1. © 2002 University of Wisconsin
Last Time
Intro
Assignment 1 brief overview
We’re working on the input file and parser
At the same time, we’ll give you vector, matrix, quaternion and transformation code, which you may use if you want
The code we give you will be in C++
A web site will appear when the parser is ready (probably before)
01/24/03
© 2002 University of Wisconsin

2. © 2002 University of Wisconsin
Today
Photo-realistic lighting overview
The global illumination equation
01/24/03
© 2002 University of Wisconsin

3. Why Photorealistic Rendering?
The aim of photo-realistic rendering was once to produce an image indistinguishable from a photograph
Now, it’s more subtle: to present an image that generates the same perception as being in a scene
What applications care about the original goal?
What applications care about the current goal?
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4. © 2002 University of Wisconsin
Our plan…
For the moment, we will concentrate on creating something that looks like a photograph
Later, we will look at some of the issues in perceptual-based rendering
They all start with photo-realistic rendering
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5. © 2002 University of Wisconsin
Photometry
The “measurement of light”, apparently Lambert coined the term in 1760 (OED)
We are interested in measuring the light that reaches an image plane of some kind
Photometry is a physical science, although a special case of radiometry: the measurement of radiation
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6. © 2002 University of Wisconsin
Measuring Light
Light is electromagnetic radiation
At any place, at any moment, you can measure the “flow” of light through that point in a given direction
The plenoptic function describes the light in a region: (x,,,t)
The plenoptic function over an area defines the light field in that region
What are the best units?
It depends what you want to do with it
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7. © 2002 University of Wisconsin
Radiance
We care about the light emitted by surfaces
We also typically assume we are dealing with first-bounce surfaces in a vacuum
More on participating media (smoke, fog, dust) later
More on translucent and phosphorescent surfaces later
Radiance is one quantity used to measure light
It has the property that it is constant along lines in a vacuum, so radiance does not attenuate with distance and we don’t need r2 terms in equations
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8. © 2002 University of Wisconsin
Measuring Angle
To define radiance, we require the concept of solid angle
The solid angle subtended by an object from a point P is the area of the projection of the object onto the unit sphere centered at P
Measured in steradians, sr
Definition is analogous to projected angle in 2D
If I’m at P, and I look out, solid angle tells me how much of my view is filled with an object
01/24/03
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9. Solid Angle of a Small Patch
Later, it will be important to talk about the solid angle of a small piece of surface
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10. © 2002 University of Wisconsin
Radiance
Radiance is the amount of energy traveling at some point in a specified direction, per unit time, per unit area perpendicular to the direction of travel, per unit solid angle
Usually denoted L(x,,)
Units Wm-2sr-1, power per unit area per unit solid angle
Note uses foreshortened area. Depends on orientation of patch to direction of travel. Why this? Best definition for expressing the physics. Other papers use other definitions. Direction specified in several ways. Theta/phi or point to point.
01/24/03
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11. © 2002 University of Wisconsin
Energy from Radiance
You have to integrate radiance to get anything useful – it’s defined per unit time, per area, per solid angle
Energy radiated in the small solid angle, d, from the small area dx, in time dt is:
projected area
What about power?
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12. © 2002 University of Wisconsin
Spectral Quantities
To handle color properly, it is important to talk about spectral radiance
Defined at a particular wavelength, per unit wavelength: L(x,,)
To get total radiance, integrate over spectrum:
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13. © 2002 University of Wisconsin
Radiosity
Radiosity is the total power leaving a surface, per unit area on the surface
Usually denoted B
To get it, integrate radiance over the hemisphere of outgoing directions:
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14. © 2002 University of Wisconsin
Irradiance
Irradiance is the total power arriving at a surface, per unit area on the surface
Usually denoted I
To get it, integrate radiance over the hemisphere of incoming directions
To remember the name, think: What does it mean to irradiate something?
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15. © 2002 University of Wisconsin
Exitance
Light sources emit light, they are sources of radiance
Exitance is the equivalent of radiosity for emitters:
Split out exitance from radiosity to simplify later equations
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16. © 2002 University of Wisconsin
Reflectance
We have all the things we need dealing with the transport of light
Reflectance is all about the way light interacts with surfaces
It is an entire field of study on its own
The most important quantity is the BRDF…
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17. © 2002 University of Wisconsin
BRDF
Bidirectional reflectance distribution function
The ratio of the radiance in the outgoing direction to the incident irradiance
Units sr-1, Range 0 - inf, Symmetric (Helmholtz reciprocity principle) Hard to measure, changes with time and interaction, generally approximated in some way (to reduce number of parameters).
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18. © 2002 University of Wisconsin
BRDF Properties
Easy to compute radiance leaving due to irradiance from one or all directions
Integrate over incoming hemisphere to get all outgoing light in one direction
Not an arbitrary function:
Must be symmetric: bd(x,o,o,i,i)= bd(x,i,I,o,o)
Cannot be large in too many places - light cannot be created, it’s a distribution function
Depends on wavelength also, but we will mostly ignore that
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19. © 2002 University of Wisconsin
Special BRDFs
Diffuse surfaces are the simplest BRDF:
Diffuse surfaces reflect incoming irradiance equally in all directions, regardless of where it comes from
Hence, the angle measures are irrelevant: bd(x,o,o,i,i)=  (x)
Ideal specular surfaces have a BRDF that is infinite in the reflection direction, and zero elsewhere
Many other models, which we will look at later
01/24/03
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20. Global Illumination Equation
All the light in the world must balance out – energy that is reflected or emitted must arrive somewhere
Radiance
Exitance
BRDF
Irradiance
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21. © 2002 University of Wisconsin
Next time
The next several lectures are about solving various simplifications to the global illumination equation
01/24/03
© 2002 University of Wisconsin