Rendering equation

In computer graphics, the rendering equation is an integral equation in which the equilibrium radiance leaving a point is given as the sum of emitted plus reflected radiance under a geometrical optics approximation.

It was independently introduced into computer graphics by David Immel et al.[1] and James Kajiya[2] in 1986.

The various realistic rendering techniques in computer graphics attempt to solve this equation.

The physical basis for the rendering equation is the law of conservation of energy.

) multiplied by the surface reflection and cosine of the incident angle.

The rendering equation may be written in the form where Two noteworthy features are: its linearity—it is composed only of multiplications and additions, and its spatial homogeneity—it is the same in all positions and orientations.

It is a Fredholm integral equation of the second kind, similar to those that arise in quantum field theory.

One approach to solving the equation is based on finite element methods, leading to the radiosity algorithm.

Another approach using Monte Carlo methods has led to many different algorithms including path tracing, photon mapping, and Metropolis light transport, among others.

Although the equation is very general, it does not capture every aspect of light reflection.