Volumetric path tracing is a method for rendering images in

computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...

which was first introduced by Lafortune and Willems. This method enhances the rendering of the lighting in a scene by extending the

path tracing Path tracing is a computer graphics Monte Carlo method of rendering images of three-dimensional scenes such that the global illumination is faithful to reality. Fundamentally, the algorithm is integrating over all the illuminance arriving to ...

method with the effect of

light scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...

. It is used for photorealistic effects of participating media like fire, explosions, smoke, clouds, fog or soft shadows. Like in the path tracing method, a ray gets followed backwards, beginning from the eye, until reaching the light source. In volumetric path tracing, scattering events can occur along with ray tracing. When a light ray hits a surface, a certain amount gets scattered into the media.

Description

The algorithm is based on the volumetric rendering equation, which extends the

rendering equation In computer graphics, the rendering equation is an integral equation in which the equilibrium radiance leaving a point is given as the sum of emitted plus reflected radiance under a geometric optics approximation. It was simultaneously introduced ...

with a scattering term. It is composed of an absorption, out-scattering, emission and an in-scattering part. The absorption and out-scattering together form the extinction term. The in-scattering is the most expensive part to calculate because it needs an integration over all paths in the scene that consist of

radiance In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiatio ...

. Therefore, thousands of paths need to be traced to get a result with a good quality without much noise. For a better handling, the in-scattering term can be split into two components, the single scattering and the multiple scattering.

Algorithm

In volumetric path tracing, a distance between the ray and the surface gets

sampled Sample or samples may refer to: Base meaning * Sample (statistics), a subset of a population – complete data set * Sample (signal), a digital discrete sample of a continuous analog signal * Sample (material), a specimen or small quantity of so ...

and compared with the distance of the nearest intersection of the ray with the surface. If the sampled distance is smaller, a scatter event occurs. In that case the path gets evaluated and traced from the scatter point in the media, not from the surface point on which it falls. The rest of the procedure continues the same, until reaching the light source.

Sampling

A possible way of sampling distances is the ''ray marching'' method. It works similar to ray tracing but operates on a

distance field A distance transform, also known as distance map or distance field, is a derived representation of a digital image. The choice of the term depends on the point of view on the object in question: whether the initial image is transformed into another ...

of the scene, and acts in discrete steps. The scattering inside the media can be determined by a phase function using

importance sampling Importance sampling is a Monte Carlo method for evaluating properties of a particular distribution, while only having samples generated from a different distribution than the distribution of interest. Its introduction in statistics is generally att ...

. Therefore, the ''Henyey–Greenstein phase function'' can be applied. It is a non-

isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...

phase function for simulating the scattering of materials like oceans, clouds or skin.

References

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Description

Algorithm

Sampling

References

Further reading