Overview

Monte Carlo ray-tracing techniques are the most general class of global illumination methods. All of these methods use point sampling to estimate the illumination in a model. A point sample consists of tracing a ray through the model and computing the radiance in the direction of this ray. This concept has several advantages over finite element radiosity techniques:

• Geometry can be procedural.

• No tessellation is necessary.

• It is not necessary to precompute a representation for the solution.

• Geometry can be duplicated using instancing.

• Any type of BRDF can be handled.

• Specular reflections (on any shape) are easy.

• Memory consumption is low.

• The accuracy is controlled at the pixel/image level.

• Complexity has empirically been found to be O(log N) where N is number of scene elements. Compare this with O( N log N) for the fastest finite element methods [17].

In addition the Monte Carlo ray-tracing algorithms that we describe here have the property that they are unbiased. In practice this means that the only error in the result is seen as variance (noise).

This chapter contains a review of the basic ray-tracing algorithm as well as several extensions for simulating global illumination.

3.1 Classic Ray Tracing

Ray tracing was popularized for computer graphics by Whitted in 1980 [120] with the introduction of the recursive ray-tracing algorithm. Ray tracing is an elegant and simple algorithm that makes it easy to render shadows and specular surfaces. An example of a ray-traced image is...