CS 779: RenderingTodayWhat’s It AboutWho’s it forHow it will be runThe grades will be based on…BooksPapersSoftwareTAPhysically-Based RenderingA Gentle IntroductionA Single PixelDiffuse ReflectanceLightsSlide 16An Equation to SolveMonte Carlo EstimationFrom the past…Next time01/19/05 © 2005 University of WisconsinCS 779: RenderingProf Stephen ChenneySpring 2005http://www.cs.wisc.edu/~cs779-101/19/05 © 2005 University of WisconsinToday•Course overview and information•Introduction to Physically-Based Rendering01/19/05 © 2005 University of WisconsinWhat’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•Proxies01/19/05 © 2005 University of WisconsinWho’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 pictures01/19/05 © 2005 University of WisconsinHow 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-loaded01/19/05 © 2005 University of WisconsinThe grades will be based on…•Programming and reading assignments•In–class presentations•A project01/19/05 © 2005 University of WisconsinBooks•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 reserve01/19/05 © 2005 University of WisconsinPapers•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–Citeseer01/19/05 © 2005 University of WisconsinSoftware•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 WisconsinTA•Shaohua Fan is your source for help with the software–An expert on Monte-Carlo rendering algorithms–He has used PBRT extensively•Email [email protected] for all questions01/19/05 © 2005 University of WisconsinPhysically-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 results01/19/05 © 2005 University of WisconsinA 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 light01/19/05 © 2005 University of WisconsinA Single Pixel•Assume we want the pixel to contain the total amount of light arriving at itPixelPiece of surface that projects to pixel, A AedALI exThe integral over all points xA that are seen by the pixel, summing the power leaving that point toward the eyexe01/19/05 © 2005 University of WisconsinDiffuse 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 AdAIrI x201/19/05 © 2005 University of WisconsinLights•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 WisconsinLights•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 AdArEIdArEdAIrxxxcos18cos4222x01/19/05 © 2005 University of WisconsinAn 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 AdArEIxcos182201/19/05 © 2005 University of WisconsinMonte Carlo Estimation•1 sample: evaluate the point seen through the center of the pixel, multiply by pixel area•Multiple samples: Average over all resultsccpixelrEAIxxcos)(1822NiipixelirENAI122cos)(18xx01/19/05 © 2005 University of