Dec 14, 1998

Publications (Classics, ordered by time of publication) on Light Rendering :

• 3D Graphics & the Wave Theory, by H.P. Moravec, Computer Graphics (SIGGRAPH'81).
• The Rendering Equation, by J.T.Kajiya, Computer Graphics (SIGGRAPH'86).
• Illumination from Curved Reflectors, by D. Mitchell & P. Hanran (SIGGRAPH'92).

BibTeX references.

Scribe source of the paper.

A general overview of a new way of viewing light for computer graphics. He suggests using waves as the basis, and discusses the computational requirements and new capabilities - illumination by wave fronts, rather than light rays.

A continuing trend in computer representation of 3D synthetic scenes is the ever more accurate modelling of complex illumination effects. Such effects provide cues necessary for a convincing illusion of reality. The best current methods simulate multiple specular reflections and refractions, but handle at most one scattering bounce per light ray. They cannot accurately simulate diffuse light sources, nor indirect lighting via scattering media, without prohibitive increases in the already very large computing costs.

Conventional methods depend implicitly on a particle model: light propagates in straight and conceptually infinitely thin rays. This paper argues that a wave model has important computational advantages for the complex situations. In this approach, light is represented by wave fronts which are stored as 2D arrays of complex numbers.

The propagation of such a front can be simulated by a linear transform. Several advantages occur. Propagations in a direction orthogonal to the plane of a front are convolutions which can be done by FFT in O(n log n) time rather than the n² time for a similar operation using rays. A typical speedup is about 10,000. The wavelength of the illumination sets a resolution limit which prevents unnecessary computation of elements smaller than will be visible. The generated wavefronts contain multiplicities of views of the scene, which can be individually extracted by passing them through different simulated lenses. Lastly the wavefront calculations are ideally suited for implementation on available array processors, which provide more cost effective calculation for this task than general purpose computers.

The wave method eliminates the aliasing problem; the wavefronts are inherently spatially filtered, but substitutes diffraction effects and depth of focus limitations instead.

We present an integral equation which generalizes a variety of known rendering algorithms. In the course of discussing a Monte Carlo solution a new form of variance reduction is presented, called hierarchical sampling, and a number of elaborations are given that show that it may be an efficient new technique for a wide variety of Monte Carlo procedures. The resulting rendering algorithm extends the range of optical phenomena which can be effectively simulated.

Web link of interest:

• Rendering equation formulation of Image synthesis (from Charles Grant thesis).

A technique is presented to compute the reflected illumination from curved mirror surfaces onto other surfaces. In accordance with Fermat's principle, this is equivalent to finding extremal paths from the light source to the visible surface via the mirrors. Once pathways of illumination are found, irradiance is computed from the Gaussian curvature of the geometrical wavefront. Techniques from optics, differential geometry and interval analysis are applied to solve these problems.

Keywords: Automatic differentiation, caustics, differential geometry, geometrical optics, global illumination, interval arithmetic, ray tracing, wavefronts.

"the majority of time is spent solving for path extrema."

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