays on all - even on diffuse - surfaces and thus the global illumination is simulated.
In practice, pure path tracing is usually too slow, which is why it can be combined with photon mapping .
The idea for path tracing was published in 1986 by James Kajiya together with the rendering equation as a SIGGRAPH publication, at that time under the name Integral equation technique.