Graphics Reference
In-Depth Information
has to be employed if the scene contains point sources—the probability of a ran-
dom path or ray hitting a point source is zero; there is literally no chance of ever
hitting it.
How well MCPT works in practice depends on the number of samples and
how they are chosen. If the number of samples is too low, there are not enough
paths to be sufficiently representative and the resulting error will show in the final
image as excessive or objectionable noise. But increasing the number of samples
increases the rendering time. Unfortunately the number of samples required to
get the error below a certain threshold is quadratic: four times as many samples
are needed to get half the error.
How the samples are chosen is also critical to the success of MCPT. As Kajiya
showed, certain light paths are more “important” than others, in the sense that
they carry more radiant power. For example, in a highly specular environment,
light paths that are close to the path of mirror reflection carry most of the power. In
contrast, the light following a path that bounces away from the specular direction
carries far less light to the viewpoint. Avoiding these paths in favor of the more
important paths can make MCPT more efficient, but it can also introduce bias. For
example, if only specular paths are followed, diffuse reflection will not appear in
the final image. When paths are chosen according to a nonuniform distribution,
they must be weighed accordingly in the final average. Much research has gone
into how sample points and light paths can be chosen judiciously without biasing
the results.
2.3.3 Bidirectional Path Tracing
Basic MCPT depends on random paths from the viewpoint eventually finding
their way to a light source. In a purely Lambertian environment with a large light
source, a sufficient number of paths can be expected to do so. However, following
random paths is generally too wasteful. A different approach is to start tracing
paths from the light source and track them to the viewpoint, so that all paths carry
light. But the problem then becomes how to get enough paths to actually reach
the camera. The idea of
bidirectional path tracing
[Lafortune and Willems 93] is
to trace paths from both the viewpoint and the light, then join them somehow to
get a collection of representative light-to-viewpoint paths.
2.3.4 Metropolis Light Transport
Another method that traces paths from the light and the viewpoint separately is
photon mapping
, developed by Henrik Wann Jensen. The method is described in
detail in Section 2.4. Basically the approach has two phases: the first involves a
