THE RENDERING EQUATION

Question 1

Lo(x,ωo,λ,t)

Answer 1

The spectral radiance arriving along ω0 from point x
ω0 = represents light out of the scene - o for out
Spectral radiance takes in the wavelength(λ) and the time (t)

Question 2

Le(x, ωo,λ,t)

Answer 2

Represents the emitted light from point x along ωo
So if point x is a light source

Question 3

Li(x,ωi,λ,t)

Answer 3

Light (i for incident or incoming) arriving at point x from elsewhere

Question 4

fr(x, ωi, ωo)

Answer 4

Bidirectional reflectance distribution function (BRDF)
A function that modifies the incidence light modeled off point x

Question 5

( -ωi . n)

Answer 5

Dot product of the surface normal and the incidence light at point x
Essentially taking into account the angle at which the incidence light hits - if it is along the plane its effect is 0
because dot product is the cosine f

Question 6

Integral Ω

Answer 6

We are integrating over the sum of all ω so taking into account all incidence and emitted light at point x
big omega represents the hemisphere of all these light rays

Question 7

Solving the rendering equation

Answer 7

We cannot actually solve the rendering equation because there will be an infinite number of light rays incidence and emitted
Infinitely recursive, all lights arrived at x because they arrived from elsewhere - have to backtrack to that point and again and again and all points are affected by each other

Question 8

Which visual effects are naturally modelled by the rendering equation

Answer 8

Depth of field, motion blur, fluorescene and phosphorescnece