Local shading considers a small set of chosen light paths. Global illumination instead accounts for light that may bounce through the scene before reaching the camera.

A common statement is the rendering equation

$$ L_o(x,\omega_o)=L_e(x,\omega_o)+ \int_{\Omega} f_r(x,\omega_i,\omega_o) L_i(x,\omega_i) \max(0,\mathbf n\cdot\omega_i),d\omega_i. $$

Here $L_o$ is outgoing radiance, $L_e$ is emitted light, $L_i$ is incoming radiance, and $f_r$ is the surface's bidirectional reflectance distribution function. The integral sums contributions arriving from directions over the visible hemisphere $\Omega$.

The equation is recursive because incoming radiance at one surface often comes from outgoing radiance at another. Effects such as indirect diffuse light, color bleeding and soft interreflection arise from these multi-bounce paths.

Closed-form solutions are rare for realistic scenes. Rendering methods therefore approximate the integral and the recursive transport using sampling, analytic approximations or combinations of both.