ABSTRACT
This chapter provides the machinery for the probability operations. These techniques will also prove useful for numerically evaluating complicated integrals using Monte Carlo integration. Many applications in graphics require "fair" sampling of unusual spaces, such as the space of all possible lines. For example, need to generate random edges within a pixel, or random sample points on a pixel that vary in density according to some density function. Many graphics algorithms use probability to construct random samples to solve integration and averaging problems. The chapter outlines the basic Monte Carlo solution methods for definite integrals. These techniques are then straightforwardly applied to certain integral problems. All of the basic material is also covered in several of the classic Monte Carlo texts. The chapter reviews the three most often used: function inversion, rejection, and Metropolis by nonuniform points or uniform points on non-rectangular domains.
