Rendering equation

In computer graphics, the rendering equation is an integral equation that expresses the amount of light leaving a point on a surface as the sum of emitted light and reflected light. It was independently introduced into computer graphics by David Immel and colleagues and by James Kajiya in 1986. The equation is important in the theory of physically based rendering because it describes the relationships between the bidirectional reflectance distribution function (BRDF) and the radiometric quantities used in rendering. It is defined at every point on every surface in the scene, including points hidden from the camera, and the incoming light quantities on its right side usually come from the outgoing light at other points. The radiosity rendering method solves a discrete approximation of the system of equations, distributed ray tracing evaluates the integral by Monte Carlo sampling of incoming light directions, and path tracing improves and simplifies that method. The equation can be extended to fluorescence, and, by using a bidirectional scattering distribution function in place of a BRDF, to transparent and translucent materials.