• idea: replace aliasing with the appropriate noise
• rays are stochastically distributed over...

  time:	to produce motion blur
  lens area:	to produce depth of field
  reflection angle:	to produce glossiness
  transmission angle:	to produce translucency
  shadow ray:	to produce glossiness
  space:	to anti-alias

• The human eye samples using a Poisson Disk distribution
  • a finite number of photoreceptors
  • cones in the eye are distributed stochastically, but such that no two cones are closer than a certain distance
    • draw locations of cones
    • place a disk of radius r about each cone
    • no other cone will fall within that disk
  • can use this approach in ray tracing but it is quite expensive

• [image: poisson disk distribution]

• We can approximate a Poisson disk distribution using Jittering
• idea: begin with a regular gird then jitter the center points randomly
• [image: shows two 4x4 pixel grids. The first, labelled "Uniform Distribution," shows a ray going through the center of each pixel. The second grid, labelled "Jittered," shows the rays going through random locations within each pixel.]
  • removes high frequencies
  • introduces noise in place of high frequencies

1. Anti-aliasing
   • send multiple rays per pixel, but send them at stochastically jittered locations

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2. Glossiness (blurred reflection)
   • tracing a ray according to the reflection angle produces sharp reflections
   • [image: shows a ray reflecting off of a surface]
   • we can create a blurred reflection by sending multiple secondary rays jittered about the reflection ray
   • [image: shows the reflection ray being tweaked somewhat to provide randomness. We must tweak the rays only within a certain bound, so as to not introduce excessive error]

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3. Translucency
   • tracing a single transmitted ray gives a sharp transparency. To simulate a translucent material (bathroom glass), send multiple transmission rays and jitter them about the actual transmitted ray
   • [image: a transmission ray being jittered within a certain bound]
   • This will "blur" the transparency

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4. Penumbra
   • Since lights in the real world are not point light sourcees, shadows are not sharp
   • [image: two contrasting examples. One shows an object occluding a surface from a point light source, and the sharp shadow that results. The other shows a similar object occluding a surface from an area light source, with the resulting umbra (hard shadow) and penumbra (soft shadow) ]
   • Penumbra - shadows generated by partially obscured lights
   • idea: send out multiple shadow rays from the surface intersection point to the light source (area light source). Jitter the rays within some limit. The intensity of the surface point depends on the number of the jittered rays that reach the light
   • [image: illustrates the above concept]

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5. Depth of field
   • focus at a particular distance. Objects at other distances appear out of focus
   • jitter rays slightly so that this effect is simulated
   • rays should be jittered to stay within a cone
   • the cone size depends on the distance from the focal point of the object
   • [image: complicated diagram, uses the notation explained below]
     • P_f = focal point
     • F = focal point of lens
     • n = aperture number
     • P = distance from lens to focal point
     • V_p = distance from lens to image plane
     • P_D = a point not on focal plane
     • D = distance to P_D
     • r = radius of cone for object at distance D
     • C = circle of confusion
   • For an object located at P_D, we send out a group of jittered rays that all lie within a cone of radius r.
   • This will simulate a lens without having to actually provide the lens
   • How do we get r?
   • 
   • Thus, we send out jittered rays that fall within a cone whose radius depends on the distance of the object from the focal point

   • Alternatively: (more accurate, more complex)
     • Determine the focal point by sending a ray from the center of the lens to the point on the screen, then use the lens qualities to get the focal point.
     • Next, choose some jittered point on the lens
     • Trace a ray from that point through the focal point, then determine intensity information
     • [image: shows a ray passing through a lens, hitting a "focal point" in midair, then refracting somewhat to strike an object]

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6. Motion Blur
   • distribute rays over time - static objects will appear normal, but moving objects will be blurred depending on their velocity
   • jitter the rays with respect to time
   • determine object positions at each of the jittered time values
   • send the ray with the objects positioned appropriately
   • combine the rays back into one to get the motion blurred object

For each ray do:

1. jitter the spatial screen location of the ray
2. select a time for the ray and move objects to that time
3. perform depth of field calculation by sending a ray from the eye point (center of the lens) to the ray point on the screen. Jitter a point on the lens, then trace a ray from that point to the focal point of the original ray. Determine which object is visible.
4. send shadow rays to the light sources by jittering the rays about the actual shadow ray
5. jitter rays about the reflection ray to produce glossiness
6. jitter rays about the tranmission ray to produce translucency
7. [image: gives a visual representation of the above]