Description
The rendering equation of Kajiya adheres to three particular principles of optics; the Principle of global illumination, the Principle of Equivalence (reflected light is equivalent to emitted light), and the Principle of Direction (reflected light and scattered light have a direction).
In the real world, objects and surfaces are visible due to the fact that they are reflecting light. This reflected light then illuminates other objects in turn. From that simple observation, two principles follow.
I. For a given indoor scene, every object in the room must contribute illumination to every other object.
II. Second, there is no distinction to be made between illumination emitted from a light source and illumination reflected from a surface.
Invented in 1984, a rather different method called radiosity was faithful to both principles. However, radiosity equivocates the illuminance falling on a surface with the luminance that leaves the surface. This forced all surfaces to be Lambertian, or "perfectly diffuse". While radiosity received a lot of attention at its invocation, perfectly diffuse surfaces do not exist in the real world. The realization that illumination scattering throughout a scene must also scatter with a direction was the focus of research throughout the 1990s, since accounting for direction always exacted a price of steep increases in calculation times on desktop computers. Principle III follows.
III. The illumination coming from surfaces must scatter in a particular direction that is some function of the incoming direction of the arriving illumination, and the outgoing direction being sampled.
Kajiya's equation is a complete summary of these three principles, and path tracing, which approximates a solution to the equation, remains faithful to them in its implementation. There are other principles of optics which are not the focus of Kajiya's equation, and therefore are often difficult or incorrectly simulated by the algorithm. Path Tracing is confounded by optical phenomena not contained in the three principles. For example,
- Bright, sharp caustics; radiance scales by the density of illuminance in space.
- Subsurface scattering; a violation of principle III above.
- Chromatic aberration. fluorescence. iridescence. Light is a spectrum of frequencies.
Read more about this topic: Path Tracing
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“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St. Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)