= Light transport =

== Radiometry recap ==

What is radiant flux?
* total amount of energy passing through a surface (measured per second)
* Radiant flux in Watts or Joules/second

=== Why do we not use radiant flux? ===

* When we emasure a high flux val, we dont know if lots of energy through a
  small surface, or a little energy through a huge surface
* TLDR its to ambiguous

New unit irradiance
* Flux per unit area
* IE Watt/m^2

=== Why do we not use irradiance? ===

We know the surface, but we still need an angle
* Could be lost of energy in a huge angle
* little energy in a small angle

New unit Radiance
* Flux per unit area angle
* W / (m^2 * radians)

== Basic question ==

How do we calculate how much light exits a surface point in a given direction

[[maxwell_equations|Maxwell equations]]!

In practive, we dont do that. We try to think of light as a ray unless we have
to

Instead we use the rendering equation!

Terms used in diagrams

* V - direction towards the viewer
* N - surface normal
* L - vector pointing towards the light source
* R - reflected ray direction
* Theta,,i,, and Theta,,r,, - incident and reflected angles

To calcuate R `R = L - 2N(L * N)`

== Light attentuation ==

* The amount of intensity light looses as it travels farther away. Light looses
  energy as well as it reflects off of surfaces
* How can we calculate attentuation?

`L * N`

Assuming that L and N are normalized, the attentuation will be equal to
`cos(theta)` where theta is the angle between L and N. This is true because of
the dot product.

== Materials ==

How can we simluate the look of different materials?

Based on how they relfect light.

* Specular surface reflects exactly one ray
  * One incoming direction
  * One outgoing direction
* Diffuse spreads ray into smaller rays in all directions
  * On incoming direction
  * many outgoing direction
  * many outgoing intesntiy
* Spread breaks out the ray into a few smaller rays in a single direction

To simulate a surface, we can use a probability density function that takes

* incoming light direction
* point on surface

This method will output the _probability of a given outward direction_

Something like `probability of happening = f(incoming direction, point, outgoing direction)`.

This is known as the _Bidirectional reflectance distribution function (BRDF)_.