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State of the Art in Monte Carlo Ray Tracing for Realistic Image Synthesis

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State of the Art in Monte Carlo Ray Tracing for Realistic Image Synthesis Siggraph 2001 Course 29 Monday, August 13, 2001 Organizer Henrik Wann Jensen Stanford University Lecturers James Arvo Caltech Marcos Fajardo ICT/USC Pat Hanrahan Stanford University Henrik Wann Jensen Stanford University Don Mitchell Matt Pharr Exluna Peter Shirley University of Utah Abstract This full day course will provide a detailed overview of state of the art in Monte Carlo ray tracing. Recent advances in algorithms and available compute power have made Monte Carlo ray tracing based methods widely used for simulating global illumination. This course will review the fundamentals of Monte Carlo methods, and provide a detailed description of the theory behind the latest tech- niques and algorithms used in realistic image synthesis. This includes path tracing, bidirectional path tracing, Metropolis light transport, scattering equations, irradi- ance caching and photon mapping. Lecturers Jim Arvo Computer Science 256-80 1200 E. California Blvd. California Institute of Technology Pasadena, CA91125 Phone: 626 395 6780 Fax: 626 792 4257 [email protected] http://www.cs.caltech.edu/ arvo James Arvo has been an Associate Professor of Computer Science at Caltech since 1995. From 1990 to 1995 he was a senior researcher in the Program of Computer Graphics at Cornell University. He received a B.S. in Mathematics from Michigan Technological University, an M.S. in Mathematics from Michigan State Univer- sity, and a Ph.D. in Computer Science from Yale University in 1995. His research interests include physically-based image synthesis, Monte Carlo methods, human- computer interaction, and symbolic computation. Dr. Arvo received a young in- vestigator award from the U.S. Army Research Office 1996, an Alfred P. Sloan Research Fellowship in 1997, and a National Science Foundation Career Award in 1999 for his work in image synthesis. Marcos Fajardo Institute for Creative Technologies University of Southern California 13274 Fiji Way Marina del Rey, CA 90292 Phone: 310 574 7810, ext 1810 Fax: 310 574 5725 [email protected] Marcos Fajardo is a Research Associate at the University of Southern California’s Institute for Creative Technologies, working with Dr. Paul Debevec on global il- lumination and inverse global illumination techniques in large scale environments. He studied Computer Science at the University of Malaga, Spain, and has been working on different commercial renderers over the past 5 years, as well as con- sulting with animation studios on practical global illumination issues. His latest rendering code is codenamed Arnold. Pat Hanrahan Gates Computer Science 370B Stanford University CA 94305-4070 Phone: 650 723 8530 Fax: 650 723 0033 [email protected] http://graphics.stanford.edu/ hanrahan Pat Hanrahan is the CANON USA Professor of Computer Science and Electri- cal Engineering at Stanford University where he teaches computer graphics. His current research involves visualization, image synthesis, and graphics systems and architectures. Before joining Stanford he was a faculty member at Princeton. He has also worked at Pixar where he developed developed volume rendering soft- ware and was the chief architect of the RenderMan(TM) Interface - a protocol that allows modeling programs to describe scenes to high quality rendering programs. Previous to Pixar he directed the 3D computer graphics group in the Computer Graphics Laboratory at New York Institute of Technology. Professor Hanrahan has received three university teaching awards. In 1993 he received an Academy Award for Science and Technology, the Spirit of America Creativity Award, the SIGGRAPH Computer Graphics Achievement Award, and he was recently elected to the National Academy of Engineering. Henrik Wann Jensen Gates Computer Science 362B Stanford University CA 94305-4070 Phone: 650 725 3696 Fax: 650 723 0033 [email protected] http://graphics.stanford.edu/ henrik Henrik Wann Jensen is a Research Associate at Stanford University where he is working with professor Pat Hanrahan in the Computer Graphics Group on realistic image synthesis, global illumination and new appearance models. He is the author of ”Realistic Image Synthesis using Photon Mapping”, AK Peters 2001. Prior to coming to Stanford in 1999, he was working in a postdoctoral position at MIT, and as a research scientist in industry where he added photon maps to a commercial renderer. He received his M.Sc. and Ph.D. in Computer Science from the Technical University of Denmark for developing the photon mapping method. Don Mitchell 2621 168th Ave. NE Bellevue, WA 98008 [email protected] Don Mitchell’s background is in Physics. He worked for Ed Stone at Caltech for several years, on heavy-nuclei cosmic radiation, but then dropped out to take a job working with computer researchers at Bell Telephone Laboratories in 1981. He did some research on distributed databases and deadlock detection before becoming interested in 3D image synthesis. Until 1993, he worked at AT&T, mostly on the numerical and signal processing issues in ray tracing. From 1991 to 1994, he became a graduate student at Princeton University, to work with Pat Hanrahan and David Dobkin. While at Princeton, he became interested in 3D game technology, MUDs, virtual worlds and the blossoming revolution of personal computers. And so in 1994, he joined the virtual worlds group at Microsoft Research. In October 2000, he retired, and is currently planning a start-up company with a few friends to further explore massively multi-user games and virtual worlds. Don Mitchell has published several SIGGRAPH papers on efficient sampling techniques. Matt Pharr Exluna 1900 Addison St, Suite 200 Berkeley CA 94704 [email protected] Matt Pharr is a co-founder of Exluna, Inc., where he has contributed substantially to the design and implementation of the Entropy rendering architecture. He is cur- rently working on interactive rendering technologies. He is expected to complete his Ph.D. in Computer Science at Stanford University in 2001. Matt has published three papers at SIGGRAPH over the past five years on the topics of light scatter- ing, Monte Carlo, and rendering of large scenes. He was a part-time member of Pixar’s Rendering R&D group from 1998-2000, contributing to development of PhotoRealistic RenderMan and next generation rendering architectures. He has a B.S degree in Computer Science from Yale University and an M.S. from Stanford. Peter Shirley Computer Science Department 50 Central Campus Drive University of Utah Salt Lake City, UT 84112 Phone: 801 585 1883 Fax: 801 581 5843 [email protected] http://www.cs.utah.edu/ shirley Peter Shirley is an Associate Professor in the School of Computing at the Univer- sity of Utah in Salt Lake City. His interests include computer graphics in general, with particular emphasis on rendering. He is the author or co-author of 50 techni- cal articles on topics including rendering, simulation, visualization, and algorithm analysis. He is the author of ”Realistic Ray Tracing” with AK Peters. Prior to join- ing University of Utah in 1996, he has worked at the Cornell program of Computer Graphics and the Indiana University Computer Science Department. He holds a B.A. in Physics from Reed College and a Ph.D. in Computer Science from the University of Illinois at Champaign-Urbana. Course Syllabus 8:30 Introduction and Welcome Henrik Wann Jensen 8:35 Fundamentals of Monte Carlo Integration Peter Shirley An overview of Monte Carlo integration techniques. Rejection methods Importance sampling Stratified sampling 9:15 Quasi-Monte Carlo Techniques Don Mitchell Hammersley points Arbitrary-edge discrepancy Applications of quasirandom techniques to distribution ray tracing Spectral sampling techniques 10:00 Break 10:15 Sampling Techniques James Arvo Sampling of special geometries and reflection models Russian roulette 11:00 Direct Illumination Peter Shirley Sampling of light sources Special types of light sources Efficient sampling of many light sources 11:30 Variance Reduction Techniques James Arvo Combined estimators Hybrid sampling methods. 12:00 Lunch 1:30 Solving the Rendering Equation Pat Hanrahan The path integral formulation Path tracing Adjoint techniques Bidirectional transport Bidirectional path tracing 2:30 Metropolis Sampling Matt Pharr One dimensional setting Motion blur Metropolis light tansport 3:00 Break 3:15 Scattering Equations Matt Pharr Sampling phase functions Sampling exponential distributions Reflection equations Adding equations 3:45 Monte Carlo Ray Tracing in Action Marcos Fajardo Example images and animations 4:05 Biased Techniques Henrik Wann Jensen Biased vs. consistent methods Filtering Techniques Irradiance Caching Photon Mapping 5:00 Conclusion and Questions Contents 1 Introduction 13 1.1 Purpose of this Course . 14 1.2 Prerequisites . 14 1.3 Acknowledgements . 14 2 Fundamentals of Monte Carlo Integration 15 2.1 Background and Terminology . 15 2.1.1 One-dimensional Continuous Probability Density Functions 15 2.1.2 One-dimensional Expected Value . 16 2.1.3 Multi-dimensional Random Variables . 17 2.1.4 Variance . 18 2.1.5 Estimated Means . 19 2.2 Monte Carlo Integration . 19 2.2.1 Quasi-Monte Carlo Integration . 21 2.2.2 Multidimensional Monte Carlo Integration . 22 2.3 Choosing Random Points . 23 2.3.1 Function inversion . 24 2.3.2 Rejection . 26 2.3.3 Metropolis . 27 2.4 Monte Carlo Simulation . 29 2.5 Density Estimation . 30 3 Direct Lighting via Monte Carlo Integration 31 3.1 Mathematical framework . 31 3.2 Sampling a spherical luminaire . 33 3.3 Non-diffuse Luminaries . 36 3.4 Direct Lighting from Many Luminaires . 37 9 3.4.1 Constant αi ......................... 38 3.4.2 Linear αi .......................... 39 4 Stratified Sampling of 2-Manifolds 41 4.1 Introduction . 41 4.2 A Recipe for Sampling Algorithms . 43 4.3 Analytic Area-Preserving Parametrizations . 48 4.3.1 Sampling Planar Triangles . 48 4.3.2 Sampling the Unit Disk . 49 4.3.3 Sampling the Unit Hemisphere . 50 4.3.4 Sampling a Phong Lobe .
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