Today

1
Today

• Photorealistic rendering
• Algorithms for producing high-quality images
• Ways of deciding which algorithm for use

2
Lighting Revisited

• Some applications are intended to produce
  pictures that look photorealistic, or close to it
• The image should look like a photograph
• A better metric is perceptual the image should
  generate a target set of perceptions
• Applications include Film special effects,
  Training simulations, Computer games,
  Architectural visualizations, Psychology
  experiments,
• To achieve the goal of photorealism, we must
  think carefully about light and how it interacts
  with surfaces
• What you should take away The various aspects of
  light interaction and how algorithms capture or
  ignore them

3
The Light of Mies van der Rohe
Image by Henrik Wann Jensen
4
Global Illumination Equation

• If we wish to compute perfect illumination, we
  need to solve the global illumination equation
• The light leaving a point (what we see) is a
  combination of light it emits and light it
  reflects
• The light it reflects depends on what light
  arrives and how it reflects it

Emitted light
Sum
Reflection BRDF
Incoming light
Light leaving
Incoming light reflected at the point
5
Photorealistic Lighting

• Photorealistic lighting requires solving the
  equation!
• Not possible in the general case with todays
  technology
• Light transport is concerned with the incoming
  light part of the equation
• Notice the chicken and egg problem
• To know how much light leaves a point, you need
  to know how much light reaches it
• To know how much light reaches a point, you need
  to know light leaves every other point
• Reflectance modeling is concerned with the BRDF
• Hard because BRDFs are high dimensional functions
  that tend to change as surfaces change over time

6
Classifying Rendering Algorithms

• We cant solve the general global illumination
  equation
• But we can solve some special cases, to some
  degree of accuracy
• We can classify rendering algorithms according to
  the type of light interactions they capture
• For example The OpenGL lighting model captures
• Direct light to surface to eye light transport
• Diffuse and rough specular surface reflectance
• It actually doesnt do light to surface transport
  correctly, because it doesnt do shadows
• We would like a way of classifying interactions
  light paths

7
Classifying Light Paths

• Classify light paths according to where they come
  from, where they go to, and what they do along
  the way
• Assume only two types of surface interactions
• Pure diffuse, D
• Pure specular, S
• Assume all paths of interest
• Start at a light source, L
• End at the eye, E
• Use regular expressions on the letters D, S, L
  and E to describe light paths
• Valid paths are L(DS)E

?
Light
Eye
8
Simple Light Path Examples

• LE
• The light goes straight from the source to the
  viewer
• LDE
• The light goes from the light to a diffuse
  surface that the viewer can see
• LSE
• The light is reflected off a mirror into the
  viewers eyes
• L(SD)E
• The light is reflected off either a diffuse
  surface or a specular surface toward the viewer
• Which does OpenGL (approximately) support?

9
More Complex Light Paths

• Find the following
• LE
• LDE
• LSE
• LDDE
• LDSE
• LSDE

Modified Cornell box, due to Henrik Wann Jensen
10
More Complex Light Paths
LE
LDDE
LSDE
LSE
LDSE
LDE
11
The OpenGL Model

• The standard graphics lighting model captures
  only L(DS)E
• It is missing
• Light taking more than one diffuse bounce LDE
• Should produce an effect called color bleeding,
  among other things
• Approximated, grossly, by ambient light
• Light refracted through curved glass
• Consider the refraction as a mirror bounce
  LDSE
• Light bouncing off a mirror to illuminate a
  diffuse surface LSDE
• Many others

12
Raytracing

• Cast rays out from the eye, through each pixel,
  and determine what they hit first
• Cast additional rays from the hit point to
  determine the pixel color
• Shadow rays toward each light. If they hit
  something, then the object is shadowed from that
  light, otherwise use standard model for the
  light
• Reflection rays for mirror surfaces, to see what
  should be reflected in the mirror
• Transmission rays to see what can be seen through
  transparent objects
• Sum all the contributions to get the pixel color

13
Raytracing
Shadow rays
Reflection ray
Transmitted ray
14
Recursive Ray Tracing

• When a reflected or refracted ray hits a surface,
  repeat the whole process from that point
• Send out more shadow rays
• Send out new reflected ray (if required)
• Send out a new refracted ray (if required)
• Generally, reduce the weight of each additional
  ray when computing the contributions to surface
  color
• Stop when the contribution from a ray is too
  small to notice
• What light paths does recursive ray tracing
  capture?

15
PCKTWTCH by Kevin Odhner, POV-Ray
16
Kettle, Mike Miller, POV-Ray
17
(No Transcript)
18
Raytracing Implementation

• Raytracing breaks down into two tasks
• Constructing the rays to cast
• Intersecting rays with geometry
• The former problem is simple vector arithmetic
• The intersection problem arises in many areas of
  computer graphics
• Collision detection
• Other rendering algorithms

19
Raytracing Summary

• Raytracing can do reflection and refraction, its
  primary advantage over OpenGLs model
• Raytracing can also do
• Soft shadows from area light sources
• Texture, bump and displacement mapping, easily
• Distributed ray tracing Depth of field, motion
  blur and soft reflections
• Relatively simple to implement
• A basic raytracer can be written in a few hundred
  lines of code
• But its slow fails to take advantage of
  coherence

20
Distribution Raytracing
Depth of Field
21
Raytracing And Light Paths

• A ray can be traced from its origin through any
  number of specular bounces, until it hits
  something diffuse
• We know which way to send the ray after a
  specular bounce
• We dont know where to send it after a diffuse
  bounce
• Rays do Origin-S-Hit
• Which light paths does a basic raytracer capture?
• Which can it not capture?

22
Correct
Raytraced
23
Missing Paths

• Basic recursive raytracing cannot do
• LSDE Light bouncing off a shiny surface like a
  mirror and illuminating a diffuse surface
• LDE Light bouncing off one diffuse surface to
  illuminate others
• Problem The raytracer doesnt know where to send
  rays out of the diffuse surface to capture the
  incoming light
• Also a problem for rough specular reflection
• Fuzzy reflections in rough shiny objects

24
Bi-directional Raytracing

• Cast rays from the light sources out into the
  scene
• Light-ray tracing, starting at the light
• When a ray hits a diffuse surface, accumulate
  some light there
• Surfaces record the amount of light that hits
  them
• Store the light in texture maps
• Store the light in quadtrees
• Store the light in photon maps
• Cast rays from the eye out into the scene
• When a ray hits a diffuse surface, look up the
  amount of light that hit it in the light-ray
  phase
• What paths does it capture?
• What sort of visual effects do you see?

25
Caustics
Standard raytracer
Bi-directional raytracer
More rays in the light pass
Note the LSDSE paths
26
Refraction caustic
27
Refraction caustics
28
Still Missing

• LDE paths Diffuse-diffuse transport
• Formulated and solved with radiosity methods
• L(SD)E paths
• Solved with Monte-Carlo renderers
• Send out random rays of light and see where they
  go
• Very very inefficient (in terms of time)
• Also solvable with multi-pass methods, but also
  very very inefficient (in terms of space), and
  subject to aliasing
• An unsolved (unsolvable?) problem

29
Real World LDE Paths
30
Radiosity Assumptions

• All surfaces are perfectly diffuse
• Means that is doesnt matter which way light hits
  or leaves a surface
• Illumination is constant over a patch
• Can break the world up into a discrete number of
  pieces
• Problems at sharp illumination boundaries -
  shadows
• Ways around these problems, but less efficient
  and less able to manage scene complexity
• Assumptions allow us to solve for LDE paths

31
Radiosity Equation

• Derived from the global illumination equation
  using radiosity assumptions
• Bi is the radiosity (brightness) of patch i
• ?i is the diffuse reflection coefficient
• Fij is the form factor, which quantifies how much
  light patch j contributes to patch i
• The brightness of each patch depends on how much
  light it gets from all the others, and its
  diffuse reflection

32
Solving the Radiosity Eqn

• Radiosity algorithms use one of several methods
  to solve the radiosity equation
• Basically a very large linear system, so
  techniques can all be mapped onto linear system
  solvers
• A large part of the computation is in finding
  form factors
• Describe how much light gets from each patch to
  every other patch
• Geometric in nature - do not depend on the
  illumination, just the layout of the scene
• Another key factor is finding good meshing
  strategies - ways of laying out the patches

33
Radiosity Example

• Color bleeding is extreme in this example
• Textures are applied after solving for
  illumination
• Some meshing artifacts are visible - note the
  banding around the pictures on the wall

34
Radiosity Meshing

• Each patch is colored with its illumination
• Note the discrete nature of the solution
• The previous image was obtained by pushing color
  to vertices and then Gourand shading