Preface

“Things have not changed that much in the past eight years,” was our thought entering into this fourth edition. “How hard could it be to update the book?” A year and a half later, and with three more experts recruited, our task is done. We could probably spend another year editing and elaborating, at which time there would be easily a hundred more articles and presentations to fold in. As a data point, we made a Google Doc of references that is more than 170 pages long, with about 20 references and related notes on each page. Some references we cite could and do each take up a full section in some other book. A few of our chapters, such as that on shadows, have entire books dedicated to their subjects. While creating more work for us, this wealth of information is good news for practitioners. We will often point to these primary sources, as they offer much more detail than appropriate here.

This book is about algorithms that create synthetic images fast enough that the viewer can interact with a virtual environment. We have focused on three-dimensional rendering and, to a limited extent, on the mechanics of user interaction. Modeling, animation, and many other areas are important to the process of making a real-time application, but these topics are beyond the scope of this book.

We expect you to have some basic understanding of computer graphics before reading this book, as well as knowledge of computer science and programming. We also focus on algorithms, not APIs. Many texts are available on these other sub jects. If some section does lose you, skim on through or look at the references. We believe that the most valuable service we can provide you is a realization of what you yet do not know about—a basic kernel of an idea, a sense of what others have discovered about it, and ways to learn more, if you wish.

We make a point of referencing relevant material as possible, as well as providing a summary of further reading and resources at the end of most chapters. In prior editions we cited nearly everything we felt had relevant information. Here we are more a guidebook than an encyclopedia, as the field has far outgrown exhaustive (and exhausting) lists of all possible variations of a given technique. We believe you are better served by describing only a few representative schemes of many, by replacing original sources with newer, broader overviews, and by relying on you, the reader, to pursue more information from the references cited.

Most of these sources are but a mouse click away; see realtimerendering.com for the list of links to references in the bibliography. Even if you have only a passing interest in a topic, consider taking a little time to look at the related references, if for nothing else than to see some of the fantastic images presented. Our website also contains links to resources, tutorials, demonstration programs, code samples, software libraries, book corrections, and more.

Our true goal and guiding light while writing this book was simple. We wanted to write a book that we wished we had owned when we had started out, a book that both was unified yet also included details and references not found in introductory texts. We hope that you will find this book, our view of the world, of use in your travels.

Acknowledgments for the Fourth Edition

We are not experts in everything, by any stretch of the imagination, nor perfect writers. Many, many people’s responses and reviews improved this edition immeasurably, saving us from our own ignorance or inattention. As but one example, when we asked around for advice on what to cover in the area of virtual reality, Johannes Van Waveren (who did not know any of us) instantly responded with a wonderfully detailed outline of topics, which formed the basis for that chapter. These kind acts by computer graphics professionals were some of the great pleasures in writing this book. One person is of particular note: Patrick Cozzi did a yeoman’s job, reviewing every chapter in the book. We are grateful to the many people who helped us along the way with this edition. We could write a sentence or three about everyone who helped us along the way, but this would push us further past our book-breaking page limit.

To all the rest, in our hearts we give our appreciation and thanks to you: Sebastian Aaltonen, Johan Andersson, Magnus Andersson, Ulf Assarsson, Dan Baker, Chad Barb, Rasmus Barringer, Michal Bastien, Louis Bavoil, Michael Beale, Adrian Bentley, Ashwin Bhat, Antoine Bouthors, Wade Brainerd, Waylon Brinck, Ryan Brucks, Eric Bruneton, Valentin de Bruyn, Ben Burbank, Brent Burley, Ignacio Castano, Cem Cebenoyan, Mark Cerny, Matthaeus Chajdas, Danny Chan, Rob Cook, JeanLuc Corenthin, Adrian Courreges, Cyril Crassin, Zhihao Cui, Kuba Cupisz, Robert Cupisz, Michal Drobot, Wolfgang Engel, Eugene d’Eon, Matej Drame, Michal Drobot, Alex Evans, Cass Everitt, Kayvon Fatahalian, Adam Finkelstein, Kurt Fleischer, Tim Foley, Tom Forsyth, Guillaume Francois, Daniel Girardeau-Montaut, Olga Gocmen, Marcin Gollent, Ben Golus, Carlos Gonzalez-Ochoa, Judah Graham, Simon Green, Dirk Gregorius, Larry Gritz, Andrew Hamilton, Earl Hammon, Jr., Jon Harada, Jon Hasselgren, Aaron Hertzmann, Stephen Hill, Rama Hoetzlein, Nicolas Holzschuch, Liwen Hu, John “Spike” Hughes, Ben Humberston, Warren Hunt, Andrew Hurley, John Hutchinson, Milan Ikits, Jon Jansen, Jorge Jimenez, Anton Kaplanyan, Gokhan Karadayi, Brian Karis, Nicolas Kasyan, Alexander Keller, Brano Kemen, Emmett Kilgariff, Byumjin Kim, Chris King, Joe Michael Kniss, Manuel Kraemer, Anders Wang Kristensen, Christopher Kulla, Edan Kwan, Chris Landreth, David Larsson, Andrew Lauritzen, Aaron Lefohn, Eric Lengyel, David Li, Ulrik Lindahl, Edward Liu, Ignacio Llamas, Dulce Isis Segarra Lopez, David Luebke, Patrick Lundell, Miles Macklin, Dzmitry Malyshau, Sam Martin, Morgan McGuire, Brian McIntyre, James McLaren, Mariano Merchante, Arne Meyer, Sergiy Migdalskiy, Kenny Mitchell, Gregory Mitrano, Adam Moravanszky, Jacob Munkberg, Kensaku Nakata, Srinivasa G. Narasimhan, David Neubelt, Fabrice Neyret, Jane Ng, Kasper Hpy Nielsen, Matthias Niefiner, Jim Nilsson, Reza Nourai, Chris Oat, Ola Olsson, Rafael Orozco, Bryan Pardilla, Steve Parker, Ankit Patel, Jasmin Patry, Jan Pechenik, Emil Persson, Marc Petit, Matt Pettineo, Agnieszka Piechnik, Jerome Platteaux, Aras PranckeviCius, Elinor Quittner, Silvia Rasheva, Nathaniel Reed, Philip Rideout, Jon Rocatis, Robert Runesson, Marco Salvi, Nicolas Savva, Andrew Schneider, Michael Schneider, Markus Schuetz, Jeremy Selan, Tarek Sherif, Peter Shirley, Peter Sikachev, Peter-Pike Sloan, Ashley Vaughan Smith, Rys Sommefeldt, Edvard S0rgard, Tiago Sousa, Tomasz Stachowiak, Nick Stam, Lee Stemkoski, Jonathan Stone, Kier Storey, Jacob Strom, Filip Strugar, Pierre Terdiman, Aaron Thibault, Nicolas Thibieroz, Robert Toth, Thatcher Ulrich, Mauricio Vives, Alex Vlachos, Evan Wallace, Ian Webster, Nick Whiting, Brandon Whitley, Mattias Widmark, Graham Wihlidal, Michael Wimmer, Daniel Wright, Bart Wronski, Chris Wyman, Ke Xu, Cem Yuksel, and Egor Yusov. We thank you for your time and effort, selflessly offered and gratefully received.

Finally, we want to thank the people at Taylor & Francis for all their efforts, in particular Rick Adams, for getting us going and guiding us along the way, Jessica Vega and Michele Dimont, for their efficient editorial work, and Charlotte Byrnes, for her superb copyediting.

Tomas Akenine-Möller

Eric Haines

Naty Hoffman

Angelo Pesce

Michal Iwanicki

Sébastien Hillaire

February 2018

Acknowledgments for the Third Edition

Special thanks go out to a number of people who went out of their way to provide us with help. First, our graphics architecture case studies would not have been anywhere as good without the extensive and generous cooperation we received from the companies making the hardware. Many thanks to Edvard S0rgard, Borgar Ljosland, Dave Shreiner, and J0rn Nystad at ARM for providing details about their Mali 200 architecture. Thanks also to Michael Dougherty at Microsoft, who provided extremely valuable help with the Xbox 360 section. Masaaki Oka at Sony Computer Entertainment provided his own technical review of the PLAYSTATION^® 3 system case study, while also serving as the liaison with the Cell Broadband Engine^™ and RSX^® developers for their reviews.

In answering a seemingly endless stream of questions, fact-checking numerous passages, and providing many screenshots, Natalya Tatarchuk of ATI/AMD went well beyond the call of duty in helping us out. In addition to responding to our usual requests for information and clarification, Wolfgang Engel was extremely helpful in providing us with articles from the upcoming ShaderX ⁶ book and copies of the difficult-toobtain ShaderX ² books [427, 428], now available online for free. Ignacio Castano at NVIDIA provided us with valuable support and contacts, going so far as to rework a refractory demo so we could get just the right screenshot.

The chapter reviewers provided an invaluable service to us. They suggested numerous improvements and provided additional insights, helping us immeasurably. In alphabetical order they are: Michael Ashikhmin, Dan Baker, Willem de Boer, Ben Diamand, Ben Discoe, Amir Ebrahimi, Christer Ericson, Michael Gleicher, Manny Ko, Wallace Lages, Thomas Larsson, Gregory Massal, Ville Miettinen, Mike Ramsey, Scott Schaefer, Vincent Scheib, Peter Shirley, K.R. Subramanian, Mauricio Vives, and Hector Yee.

We also had a number of reviewers help us on specific sections. Our thanks go out to Matt Bronder, Christine DeNezza, Frank Fox, Jon Hasselgren, Pete Isensee, Andrew Lauritzen, Morgan McGuire, Jacob Munkberg, Manuel M. Oliveira, Aurelio Reis, Peter-Pike Sloan, Jim Tilander, and Scott Whitman.

We particularly thank Rex Crowle, Kareem Ettouney, and Francis Pang from Media Molecule for their considerable help in providing fantastic imagery and layout concepts for the cover design.

Many people helped us out in other ways, such as answering questions and providing screenshots. Many gave significant amounts of time and effort, for which we thank you. Listed alphabetically: Paulo Abreu, Timo Aila, Johan Andersson, Andreas B^rentzen, Louis Bavoil, Jim Blinn, Jaime Borasi, Per Christensen, Patrick Conran, Rob Cook, Erwin Coumans, Leo Cubbin, Richard Daniels, Mark DeLoura, Tony DeRose, Andreas Dietrich, Michael Dougherty, Bryan Dudash, Alex Evans, Cass Everitt, Randy Fernando, Jim Ferwerda, Chris Ford, Tom Forsyth, Sam Glassenberg, Robin Green, Ned Greene, Larry Gritz, Joakim Grundwall, Mark Harris, Ted Himlan, Jack Hoxley, John “Spike” Hughes, Ladislav Kavan, Alicia Kim, Gary King, Chris Lambert, Jeff Lander, Daniel Leaver, Eric Lengyel, Jennifer Liu, Brandon Lloyd, Charles Loop, David Luebke, Jonathan Maim, Jason Mitchell, Martin Mittring, Nathan Monteleone, Gabe Newell, Hubert Nguyen, Petri Nordlund, Mike Pan, Ivan Pedersen, Matt Pharr, Fabio Policarpo, Aras Pranckevicius, Siobhan Reddy, Dirk Reiners, Christof Rezk-Salama, Eric Risser, Marcus Roth, Holly Rushmeier, Elan Ruskin, Marco Salvi, Daniel Scherzer, Kyle Shubel, Philipp Slusallek, Torbjiörn Soiderman, Tim Sweeney, Ben Trumbore, Michal Valient, Mark Valledor, Carsten Wenzel, Steve Westin, Chris Wyman, Cem Yuksel, Billy Zelsnack, Fan Zhang, and Renaldas Zioma.

We also thank many others who responded to our queries on public forums such as GD Algorithms. Readers who took the time to send us corrections have also been a great help. It is this supportive attitude that is one of the pleasures of working in this field.

As we have come to expect, the cheerful competence of the people at A K Peters made the publishing part of the process much easier. For this wonderful support, we thank you all.

On a personal note, Tomas would like to thank his son Felix and daughter Elina for making him understand (again) just how fun it can be to play computer games (on the Wii), instead of just looking at the graphics, and needless to say, his beautiful wife Eva…

Eric would also like to thank his sons Ryan and Evan for their tireless efforts in finding cool game demos and screenshots, and his wife Cathy for helping him survive it all.

Naty would like to thank his daughter Karen and son Daniel for their forbearance when writing took precedence over piggyback rides, and his wife Dorit for her constant encouragement and support.

Tomas Akenine-Möller

Eric Haines Naty Hoffman

March 2008

Acknowledgments for the Second Edition

One of the most agreeable aspects of writing this second edition has been working with people and receiving their help. Despite their own pressing deadlines and concerns, many people gave us significant amounts of their time to improve this book. We would particularly like to thank the major reviewers. They are, listed alphabetically: Michael Abrash, Ian Ashdown, Ulf Assarsson, Chris Brennan, Sebastien Domine, David Eberly, Cass Everitt, Tommy Fortes, Evan Hart, Greg James, Jan Kautz, Alexander Keller, Mark Kilgard, Adam Lake, Paul Lalonde, Thomas Larsson, Dean Macri, Carl Marshall, Jason L. Mitchell, Kasper Hpy Nielsen, Jon Paul Schelter, Jacob Stroom, Nick Triantos, Joe Warren, Michael Wimmer, and Peter Wonka. Of these, we wish to single out Cass Everitt at NVIDIA and Jason L. Mitchell at ATI Technologies for spending large amounts of time and effort in getting us the resources we needed. Our thanks also go out to Wolfgang Engel for freely sharing the contents of his upcoming book, ShaderX [426], so that we could make this edition as current as possible.

From discussing their work with us, to providing images or other resources, to writing reviews of sections of the book, many others helped in creating this edition. They all have our gratitude. These people include: Jason Ang, Haim Barad, Jules Bloomenthal, Jonathan Blow, Chas. Boyd, John Brooks, Cem Cebenoyan, Per Christensen, Hamilton Chu, Michael Cohen, Daniel Cohen-Or, Matt Craighead, Paul Debevec, Joe Demers, Walt Donovan, Howard Dortch, Mark Duchaineau, Phil Dutre, Dave Eberle, Gerald Farin, Simon Fenney, Randy Fernando, Jim Ferwerda, Nickson Fong, Tom Forsyth, Piero Foscari, Laura Fryer, Markus Giegl, Peter Glaskowsky, Andrew Glassner, Amy Gooch, Bruce Gooch, Simon Green, Ned Greene, Larry Gritz, Joakim Grundwall, Juan Guardado, Pat Hanrahan, Mark Harris, Michael Herf, Carsten Hess, Rich Hilmer, Kenneth Hoff III, Naty Hoffman, Nick Holliman, Hugues Hoppe, Heather Horne, Tom Hubina, Richard Huddy, Adam James, Kaveh Kardan, Paul Keller, David Kirk, Alex Klimovitski, Jason Knipe, Jeff Lander, Marc Levoy, J.P. Lewis, Ming Lin, Adrian Lopez, Michael McCool, Doug McNabb, Stan Melax, Ville Miettinen, Kenny Mitchell, Steve Morein, Henry Moreton, Jerris Mungai, Jim Napier, George Ngo, Hubert Nguyen, Tito Pagan, Jorg Peters, Tom Porter, Emil Praun, Kekoa Proudfoot, Bernd Raabe, Ravi Ramamoorthi, Ashutosh Rege, Szymon Rusinkiewicz, Chris Seitz, Carlo Sequin, Jonathan Shade, Brian Smits, John Spitzer, Wolfgang Strafier, Wolfgang StUrzlinger, Philip Taylor, Pierre Terdiman, Nicolas Thibieroz, Jack Tumblin, Fredrik Ulfves, Thatcher Ulrich, Steve Upstill, Alex Vlachos, Ingo Wald, Ben Watson, Steve Westin, Dan Wexler, Matthias Wloka, Peter Woytiuk, David Wu, Garrett Young, Borut Zalik, Harold Zatz, Hansong Zhang, and Denis Zorin. We also wish to thank the journal ACM Transactions on Graphics for providing a mirror website for this book.

Alice and Klaus Peters, our production manager Ariel Jaffee, our editor Heather Holcombe, our copyeditor Michelle M. Richards, and the rest of the staff at A K Peters have done a wonderful job making this book the best possible. Our thanks to all of you.

Finally, and most importantly, our deepest thanks go to our families for giving us the huge amounts of quiet time we have needed to complete this edition. Honestly, we never thought it would take this long!

Tomas Akenine-Möller

Eric Haines

May 2002

Acknowledgments for the First Edition

Many people helped in making this book. Some of the greatest contributions were made by those who reviewed parts of it. The reviewers willingly gave the benefit of their expertise, helping to significantly improve both content and style. We wish to thank (in alphabetical order) Thomas Barregren, Michael Cohen, Walt Donovan, Angus Dorbie, Michael Garland, Stefan Gottschalk, Ned Greene, Ming C. Lin, Jason L. Mitchell, Liang Peng, Keith Rule, Ken Shoemake, John Stone, Phil Taylor, Ben Trumbore, Jorrit Tyberghein, and Nick Wilt. We cannot thank you enough.

Many other people contributed their time and labor to this project. Some let us use images, others provided models, still others pointed out important resources or connected us with people who could help. In addition to the people listed above, we wish to acknowledge the help of Tony Barkans, Daniel Baum, Nelson Beebe, Curtis Beeson, Tor Berg, David Blythe, Chas. Boyd, Don Brittain, Ian Bullard, Javier Castellar, Satyan Coorg, Jason Della Rocca, Paul Diefenbach, Alyssa Donovan, Dave Eberly, Kells Elmquist, Stuart Feldman, Fred Fisher, Tom Forsyth, Marty Franz, Thomas Funkhouser, Andrew Glassner, Bruce Gooch, Larry Gritz, Robert Grzeszczuk, Paul Haeberli, Evan Hart, Paul Heckbert, Chris Hecker, Joachim Helenklaken, Hugues Hoppe, John Jack, Mark Kilgard, David Kirk, James Klosowski, Subodh Kumar, Andre LaMothe, Jeff Lander, Jens Larsson, Jed Lengyel, Fredrik Liliegren, David Luebke, Thomas Lundqvist, Tom McReynolds, Stan Melax, Don Mitchell, Andre Moller, Steve Molnar, Scott R. Nelson, Hubert Nguyen, Doug Rogers, Holly Rushmeier, Gernot Schaufler, Jonas Skeppstedt, Stephen Spencer, Per Stenstrom, Jacob Strom, Filippo Tampieri, Gary Tarolli, Ken Turkowski, Turner Whitted, Agata and Andrzej Wojaczek, Andrew Woo, Steve Worley, Brian Yen, Hans-Philip Zachau, Gabriel Zachmann, and Al Zimmerman. We also wish to thank the journal ACM Transactions on Graphics for providing a stable website for this book.

Alice and Klaus Peters and the staff at AK Peters, particularly Carolyn Artin and Sarah Gillis, have been instrumental in making this book a reality. To all of you, thanks.

Finally, our deepest thanks go to our families and friends for providing support throughout this incredible, sometimes grueling, often exhilarating process.

Tomas Möiler

Eric Haines

March 1999