01/19/05© 2005 University of Wisconsin CS 779: Rendering Prof Stephen Chenney Spring

01/19/05© 2005 University of Wisconsin Today Course overview and information Introduction to Physically-Based Rendering

01/19/05© 2005 University of Wisconsin What’s It About A bunch of topics related to rendering: creating images with a computer Broadly: –Physically-based rendering Ray tracing, the physics, reflectance models, algorithms galore –Stylized Rendering Lots of ways to do non-photorealistic rendering –Image-based rendering Reprojecting images in various ways –Point-based rendering No geometry – just points –Large-database rendering (if time) Visibility Proxies

01/19/05© 2005 University of Wisconsin Who’s it for I am assuming a working knowledge of graphics at the CS 559 level You will find this class easier if: –You are comfortable with the tools of graphics –You know multi-variate calculus (the basics) –You know probability and statistics (not much) –You can program in C++ –You can give talks – or you’ll learn how You will find this class harder if: –Your knowledge of things like transformations and vectors is sketchy –You aren’t great at calc –You’re not really interested in making pictures

01/19/05© 2005 University of Wisconsin How it will be run This is a graduate class, and will be run like one –Classes will be cancelled –You will be expected to do a lot of things on your own –If you took 559 from me, this will look like chaos The lecture material will be front-loaded –3 lectures a week for several weeks –Then 2 lectures a week –Then no lectures a week The project work will be back-loaded

01/19/05© 2005 University of Wisconsin The grades will be based on… Programming and reading assignments In–class presentations A project

01/19/05© 2005 University of Wisconsin Books There is no book that covers all the material –Not even Glassner’s “Principles of Digital Image Synthesis”, all 2 volumes of it Pharr and Humphreys “Physically-Based Rendering” is a required book –It is the textbook for the first half of the course –It is a reference book for the software for assignments The web site lists will list good references –You are not required to buy them – but in the end you will probably decide some are useful enough to own –I will attempt to make sure the library has them on reserve

01/19/05© 2005 University of Wisconsin Papers Original papers will be required reading Several sources: –ACM Digital Library, available through the university library –Eurographics digital library – I have access, and can obtain papers –Citeseer

01/19/05© 2005 University of Wisconsin Software PBRT for anything related to physically-based rendering –The software from the textbook –Contains vast amounts of helpful code and libraries –Well documented via the book and the code –Read Chapter 1 of the book to understand how the book and the code fit together –We will make it available from the class account OpenGL for real time rendering Anything else you want (really)

01/19/05© 2005 University of Wisconsin TA Shaohua Fan is your source for help with the software –An expert on Monte-Carlo rendering algorithms –He has used PBRT extensively for all

01/19/05© 2005 University of Wisconsin Physically-Based Rendering Aim: generate images that accurately reflect reality –Applications? Physics: describing light and how it behaves Math: Integral equations Algorithms: How to solve integral equations Models: How to describe the world Display: How to present the results

01/19/05© 2005 University of Wisconsin A Gentle Introduction Consider a pinhole camera imaging an infinite plane, with a single “point” light source Difficult concept #1: The arrows could go either way –We can consider how much of the light’s power hits a pixel, or how much of the pixel’s “importance” hits the light

01/19/05© 2005 University of Wisconsin A Single Pixel Assume we want the pixel to contain the total amount of light arriving at it Pixel Piece of surface that projects to pixel, A The integral over all points x  A that are seen by the pixel, summing the power leaving that point toward the eye x e

01/19/05© 2005 University of Wisconsin Diffuse Reflectance Assume the plane is perfectly diffuse –Some proportion of all the light arriving is evenly reflected in all directions Assume total amount of light arriving at a point x is Ir(x) Power out in any single direction is then  Ir(x)/2  –All possible directions “sum” to 2 , so each direction gets 1/2  of total incoming light, of which  is reflected

01/19/05© 2005 University of Wisconsin Lights The light is a “point” source, so light arrives at any point x from a single direction –Note that we need Ir(x)dA, the amount arriving per unit surface area The light emits in all directions, so amount in any one direction is E/4  How many “directions” does the area dA catch? What does it depend on?

01/19/05© 2005 University of Wisconsin Lights The amount of light caught by a surface depends on its area, distance from the light and angle to the light –The single quantity that accounts for distance and area is “solid angle”, of which more later xx

01/19/05© 2005 University of Wisconsin An Equation to Solve To decide how bright the pixel is, just evaluate: How do we solve integrals like this? Analytically: look up the solution in a book of integrals –Most rendering integrals cannot be solved analytically –No “closed form” solution Monte-Carlo estimation –Obtain samples of the integral’s value and use statistics

01/19/05© 2005 University of Wisconsin Monte Carlo Estimation 1 sample: evaluate the point seen through the center of the pixel, multiply by pixel area Multiple samples: Average over all results

01/19/05© 2005 University of Wisconsin From the past… How does this relate to the standard OpenGL model for diffuse reflectance?

01/19/05© 2005 University of Wisconsin Next time Raytracing