Foundations of Game Engine Development Volume 1 Mathematics.pdf-资料库

15060822-6342-48b3-a796-96a6f0b379c8.pdf-第1页.png

第1页 / 共194页

15060822-6342-48b3-a796-96a6f0b379c8.pdf-第2页.png

第2页 / 共194页

15060822-6342-48b3-a796-96a6f0b379c8.pdf-第3页.png

第3页 / 共194页

15060822-6342-48b3-a796-96a6f0b379c8.pdf-第4页.png

第4页 / 共194页

15060822-6342-48b3-a796-96a6f0b379c8.pdf-第5页.png

第5页 / 共194页

15060822-6342-48b3-a796-96a6f0b379c8.pdf-第6页.png

第6页 / 共194页

15060822-6342-48b3-a796-96a6f0b379c8.pdf-第7页.png

第7页 / 共194页

15060822-6342-48b3-a796-96a6f0b379c8.pdf-第8页.png

第8页 / 共194页

Foundations of Gatne Engine Developtnent VüLUME 1 MATHEMATICS by Eric Lengyel Terathon Software LLC Lincoln, California

Foundations Volume 1: Mathematics ofGame Engine Development ISBN-13: 978-0-9858117-4-7 Copyright © 2016, by Eric Lengyel reserved. All rights retrieval information mechanical, including the prior permission transmitted, scanning, owner. of the copyright in an stored No part ofthis publication may be reproduced, or or utilized in any form, electronic system, photocopying, digitizing, or recording, without First printing Published www.terathon.com by Terathon Software LLC Series website: foundationsofgameenginedev.com About the cover: developed by the author using the Tombstone Engine. The cover image is a scene from a garue entitled The 31 st,

Preface Chapter 1 Vectors and Matrices 1.1 Vector Fundamentals 1.2 Basic Vector Operations 1.2.1 Magnitude and Scalar Multiplication 1.2.2 Addition and Subtraction 1.3 Matrix Fundamentals 1.4 Basic Matrix Operations 1.4.1 Addition, Subtraction, and Scalar Multiplication 1.4.2 Matrix Multiplication 1.5 Vector Multiplication l. 5 .1 Dot Prod uct 1.5.2 Cross Product 1.5.3 Scalar Triple Product 1.6 Vector Projection 1.7 Matrix Inversion Matrices l. 7 .1 Identity 1.7.2 Determinants 1. 7 .3 Elementaiy 1. 7.4 Inverse l. 7 .5 In verses Matrices Calculation of Small Matrices Exercises for Chapter 1 ix 1 1 3 5 8 11 16 16 16 20 20 24 30 31 36 36 37 42 45 46 51 V

Contents Chapter 2 Transforms 2.1 Coordinate Spaces 2.1.1 Transformation 2.1.2 Orthogonal 2.1.3 Transform n Transforms Compositio Matrices 2.2 Rotations About a Coordinate Axis About an Arbitrary Axis 2.2.1 Rotation 2.2.2 Rotation 2.3 Reflections 2.4 Scales 2.5 Skews 2.6 Homogeneous 2. 7 Quaternions Coordinates 2. 7 .1 Quaternion 2.7.2 Rotations Fundamentals With Quaternions Exercises for Chapter 2 Chapter 3 Geometry 3.1 Triangle 3.2 Normal Vectors Meshes 3.2.1 CalculatingNormal 3.2.2 Transforming Normal Vectors Vectors 3.3 Lines and Rays 3 .3 .1 Parametric Lines 3.3.2 Distance 3.3.3 Distance Between a Point anda Line Two Lines Between 3.4 Planes Planes Between 3.4.1 Implicit 3.4.2 Distance 3.4.3 Reflection 3.4.4 Intersection Through a Plane a Point anda Plane of a Line anda Plane 3.4.5 Intersection 3.4.6 Intersection of Three Planes of Two Planes 3.4.7 Transforming Planes vi 55 55 56 57 58 59 59 62 65 69 71 74 82 82 87 95 97 97 99 99 102 107 107 108 110 112 113 115 117 119 120 122 124

Contents 3.5 Plücker Coordinates Lines 3.5.1 Implicit 3.5.2 Homogeneous Formulas Lines 3 .5 .3 Transforming Exercises for Chapter 3 Chapter 4 Advanced Algebra 4.1 Grassmann Algebra 4.1.1 Wedge Product 4.1.2 Bivectors 4.1.3 Trivectors 4.1.4 Algebraic 4.1.5 Complements 4.1.6 Antivectors 4.1.7 Antiwedge Product Structure 4.2 Projective Geometry 4.2.1 Lines 4.2.2 Planes 4.2.3 Join and Meet 4.2.4 Line Crossing 4.2.5 Plane Distance 4.2.6 Summary and lmplementation 4.3 Matrix 4.4 Geometric Inverses Algebra 4.4.1 Geometric Product 4.4.2 Vector Division 4.4.3 Rotors 4.5 Conclusion Exercises for Chapter 4 Index vii 125 126 128 132 134 137 138 138 139 142 143 149 153 155 159 159 160 162 163 165 166 170 173 174 176 178 181 182 185

Preface of the same topics elsewhere in the literature. Along the way, we will with the usual approach This book provides a detailed game engine programmers. gebra (vectors and matrices), common to many other textbooks iarity expositions make several attempts and more correct quarter concepts gebra. intuition and provide else. anywhere earlier of these branches of the book endeavors mathematical to foreshadow Knowledge discussed details introduction to the mathematics cover the topics used by modero The first three chapters of linear al transforms, and geometry in a conventional on the subject. This is done to provide so that it's easy to make connections to similar manner a famil the discussion of a manifestly more elegant model that appears to provide in the fourth chapter. a deeper understanding of many of the Grassmann al algebra also allows and geometric us to convey of mathematics The last by introducing in the first three chapters that are difficult to find One of the goals of this book is to give practical advice. This is short code listings appearing throughout the book engineering is implemented inside real-world we've discussed pages with code listings or functions referenced in various places re have in that are illustratively been left out. This happens only when the form and behavior of the that de Chapter code listings and operations corresponding vector, to a three-dimensional For example, 1 includes sorne data structures through many how the mathematics To avoid filling accomplished showing game engines. dundant, tentionally missing fine a data structure but it doesn't used by other code listings cal. The complete code is obvious. show similar library code for a four-dimensional later in the book, because vector, it would be largely even though it's identi of code is available on the website cited below. ix

Preface X We assurne that the reader has a so lid understanding of basic trigonornetry, a appears A bit of calculus is not essential of the C++ language, and sorne farniliarity nurnbers. working knowledge floating-point this isolated usage rnathernatics sessing first two chapters. ter 3 before proceeding ity with the notation in Chapter 3, but a full grasp of to the rest of the book. Otherwise, all of the pos readers rnay wish to skip rnuch of the take a look at Chap because Chapter 4 assurnes discussed of linear algebra that ali readers in Chapter a thorough knowledge we recornrnend However, to the final chapter details and conceptual that we cover is built frorn the ground up. Advanced 3. a familiar with standard blue outline. to rnake it easier Irnportant equations and key results appearing This is intended both to highlight in the text are boxed with a and the rnost valuable information Each chapter to find when using the book as a reference. concludes with a set of exercises, and rnany of those exercises ask for a short proof of sorne kind. The exercises tional a little trickier. but interesting provided educational value, To ensure rnathernatical cited below. to provide addi others and while rnany of thern have easy solutions, are that getting stuck doesn of a srnall revelation, are designed to all of the exercises the answers 't deprive any reader are on the website This book is the first volurne in a series that covers a wide range of topics to garne engine developrnent. related Game Engine Development series can be found at the following of address: The official website for the Foundations foundationsofgarneenginedev .corn contains This website announcernents, errata, information code listings, and answers to exercises. about all of the books in the series, including

Preface xi Acknowledgements volume was made possible owes a debt of gratitude The first to the hundreds the author the Foundations of Game Engine Development was written. Special thanks extra support by making contributions go to the following by a successful of contributors series even a single people in particular before that exceed the cost of a copy of the book. crowdfunding campaign, who supported and for showing word Norbert Nopper Patsiouras Petryk Andres Hemandez Darren Ranalli Bergmeier Hauke Hildebrandt Steen Rasmussen Rodolphe Martin Hurton Yuri Kunde Schlesner Frani;ois Martijn Jaccard Bill Seitzinger Joosten Michael D. Shah Carre Castano Aguado Tonci Jukic Abreu Trevor Heldna Mike Ramsey Green Guillemot Nikolaos Gunnarsson Georges Archard Aaron Gutierrez Ian Prest Beckebans Timothy Alexandre Luis Alvarado Nicolas Kelvin Arcelay Mattias Daniel Robert Andrew Bell Andreas Marco Bouterse James Huntsman Guameri Lance Bums Daniel Carey Bertrand Ignacio S0ren Christensen TimKane Daniel Vicente Courtois Paul Demeulenaere Christopher Kingsley Frani;ois Jean-Francois AshrafEassa Jean-Baptiste Wolfgang Fredrik Brandon Jean-Frani;ois Nicholas Francis Marcus Fritzsch Javier Taylor Gerpheide Michael Nicholas Gildea Dae Myung Collin Cuellar HyukKim Damien Y oungsik Kim Engel William Leu Joel de Vahl Devic Kieron Lanning Justin Brian Sharp Sean Slavik Engkvist Shaochun Fogerty Yushuo Liu Dube Kwon-il Lee Lars Viklund Ken Voskuil Tim Stewart Brook Miles Ian Whyte My les Lin Soufi Souaiaia Tiago Sousa Aaron Spehr Squirek Moya Pérez Graham Wihlidal Soufiane Khiat Daniel Smith Lepesme Runar Thorstensen F Fortin YunlongMa Shawn Walker-Salas

资料库

Foundations of Game Engine Development Volume 1 Mathematics.pdf

相关推荐

游戏开发

热门标签

最新资料