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Bi-directional Path Tracing

In this section a hybrid two-pass algorithm is introduced that has been proposed by Lafortune which does not need mesh generation either [LW93]. This method is based on the bi-directional particle tracing since particles are shot at the same time from a selected light source and the viewpoint. After this, shadow rays are used to connect each intersection point in the light path with each intersection point in the eye path, and contributions are added to the flux of the relevant pixel.


Figure: Bi-directional path tracing

Random walks can be written as:

The direction tex2html_wrap_inline943 in the light path is sampled according to the subcritical pdf (spdf):

equation370

where tex2html_wrap_inline925 is the bi-directional reflection distribution function (BRDF). The direction tex2html_wrap_inline947 in the eye path is sampled the same way:

equation378

After generating a light path and an eye path all intersection points are linked by shadow rays. The flux is estimated by a weighted sum:

equation382

where factors tex2html_wrap_inline949 express the estimates of the flux found by i reflections on the eye path and j reflections on the eye path. These factors are evaluated differently according to the following three cases:

There are various alternatives to choose the weights tex2html_wrap_inline965 for the contributions tex2html_wrap_inline949 . For example the classical path tracing is the special case of this generic algorithm using the following weights:

equation398


next up previous
Next: Bi-directional Estimators for Light Up: A Review of Monte Previous: Monte Carlo Light Tracing

Csébfalvi Balázs
Tue Apr 15 18:39:13 METDST 1997