Book Description
This completely updated second edition illustrates the mathematical concepts that a game programmer would need to develop a professional-quality 3D engine. Although the book is geared toward applications in game development, many of the topics appeal to general interests in 3D graphics. It starts at a fairly basic level in areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D game programming such as illumination and visibility determination. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure gaps in the theory. The book assumes a working knowledge of trigonometry and calculus, but also includes sections that review the important tools used from these disciplines, such as trigonometric identities, differential equations, and Taylor series.
Customer Reviews:
One of a kind.......2007-03-23
As a professional 3D graphics programmer, I can not stress enough the quality of this book. This book covers 3D math fundamentals, algorithms, and it is complete with easy to understand (!) proofs. The math is difficult because there is so many problems to be solved in 3D (and they draw from many different branches of mathematics), but it is written in such a clear way that every topic is made approachable. Unlike esoteric Ph. D papers, you aren't assumed to have any specific knowledge of math idioms or jargon. You simply need a decent grasp of college calculus and trigonometry to make the most of it. There are a few samples too to test your knowledge.
Expect to spend at least a solid year to really make the use of this book. Treat it as you would a two - three semester course in college. During this process, you'll find yourself occasionally wanting to get more practice and referring to a respective book on it.
If you could only own two books for 3D programming, buy this first and buy Ericson's book on collision detection next.
In summary, Eric Lengyel's attention to detail and mastery of 3D math / algorithms really shines and this book is an example of it.
Great book.......2007-03-08
This book is great for anyone interested in computer graphics. Even for people who do not have a lot of math/graphics experience, this book starts you off with the basics of vectors and matrices and has exercises/solutions for each chapter. It saves you the time of looking through your old linear algebra and differential equation math books and contains the must know information you will use as a graphics programmer.
Math majors rejoice.......2007-03-02
To be honest, while I find this book to be a decent reference, I find it to be pretty inaccessible in terms of sitting down and reading through it in an attempt to learn the concepts. As a non-math major (I'm actually an engineer and software developer) these math concepts are by no means beyond me. But rather than simply being presented with equation after equation, proof after proof, what I find a lot more valuable is more discussion on the usage of these equations. Specifically I'd like to see examples, diagrams, and code, and there is precious little of any of that in this book.
In other words, this book is very much like what you expect to find in a very dry upper devision college math text for the consumption of math majors who are used to such things. But for a non math major just trying to make use of these concepts in order to get the job done and make games? eh, not so much.
Still, I do think this book is useful as a reference when I want to look up an equation as there are a ton of them crammed into this book, but for me, I just don't find this book to be very good as a learning tool.
Great book on the math needed for 3D games and graphics.......2006-11-27
This book illustrates the mathematics that a game programmer would need to develop a professional-quality 3D engine. Although the book is geared toward applications in game development, many of the topics appeal to general interests in 3D graphics. It starts at a fairly basic level in areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D game programming such as illumination, visibility determination, and collision detection. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure gaps in the theory. The book assumes a working knowledge of trigonometry and calculus, but also includes sections that review the important tools used from these disciplines, such as trigonometric identities, differential equations, and Taylor series. This book has plenty of examples and figures, making it much more illustrative than your average math book. I highly recommend it to anyone interested in implementing more advanced mathematics into their games or graphics applications. The following is the table of contents for this second edition:
Chapter 0 The Rendering Pipeline (NEW)
Chapter 1 Vectors
Chapter 2 Matrices
Chapter 3 Transforms
Chapter 4 3D Engine Geometry
Chapter 5 Ray Tracing
Chapter 6 Illumination
Chapter 7 Visibility Determination
Chapter 8 Collision Detection
Chapter 9 Polygonal Techniques
Chapter 10 Shadows (NEW)
Chapter 11 Linear Physics
Chapter 12 Rotational Physics
Chapter 13 Fluid Simulation
Chapter 14 Numerical Methods (NEW)
Chapter 15 Curves and Surfaces (NEW)
Appendix A Complex Numbers
Appendix B Trigonometry Reference
Appendix C Coordinate Systems
Appendix D Taylor Series
Appendix E Answers to Exercises
Note that there are four new chapters in this second edition.
An Essential Source for Robust 3D Graphics Engine Design.......2004-11-21
I have not yet been able to purchase the second edition of this book. However, since it is a refinement of the first edition, I feel that I am somewhat competent to review this later version of Lengyel's text on this knowledge of the fundamental chapters which are included in both editions.
Definitely, the subject of 3D Computer Graphics draws programmers and gamers inward like a bug lamp draws insects inward. The ability to express one's own inspiring representation of the world seems to attract the deepest longings of the subcreative nature of the human person. However, the coder quickly realizes that the realization of this dream is extremely difficult due to the complexities of visualization in nature. Lengyel's text helps to break through many of these complexities.
In order to make sure that the reader is "up to speed" on the essentials in mathematics which are necessary for a 3D engine, Lengyel gives a quick, but thorough, review of Vector and Matrix operations. I was indeed impressed by the amount that he condensed into the beginning of the text. While this is far from a complete treatise on Linear Algebra, this material gives the reader the basics which will be necessary for all the other chapters. This is further augmented by his treatment of 3D geometry, its representations, and calculations relevant to it.
Using this, he treats on various subjects that are extremely important for making a lean, mean, and beautiful rendering machine.
His treatment of transformations gives the reader a base in this knowledge that is independent of the rendering context. This is an excellent approach because knowledge of how something works allows for one to use it more fully. He also goes further in introducing Quaternions and deriving rotations around any arbitrary axis.
The chapter on Ray Tracing gives the necessary background for the work done in the following chapter on illumination. While the latter is often implemented by the graphics environment that the coder is using, the full knowledge of this allows for further application in subjects such as bump mapping (which he treats) as well as reflective surface simulation.
Perhaps the most interesting and important subject covered in the text, however, is the chapter on visibility determination. Since this is critical to the speed of rendering, this topic is central to game engine design. Lengyel works through the various methods for bounding box construction as well as bounding spheres, ellipsoids, and cylinders and then explains how these can be tested against the view frustrum in order to determine if an object should even be rendered. Another chapter on various techniques which can be applied to polygons outlines procedures for reducing the complexity of meshes, without compromising quality.
The remaining chapters touch on collision detection, linear and rotational physics, and fluid simulation. These topics allow for the addion of various levels of realism to be added to 3D engines and are of importance once the rendering environment has been established. Furthermore, his appendices are a nice addition for those times when our memories fail to recall various facts.
And so, I give this book my definite approval. It is hard to come by a text so compact, yet thorough, on the foundations truly needed for 3D Graphics. These mathematical foundations allow for greater things to be explored and should interest any 3D programmer as well as individuals with a general interest in mathematics, especially in the applications of linear algebra and calculus.
Average customer rating:
- great book for 3d math
- Perfect but needs more code
- Good book for starters
- Great (Re)Introduction to Basic Concepts
- Room for improvement
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3D Math Primer for Graphics and Game Development (Wordware Game Math Library)
Fletcher Dunn
Manufacturer: Wordware Publishing, Inc.
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ASIN: 1556229119 |
Book Description
This book covers fundamental 3D math concepts that are especially useful for computer game developers and programmers.
Customer Reviews:
great book for 3d math.......2007-10-05
great book for learning 3D math, probably the best on 3D math. The only reason I didn't give 5 stars is because author rushed through some of the topics. Overall, great book.
Perfect but needs more code.......2007-05-09
The book is the best 3D math book i have readen. The 3D math concepts explained simply and intelligibly. WARNING! You should know algebra, trigonometry to be able to read the book fluently! The absent one star is for: The book is independent of a well-known graphic API such as DirectX and OpenGL. The codes are standard c++ codes. Someone can like this, but me NOT. In my opinion, the 3D Math books for game development should select a proper graphic API and explain the concepts with these codes clearly. Because the real-world practise with knowledge is more stronger then just knowledge!
Good book for starters.......2007-03-24
Im programming a flash 3D engine from scratch. I dont use most of the concepts in this book, but I do need to understand whats going on. Trigonometry, vectors, points, matrices, operations, eulers, etc. and this book has been really helpful covering that.
Other books in the subject go straight to more complex issues skipping the contents from this book, so this is a must have unless you have a strong base already.
Great (Re)Introduction to Basic Concepts.......2007-02-08
I hadn't seen much math or geometry since high school, but this book does a great job at easing you into the underlying concepts of some pretty heavy stuff. I tried to wade through the CG "bibles" ("Real Time Rendering", "Principles of Computer Graphics in C") and quickly realized that if you're not either a CG major in college or an experienced CG pro, those books are like being in heavy seas without a life vest. (It really makes you appreciate what's involved in making those Pixar movies!)
Anyway, what I like about this book is that it explains everything first in fairly simple mathematical terms, deriving equations and proofs as it goes, and then illustrates to you visually exactly what is happening.
The majority of the material is conceptual. This is not a coding book from which you can pull easy answers. The code samples are in C++ and are confined to a few special chapters, and are really included as a programmatic interpretation of those concepts.
If you're already a CG pro, don't bother. You probably know all the info herein from the top of your head, as well as having one of those other "bibles" on your desk! But for a RAD programmer who needs a quick handle on some of the underlying concepts, this is the book!
Thanks Fletcher & Ian!
Room for improvement.......2007-02-07
I have read and studied this book up through the end of Chapter 9 (More on Matrices) so far. My overall impression is that this is a good book and you will learn from it; however, I do have suggestions.
(1) Each chapter ends with exercises. There ought to be a section at the end of the book for the exercise solutions.
(2) The explanation of projecting one vector onto another on page 61 in Chapter 5 is poor. Also, the notation the authors use is awkward. If you would like to see a much better explanation of this topic see, "Mathematics for 3D Game Programming & Computer Graphics," chapter 1, page 19 (the mathematics book is a tougher read but is definitely a good second source).
(3) Chapter 7 is titled, "Introduction to Matrices" which is well explained but leaves the reader wondering, "How on Earth are these tables of numbers useful and how are they used?!" The first paragraph states, "... they are primarily used to describe the relationship between two coordinate spaces." That's nice but nearly a complete waste of ink. That would be like going to a car dealership where the car you want to see is on the back lot but before you can go see it the salesman hands you a brochure that contains nothing but tables of numbers that mathematically describe the shape of the car. He says, "Hey, check out this baby!" And you say, "Duh! Just SHOW ME the car please!" Give us a short concise example -- a visual please and then tell us how it works.
(4) Chapter 9.3, Orthogonal Matrices, contains this statement, "... orthogonal matrices arise so frequently in practice in 3D graphics." But the authors do not provide an example. You would think that if it were such a frequent occurrence that it would merit an example.
If I had it to do over again I would purchase this book. There are no perfect books but between this book, the other one that I mentioned above, and Google, you should do well.
Book Description
"Even though I've worked with these systems for years, I found new ways of looking at several topics that make them easier to remember and use. For someone new to 3D programming, it is extremely usefulit gives them a solid background in pretty much every area they need to understand." Peter Lipson, Toys for Bob, Inc.
Based on the authors popular tutorials at the Game Developers Conference,
Essential Mathematics for Games and Interactive Applications presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix manipulation and expands on this foundation to cover such topics as texture filtering, interpolation, animation, and basic game physics.
Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout.
*Covers concepts in sufficient detail for a programmer to understand the foundations of 3D without feeling overwhelmed by proofs and theory
*Companion CD-ROM with code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction
*Provides guidance for students trying to understand how games are actually developed, including optimization techniques
Customer Reviews:
a grab bag of germane maths topics.......2007-06-12
Do you know the history of quaternions? About a century ago, they were investigated, as an exercise in pure, abstract maths. Yet in recent years, people in computer graphics found this very useful in defining certain types of rotations. Interested? Well, this book has a good, clear section that explains how they are used. That requires only some basic knowledge of trigonometry and complex numbers.
Much of the book is like this. Though perhaps with concepts more readily apparent than quaternions. Ideas drawn from three dimensional analysis. But with topics that are not typically in maths courses, relating specifically to graphical displays. Like different types of tesselations, different shaders and texture maps.
Some physics also shows up in the book. Often related to ray tracing and approximating the effects of light on a surface.
Nothing too hard, despite some remarks by other reviewers. The really advanced and specialised material, like applying Monte Carlo methods, has been omitted. This is essentially a basic text. You should have mastery of this material to do useful contributions in graphics.
Very Difficult.......2006-03-15
The book presentation is very good but the presentation of the material 'jumps right in there' with a good review and is very technical and a bit difficult to follow. It is an excellent book for someone that remembers their basic math, if your rusty, take a refresher course first.
Fabulous teaching!.......2005-07-25
See my other review. I bought this book and the other. I got stuck in that other book. I am learning linear algebra for the first time. This book is doing it! Although it gets quite abstract at times, and seems to be presenting the subject as if it is not related to 3D programming (like solving equations for an n-dimensional space), and it explains something and then says it is not used in 3D programming, it explains the concepts extremely well, and although it may take a while for a new concept to sink in for me, I do not find myself having to go elsewhere for help.
One note though, I tried to email one of the authors to find out about errata for the book and never got a response. I did eventually find it though. Don't expect the authors to be available. They do not have a message board.
One of the best game math books.......2005-04-29
If only every topic in game and graphics programming were covered as well as math. Over the past several years, a number of exceptionally good books covering math for game and graphics programming have been released, and I've had the opportunity to review most of them. Although, not surprisingly, there is some overlap between them all, each covers unique material and presents information in an original way so that collectively, the books provide an impressive body of work.
Essential Mathematics stands out as one of the best books in the pack, especially in regards to its coverage of the math behind low-level rendering techniques.
The book is broken into 4 parts. The first part, Core Mathematics, covers vectors and matrices, transformations, and number representation. This part will be useful to anyone doing 3D graphics.
Part II, Rendering, covers topics such as lighting and shading, texturing, projection, and rasterization. This part was of particular interest to me because I've been working on a commercial renderer, but it should also be useful to those who want a better understanding of what graphics engines do under the hood.
Part III, Animation, covers curves (very in depth) and representation of orientations (Euler vs. axis-angle vs. quaternions). Finally, Part IV, Simulation, covers intersection testing and rigid body dynamics. There are also a couple of appendices to help you brush up on trig and calculus, if needed.
The book includes many C++ code samples and demos, including a handy math library and a simple rendering/game engine using OpenGL and GLUT. The authors are to be commended for their writing style as well. It's very easy for a book of this nature to get bogged down in an extremely heavy academic tone, but this book manages to avoid that, making for a remarkably easy read.
I'm glad I don't have to choose just one game math book, but if I did, this would probably be the one I'd pick.
Clear, Comprehensive, and Educational........2004-05-08
The strength of this book lies in its author's ability to make complex subjects accessible to programmers of various levels. The book covers all necessary subjects of 3D development and algorithmic motion, while providing primers in the relevant Math and Trigonometry. The writing is clear, and the examples combine notation in Math, Pseudo Code, and Open-GL implementation. I could see various uses for this book; from reference guide to required course reading. It explains the most fundamental subjects of Vectors and Matrices, and later capitalizes on this knowledge towards subjects that every professional in the field should know. To make sure the book is right for you, I suggest reading the Introduction, which portrays the book accurately and proceeds to recommend alternative and additional resources.
Book Description
This book illustrates the mathematical concepts that a game developer would need to develop a professional-quality 3D engine. Although the book is geared toward applications in game development, many of the topics appeal to general interests in 3D graphics. It starts at a fairly basic level in areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D programming such as illumination and visibility determination. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure gaps in the theory. The book assumes a working knowledge of trigonometry and calculus, but also includes sections that review the important tools used from these disciplines, such as trigonometric identities, differential equations, and the Taylor series.
Key Features:
* Concentrates on key mathematical topics for programming 3D game engines
* Discusses applications in the context of the OpenGL architecture due to its cross-platform nature and long-standing industry acceptance. Makes references to modern 3D hardware such as GeForce 3 from Nvidia
* Selected topics include Quaternions, Homogeneous Coordinates, Ray Tracing, Bump Mapping, Portal Systems, Polygonal Techniques, Shadows, and Physics
* Includes exercise sets for use as a textbook
Customer Reviews:
Excellent source of applications for a Calc III class.......2007-09-10
If you're trying to find examples of 3D vector operations (dot and cross products, especially) that keep the interest of a mixed class of 18-25 year olds, this book is a fantastic source. If you're approaching the topic from the point of view of a programmer, trying to acquire the necessary math, it may be a bit dense. I'm sure many of the examples are now out-of-date, compared to current 3D implementations, but I learned quite a bit, anyway.
good reference for computer graphics math.......2004-03-24
like others books in charles media , written by someone in the industry , which means value infos will be in the book .
this book is good for someone studied linear algebra I,II + calculs courses and want to see the applied math in computer applications such as games .
i suggest before reading this book , reading a book about linear algebra + gemetry + calculs so as not to lost in that book because this book not for beginners in math .
Excellent.......2003-12-22
Excellent Book, I am very pleased with it and encourage it to anyone who already has ground knowledge in Trig + Calc. No fluffer in this book, all content and well written.
For a rock-solid understanding of 3D math.......2003-10-17
This book provides a solid foundation for anyone who wants to develop a good understanding of the math behind computer graphics. The author provides clear and concise explanations of the concepts covered, backs them up with mathematical proofs, and usually discusses how the concepts can be applied in games, often with sample code. Each chapter has accompanying exercises that I recommended working through.
The topics covered include things you would expect like matrices, vectors, transformations, 3D geometry, and lighting, but also includes are topics like collision detection, ray tracing, visibility determination, and techniques such as billboarding and shadows. It concludes with several chapters on physics including fluid simulation, and a few useful appendices covering trig, complex numbers, and Taylor series.
If you're brand new to graphics and game programming and haven't had a math class in a while, then the somewhat textbook-like language may be a little daunting, but otherwise, this book is an excellent resource for those interested in solidifying their knowledge of 3D math.
A Book for The Whole Life.......2003-09-17
Surely this is the book I was looking for.
Mostly of the 3D games books just presents codes and some few mentions to the maths techniques, without regarding the concepts behind them.
This one presents the Maths we use in 3D game development in such way that it does not bore the reader and yet makes him learn the math basis behind the 3D graphics programming, presenting, yet, some physics notes to implement a physics based engine.
If you just wanna code, certainly this is not the book for you, but if you are a serious developer (and programmer), surely this is the only book you should need.
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