Draw equation and path tracking __ Graphics

I. Drawing equation (Rendering equation)

In the previous article, we have explained in detail the important concepts and mathematical physical models of the field of graphics real sense rendering. The next thing we need to focus on is the core problem in the area of painting: How do we compute the coloring of a point (shading)? We know that the radiant brightness (Radiance) corresponds to the point of the color. So the question is described as follows:
Emits a light from the camera, intersects the model surface and points to p, and calculates the radiation brightness in the direction of the line of sight. According to the derivation process of BRDF, we know that given the direction of incident and the direction of ejection, the radiant brightness in the direction of the ejection is equal to the irradiance of the BRDF times the incident light in the surface micro-element, namely:
Lo (P,ωo) =f (p,ωo,ωi) Ei L O (p, ωo) = f (P, Ωo, ωi) E i l_o (p,\omega_o) =f (p,\omega_o,\omega_i) e_i because the surface of an object cannot accept only one Direction The irradiance of the light, so we take the expression of the above equation as a differential form:
Dlo (P,ωo) =f (p,ωo,ωi) dEi d L O (P, ωo) = f (P, Ωo, ωi) d E i dl_o (p,\omega_o) =f (p,\omega_o,\omega_i) de_i
According to the relationship between irradiance and radiant brightness, Dei=li (p,ωi) cosθidωi d E i = L (P, ωi) c o sθi dωi de_i=l_i (p,\omega_i) cos\theta_id\omega_i
With the upper-style can be:
Dlo (P,ωo) =f (p,ωo,ωi) Li (p,ωi) cosθid