© 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

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

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? 01/24/03 © 2002 University of Wisconsin

© 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 01/24/03 © 2002 University of Wisconsin

© 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 01/24/03 © 2002 University of Wisconsin

© 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 01/24/03 © 2002 University of Wisconsin

© 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 01/24/03 © 2002 University of Wisconsin

© 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 © 2002 University of Wisconsin

Solid Angle of a Small Patch Later, it will be important to talk about the solid angle of a small piece of surface 01/24/03 © 2002 University of Wisconsin

© 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 © 2002 University of Wisconsin

© 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? 01/24/03 © 2002 University of Wisconsin

© 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: 01/24/03 © 2002 University of Wisconsin

© 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: 01/24/03 © 2002 University of Wisconsin

© 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? 01/24/03 © 2002 University of Wisconsin

© 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 01/24/03 © 2002 University of Wisconsin

© 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… 01/24/03 © 2002 University of Wisconsin

© 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). 01/24/03 © 2002 University of Wisconsin

© 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 01/24/03 © 2002 University of Wisconsin

© 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 © 2002 University of Wisconsin

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 01/24/03 © 2002 University of Wisconsin

© 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