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3D Game Engine Design A Practical Approach to Real-Time Computer Graphics Second Edition David H. Eberly Geometric Tools, Inc. AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Morgan Kaufmann is an imprint of Elsevier

Senior Editor Tim Cox Publishing Services Manager George Morrison Senior Production Editor Brandy Lilly Project Management Elisabeth Beller Cover Design Chen Design Associates, San Francisco Text Design Rebecca Evans Composition Windfall Software, using ZzTEX Technical Illustration Dartmouth Publishing Copyeditor Yonie Overton Proofreader Indexer Interior and Cover Printer Hing Yip Printers, Ltd. Jennifer McClain Steve Rath Morgan Kaufmann Publishers is an imprint of Elsevier. 500 Sansome Street, Suite 400, San Francisco, CA 94111 This book is printed on acid-free paper. © 2007 by Elsevier Inc. All rights reserved. Designations used by companies to distinguish their products are often claimed as trademarks or registered trademarks. In all instances in which Morgan Kaufmann Publishers is aware of a claim, the product names appear in initial capital or all capital letters. Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration. No part of this publication may be reproduced, stored in a retrieval system, or trans- mitted in any form or by any means—electronic, mechanical, photocopying, scan- ning, or otherwise—without prior written permission of the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights De- partment in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail: permissions@elsevier.com. You may also complete your request online via the Elsevier homepage (http://elsevier.com), by selecting “Support & Contact” then “Copyright and Permission” and then “Obtaining Permissions.” Library of Congress Cataloging-in-Publication Data: Application submitted ISBN 13: 978-0-12-229063-3 ISBN 10: 0-12-229063-1 For information on all Morgan Kaufmann publications, visit our Web site at www.mkp.com or www.books.elsevier.com. Printed in the United States of America 10 09 08 07 06 5 4 3 2 1

Trademarks The following trademarks, mentioned in this book and the accompanying CD-ROM, are the property of the following organizations: AltiVec is a trademark of Freescale Semiconductor. DirectX, Direct3D, Visual C++, Windows, Xbox, and Xbox 360 are trademarks of Microsoft Corporation. GameCube is a trademark of Nintendo. GeForce, Riva TNT, and the Cg Language are trademarks of NVIDIA Corpora- tion. Java 3D is a trademark of Sun Microsystems. Macintosh is a trademark of Apple Corporation. Morrowind and The Elder Scrolls are trademarks of Bethesda Softworks, LLC. NetImmerse and Gamebryo are trademarks of Emergent Game Technologies. OpenGL is a trademark of Silicon Graphics, Inc. Pentium and Streaming SIMD Extensions (SSE) are trademarks of Intel Corpo- ration. PhysX is a trademark of Ageia Technologies, Inc. Playstation 2 and Playstation 3 are trademarks of Sony Corporation. PowerPC is a trademark of IBM. Prince of Persia 3D is a trademark of Brøderbund Software, Inc. 3DNow! is a trademark of Advanced Micro Devices. 3D Studio Max is a trademark of Autodesk, Inc. v

About the Author Dave Eberly is the president of Geometric Tools, Inc. (www.geometrictools.com), a company that specializes in software development for computer graphics, image analysis, and numerical methods. Previously, he was the director of engineering at Numerical Design Ltd. (NDL), the company responsible for the real-time 3D game engine, NetImmerse. He also worked for NDL on Gamebryo, which was the next- generation engine after NetImmerse. His background includes a BA degree in math- ematics from Bloomsburg University, MS and PhD degrees in mathematics from the University of Colorado at Boulder, and MS and PhD degrees in computer science from the University of North Carolina at Chapel Hill. He is the author of Game Physics (2004) and 3D Game Engine Architecture (2005) and coauthor with Philip Schneider of Geometric Tools for Computer Graphics (2003), all published by Morgan Kaufmann. As a mathematician, Dave did research in the mathematics of combus- tion, signal and image processing, and length-biased distributions in statistics. He was an associate professor at the University of Texas at San Antonio with an adjunct appointment in radiology at the U.T. Health Science Center at San Antonio. In 1991, he gave up his tenured position to retrain in computer science at the University of North Carolina. After graduating in 1994, he remained for one year as a research associate professor in computer science with a joint appointment in the Depart- ment of Neurosurgery, working in medical image analysis. His next stop was the SAS Institute, working for a year on SAS/Insight, a statistical graphics package. Finally, deciding that computer graphics and geometry were his real calling, Dave went to work for NDL (which is now Emergent Game Technologies), then to Magic Software, Inc., which later became Geometric Tools, Inc. Dave’s participation in the newsgroup comp.graphics.algorithms and his desire to make 3D graphics technology available to all are what has led to the creation of his company’s Web site and his books. vi

CONTENTS CONTENTS CONTENTS CONTENTS .............................................................. Preface ..............................................................xxixxixxixxi Preface .............................................................. Preface.............................................................. Preface Introduction 1111 Introduction ......................................................1 Introduction ......................................................1 Introduction......................................................1 ......................................................1 o o o 1.1 The Evolution of Graphics Hardware and Games 1.2 The Evolution of This Book and Its Software 1.3 A Summary of the Chapters Graphics 2222 TheTheTheThe Graphics Graphics Graphics System SystemSystemSystem.......................................7 .......................................7 .......................................7 .......................................7 o 2.1 The Foundation � � � 2.1.1 Coordinate Systems 2.1.2 Handedness and Cross Products 2.1.3 Points and Vectors o 2.2 Transformations � � 2.2.1 Linear Transformations 2.2.2 Affine Transformations vii

� � � 2.2.3 Projective Transformations 2.2.4 Properties of Perspective Projection 2.2.5 Homogeneous Points and Matrices o 2.3 Cameras � � � � � � � 2.3.1 The Perspective Camera Model 2.3.2 Model or Object Space 2.3.3 World Space 2.3.4 View, Camera, or Eye Space 2.3.5 Clip, Projection, or Homogeneous Space 2.3.6 Window Space 2.3.7 Putting Them All Together o 2.4 Culling and Clipping � � � 2.4.1 Object Culling 2.4.2 Back Face Culling 2.4.3 Clipping to the View Frustum o 2.5 Rasterizing � � � � 2.5.1 Line Segments 2.5.2 Circles 2.5.3 Ellipses 2.5.4 Triangles � 2.6 Vertex Attributes 2.6.1 Colors 2.6.2 Lighting and Materials 2.6.3 Textures � � o viii

� � � � 2.6.4 Transparency and Opacity 2.6.5 Fog 2.6.6 And Many More 2.6.7 Rasterizing Attributes o 2.7 Issues of Software, Hardware, and APIs � � 2.7.1 A General Discussion 2.7.2 Portability versus Performance o 2.8 API Conventions � � � � � � � 2.8.1 Matrix Representation and Storage 2.8.2 Matrix Composition 2.8.3 View Matrices 2.8.4 Projection Matrices 2.8.5 Window Handedness 2.8.6 Rotations 2.8.7 Fast Computations using the Graphics API Renderers 3333 Renderers ......................................................147 Renderers ......................................................147 Renderers......................................................147 ......................................................147 o o o o o 3.1 Software Rendering 3.2 Hardware Rendering 3.3 The Fixed-Function Pipeline 3.4 Vertex and Pixel Shaders 3.5 An Abstract Rendering API ix

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