the rendering equation

$$\begin{array}{c}{L}_o(\mathbf{x},{\omega }_o)=L_e(\mathbf{x},{\omega }_o)+{\int }_{\Omega }{f}_r(\mathbf{x},{\omega }_i,{\omega }_o)L_i(\mathbf{x},{\omega }_i)({\omega }_i\cdot \mathbf{n})d{\omega }_i\end{array}$$

To find the light towards the viewer from a specific point, we sum the light emitted from such point plus the integral within the unit hemisphere of the light coming from any given direction multiplied by the chances of such light rays bouncing towards the viewer¹ and also by the cosine term/irradiance factor over the normal at the point.²

Note that incoming light is outgoing light from a previous point, making the domain of the integral infinite and the equation recursive.

1. Bidirectional reflectance distribution function
2. https://en.wikipedia.org/wiki/Rendering_equation

inspiration for this post: https://blog.chuckleplant.com/2017/05/28/light-shafts.html