Lightpath notation

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The light path notation is used in the image synthesis of computer graphics . It is a notation that specifies the type of path that a light beam takes from a light source, with possible reflections , to the virtual observer (eye point). The different types of light paths differ in whether and in what order they hit diffuse or reflective surfaces.

notation

Examples of different light paths in a scene with global lighting .
1) LDSE, 2) LSSDE and 3) LDDE.

The light path notation was introduced by Paul Heckbert in 1990 . It is based on regular expressions and uses the following symbols:

L. denotes the light source,
D. denotes a diffuse surface,
S. ("Specular") refers to a reflective surface ( including light-refracting bodies),
E. ("Eye") denotes the eye point.

The following common symbols for regular expressions also apply:

| stands for "or",
* stands for any number of reflections on surfaces of the specified type,
+ stands for at least one reflection,
? stands for at most one reflection.

The reason for the distinction between light paths hitting diffuse (D) and reflective (S) surfaces is that they require different techniques to take them into account. Depending on the rendering algorithm, only certain light paths can be simulated.

The simplest case of a diffuse surface is a Lambertian surface , the simplest case of a reflective surface is a smooth dielectric , the degree of reflection and transmission of which can be calculated using Fresnel's formulas . In general lighting models , which can also include “shiny” reflections, the boundary between diffuse and specular reflection is not clearly defined.

Typical light paths

Lightpath notation can be used to indicate the capabilities of rendering algorithms. Examples are shown in the following table.

Light path meaning Examples of algorithms capable of simulating these paths
L (D | S) * E All possible light paths: a light beam can hit any number of diffuse or reflective surfaces. The simulation of all possible light paths corresponds to global lighting . Path tracing
LD * E Possible diffuse interreflection (in the example path 3) Simple radiosity
LD? S * E Possibly diffuse reflection, then any specular reflections (in the example path 1) Recursive ray tracing (according to Whitted)
LS + DE Caustics (in the example path 2). These light paths cannot be simulated with classic algorithms (simple radiosity or ray tracing). Caustic photon mapping

extension

Eric Veach has expanded the light path notation in his dissertation especially for E and L so that the start / end point and the set of outgoing / incoming directions can be specular or diffuse. With these extended, regular expressions it is possible to note different types of light sources (e.g. directed spotlight, point light source or luminous sphere) as well as camera types (e.g. pinhole camera or cameras with depth of field ).

literature

  • Paul Heckbert: Adaptive radiosity textures for bidirectional ray tracing. In ACM SIGGRAPH '90 Proceedings: 145-154. ACM Press, Dallas 1990, ISBN 0-201-50933-4
  • Eric Veach: Robust Monte Carlo Methods for Light Transport Simulation. Dissertation, Stanford University 1997 ( online )
  • Alan Watt: 3D Computer Graphics , 3rd Edition, pp. 281-283. Pearson / Addison-Wesley, Harlow (England) 2000, ISBN 978-0-201-39855-7