Physically Based Rendering, 3rd Edition

13: Monte Carlo Integration

Before we introduce the Integrators that compute radiance along ray paths between lights and the camera, we will first lay some groundwork regarding the techniques they will use to compute solutions to the integral equations that describe light scattering. These integral equations generally do not have analytic solutions, so we must turn to numerical methods. Although standard numerical integration techniques like trapezoidal integration or Gaussian quadrature are very effective at solving low-dimensional smooth integrals, their rate of convergence for the higher dimensional and discontinuous integrals that are common in rendering is poor.

Monte Carlo numerical integration methods provide one solution to this problem. ...