130 lines
3.5 KiB
Plaintext
130 lines
3.5 KiB
Plaintext
= Light transport =
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== Radiometry recap ==
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What is radiant flux?
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* total amount of energy passing through a surface (measured per second)
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* Radiant flux in Watts or Joules/second
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=== Why do we not use radiant flux? ===
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* When we emasure a high flux val, we dont know if lots of energy through a
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small surface, or a little energy through a huge surface
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* TLDR its to ambiguous
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New unit irradiance
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* Flux per unit area
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* IE Watt/m^2
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=== Why do we not use irradiance? ===
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We know the surface, but we still need an angle
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* Could be lost of energy in a huge angle
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* little energy in a small angle
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New unit Radiance
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* Flux per unit area angle
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* W / (m^2 * radians)
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== Basic question ==
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How do we calculate how much light exits a surface point in a given direction
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[[maxwell_equations|Maxwell equations]]!
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In practive, we dont do that. We try to think of light as a ray unless we have
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to
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Instead we use the rendering equation!
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Terms used in diagrams
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* V - direction towards the viewer
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* N - surface normal
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* L - vector pointing towards the light source
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* R - reflected ray direction
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* Theta,,i,, and Theta,,r,, - incident and reflected angles
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To calcuate R `R = L - 2N(L * N)`
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== Light attentuation ==
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* The amount of intensity light looses as it travels farther away. Light looses
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energy as well as it reflects off of surfaces
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* How can we calculate attentuation?
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`L * N`
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Assuming that L and N are normalized, the attentuation will be equal to
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`cos(theta)` where theta is the angle between L and N. This is true because of
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the dot product.
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== Materials ==
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How can we simluate the look of different materials?
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Based on how they relfect light.
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* Specular surface reflects exactly one ray
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* One incoming direction
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* One outgoing direction
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* Diffuse spreads ray into smaller rays in all directions
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* On incoming direction
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* many outgoing direction
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* many outgoing intesntiy
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* Spread breaks out the ray into a few smaller rays in a single direction
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To simulate a surface, we can use a probability density function that takes
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* incoming light direction
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* point on surface
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This method will output the _probability of a given outward direction_
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Something like `probability of happening = f(incoming direction, point, outgoing direction)`.
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This is known as the _Bidirectional reflectance distribution function (BRDF)_.
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What about materials that reflect some light allow some right through
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(transmitted).
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Properties of a transparent material
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* Helmholtz-reciprocity
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* direction of the ray of light can be reveresd
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* This means the odds of the light bouncing from A to B are the same as the
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odds of boucing B to A
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* Positivity
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* It is impossible for an exit direction to have a negative probability
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* Energy conservation
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* An object may reflect OR absorb incoming light, but no more light can come
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out than the incoming amount
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== Rendering equation ==
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Sum of all light reflections and absorbtions at a point
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Note that an object can emit light itself. It also receives light from
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different directions, which it will either reflect or absorb. Therefore
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`Light exiting = Emitted light + reflected incoming light`
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AKA
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{{{
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Light output(x, vector w) = Light emitted(x, vector w)
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+ Integral of (Light incoming to x from vector w * BRFD(vector w, x vector w
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prime) cos theta dw
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}}}
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Problems with above
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* The exitant radiance of a point x depends on the incoming radiance of every
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other point, which also depends on x
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* We cannot solve this integral in closed form
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* The integral is infinite dimensional
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* It is singular
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We simply dont know enough to even start
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