Last Time

1. 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) © 2002 University of Wisconsin

2. Today • Photo-realistic lighting overview • The global illumination equation © 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? © 2002 University of Wisconsin

4. 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 © 2002 University of Wisconsin

5. 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 © 2002 University of Wisconsin

6. 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 © 2002 University of Wisconsin

7. 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 © 2002 University of Wisconsin

8. 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 © 2002 University of Wisconsin

9. Solid Angle of a Small Patch • Later, it will be important to talk about the solid angle of a small piece of surface © 2002 University of Wisconsin

10. Radiance • Usually denoted L(x,,) • Units Wm-2sr-1, power per unit area per unit solid angle 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 © 2002 University of Wisconsin

11. 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? © 2002 University of Wisconsin

12. 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: © 2002 University of Wisconsin

13. 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: © 2002 University of Wisconsin

14. 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? © 2002 University of Wisconsin

15. 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 © 2002 University of Wisconsin

16. 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… © 2002 University of Wisconsin

17. BRDF • Bidirectional reflectance distribution function • The ratio of the radiance in the outgoing direction to the incident irradiance © 2002 University of Wisconsin

18. 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 © 2002 University of Wisconsin

19. 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 © 2002 University of Wisconsin

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 © 2002 University of Wisconsin

21. Next time • The next several lectures are about solving various simplifications to the global illumination equation © 2002 University of Wisconsin