The paper presents an integral equation, known as the rendering equation, that generalizes various rendering algorithms in computer graphics. The equation models the scattering of light off different types of surfaces and is expressed as: \[ I(z, z') = g(z, z') [ \epsilon(z, z') + \int_S \rho(z, z'', z'') I(z'', z'') dz'' ] \] where: - \( I(z, z') \) is the intensity of light passing from point \( z' \) to point \( z \). - \( g(z, z') \) is a geometry term that accounts for occlusion. - \( \epsilon(z, z') \) is the intensity of emitted light from \( z' \) to \( z \). - \( \rho(z, z'', z'') \) is the intensity of scattered light from \( z'' \) to \( z \) by a surface patch at \( z' \). The paper discusses several methods for solving the rendering equation, including the Neumann series, the Utah approximation, ray tracing, distributed ray tracing, and radiosity. It also introduces Markov chains as a numerical method for solving integral equations and presents hierarchical sampling techniques for variance reduction. These techniques include sequential uniform sampling, adaptive hierarchical integration, and importance sampling. The paper concludes with a comparison of the rendering equation technique to conventional ray tracing, highlighting its advantages in terms of variance reduction and efficiency.The paper presents an integral equation, known as the rendering equation, that generalizes various rendering algorithms in computer graphics. The equation models the scattering of light off different types of surfaces and is expressed as: \[ I(z, z') = g(z, z') [ \epsilon(z, z') + \int_S \rho(z, z'', z'') I(z'', z'') dz'' ] \] where: - \( I(z, z') \) is the intensity of light passing from point \( z' \) to point \( z \). - \( g(z, z') \) is a geometry term that accounts for occlusion. - \( \epsilon(z, z') \) is the intensity of emitted light from \( z' \) to \( z \). - \( \rho(z, z'', z'') \) is the intensity of scattered light from \( z'' \) to \( z \) by a surface patch at \( z' \). The paper discusses several methods for solving the rendering equation, including the Neumann series, the Utah approximation, ray tracing, distributed ray tracing, and radiosity. It also introduces Markov chains as a numerical method for solving integral equations and presents hierarchical sampling techniques for variance reduction. These techniques include sequential uniform sampling, adaptive hierarchical integration, and importance sampling. The paper concludes with a comparison of the rendering equation technique to conventional ray tracing, highlighting its advantages in terms of variance reduction and efficiency.