3D Math Primer for Graphics and Game Development covers fundamental 3D math concepts that are especially useful for computer game developers and programmers. The authors discuss the mathematical theory in detail and then provide the geometric interpretation necessary to make 3D math intuitive. Working C++ classes illustrate how to put the techniques into practice, and exercises at the end of each chapter help reinforce the concepts.

This book:

* Explains basic concepts such as vectors, coordinate spaces, matrices, transformations, Euler angles, homogenous coordinates, geometric primitives, intersection tests, and triangle meshes.

* Discusses orientation in 3D, including thorough coverage of quaternions and a comparison of the advantages and disadvantages of different representation techniques.

* Describes working C++ classes for mathematical and geometric entities and several different matrix classes, each tailored to specific geometric tasks.

* Includes complete derivations for all the primitive transformation matrices.

Fletcher Dunn and Ian Parberry

This book covers fundamental 3D fundamental maths concepts that are especially useful for computer game developers and programmers. The authors discuss the mathematical theory in detail and then provide the geometric interpretation necessary to make 3D maths intuitive. Working C++ classes illustrate how to put the techniques into practice, and exercises at the end of each chapter help to reinforce the concepts.

This book covers fundamental 3D math concepts that are especially useful for computer game developers and programmers.

Great Companion Book for Intro Graphics APIs

I am reading this book alongside Introduction to 3D Game Programming with DirectX 9.0c: A Shader Approach by Frank D. Luna, and so far 3D Math Primer has really helped. It took me from a basic trigonometry/geometry/algebra to understanding the basics of the math described in Intro to DX9, I can’t wait to get to the more complicated parts that explain the graphics pipeline. The things that Intro to DX9 took a page or so to explain 3D Math Primer is able to go into detail and explain well.

Great read

Good, with a few problems...

I needed a book to recommend to a friend whose offspring is trying his hand at game programming and needs some introductory maths to get going.

I was pleasantly surprised by the quality of this book. The content, writing and layout are excellent and the level at which it deals with the various topics is just right. I also like much of their code and the implementation details which go with it. I can wholeheartedly recommend it for beginner developers.

The reason I didn’t rate the book 100% is because there are a fair number of questionable opinions expressed by the writers. These are mostly based on their collective experience in game development and while I respect their expertise, I disagree with them on these points. A quick example. Their advice in Chapter 6, "Don’t use information hiding" almost made me choke on my tea. The reasons they give for exposing their vector class data are simply bizarre. Encapsulation is one of the three pillars of object oriented development. This is not the place to discuss the dangers developers face by subverting this powerful idea, but I strongly urge beginner programmers to ignore the authors advice on this point.

Despite these reservations, the book is a must-have for novice and intermediate programmers.

I wouldn’t use this as my primary book

I felt the first few chapters were really geared towards newcomers to 2D/3D Maths and so every topic in the earlier chapters were covered very slowly and in detail. However, as I progressed through the chapters I noticed the authors had started accelerating through the topics at a quicker pace and I was left somewhat confused and so I had to research many of the topics from other resources.

One thing I really didn’t like about the book was that the exercises were left to be done at the end of each chapter. The problem with this approach was that some chapters expanded across many pages packed with information you needed to know and thus, like a traditional maths book I would have liked to practice a few questions after each topic and not after a whole chapter.

Not sure who would find this useful

Sure the book starts off with really really simple maths, using 1d and 2d maths for a springboard. It slowly eases into vector and matrix maths, all described fairly run of the mill. So far so good.

Reading further on into geometric principles and intersections it becomes apparent that the author seems to have forgotten all about the first half of the book and is quickly rambling on using terms and symbols not previously referred to and thus will more than likely lose anyone without a mathematics degree.

Most of the articles here are locatable on the internet if you know how to use a search engine, and described in a much more user friendly way.

GREAT BOOK!

I picked up this book and within a week I was working on my own 3d engine. The explanations are very clear. This book is great for ANYONE. This is the book you are looking for!

Best Math book....period

The greatest problem for a lot of us that want to be great programmers is that we’re terrible mathematicians. And the greatest benefit of this book is that it explains it in a way anyone can understand it! I absolutely love this book. Before you even start to think about DirectX, OpenGL, whatever - you should read this book COVER TO COVER.

Gets you up to speed very quickly.

This is a must read for anyone wanting to jump into 3D graphics programming, the book is full of content, full of useful source code, and very accessible to the average reader.
The only gripe I would have is that there is a steep learning curve a few chapters in, once you finish writing the vector class the content in the next chapter is much harder. It’s not impossible to pick up, but there is a definite difference in difficulty.

READ THIS

Hi, i am a college student at Bozeman, Montana, MSU. If you do not know, the computer science course in Montana (of all places) is in the highest Tier in the nation. (That means our school competes with MIT). I can tell that this book is great. Sure there are some funny things about it, but for the most part, everything is good in this book. I really like how much stuff is covered on matrices. Not everyone gets to take Matrix Theory (Linear algebra) so this book does a decent job of explaining matrices. And especially explaining Quaternions.

Not good

Didnt learned too much from it, the explanations are very briefly specially in some chapters

For example, in the Collision Detection chapter (aka Geometric Tests, Chapter 13), he just throws the equations and miss important points to the complete understanding of the solution for the problem.

For example, in the explanation of Intersection of Ray and Plane, he just says that the parametric ray is p(t) = Po + td and the plane equation is p . n = d, then you need to solve (Po + td) . n = d, and the explanation is just it

He doesnt explain why a plane is defined by p . n = d, and why the dot product of all points in the plane and the plane normal will give the same number, and doesnt even explaning the meaning of that number (which is the plane distance from the origin along the normal, or in other words, the closest point in a plane to the origin)

All the others geometric tests explanations are made in the same way, he just throw the equations and some picture and you have to find out yourself. I was only able to understand the chapter cause i already had a good understanding of that subject, but for that guy with zero knowledge in the subject who bought this book for the first time imagining it would be a good introduction for geometric tests, he will have a hard time

Others chapters are the same way too, for example, i was hoping to understand barycentric coordinates from this book, but as always, he just throw you some equations

Maybe i misjudge the book, but thats my impression so far

If money is not your problem, buy it, but dont expect it to be your ultimate source for your doubts, you will probably have to look in another sources

great book for 3d math

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.

3D Maths for mathematicians

I bought this book thinking it would explain 3D maths to me, a programmer, but instead found it better suited to mathematicians who want to understand vectors and matrices.
There is virtually no pseudocode in the book, and only around 50 pages out of 400 cover 3D graphics in practice, and then in little depth.
The only people who will get anything from this book are people with a degree in Computer Science (and they will probably know 3D maths already).

Perfect but needs more code

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

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

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

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.

excellent book for game developers

I’m about 2/3 through this book now, and I’ve found it very helpful. The explanations are good, and what I particularly like is how he illustrates most of the topics with pictures and graphs, explaining the relevance to rendering graphics in games. Unlike most math books and courses I’ve taken, I’m not left wondering "what the heck relevance does THIS have?" every time I turn a page. He also does provide C++ code game graphics rendering at the end of most topics. The code is very useful, and well explained. I can definitely see myself using some of it in future projects.

I don’t want to kid anyone though, this material is complicated, and if you struggle with math, or don’t have a math background (some advanced high school classes or college math) then you may find this book a bit much.

Great Introduction to the Math and Algorithms Behind Rendering

The first time I tried to read this book, I took frequent breaks and only made it to about chapter 10, not really understanding a few of the proofs and algorithms. However, after going through the entire book all at once in about a week, I was able to understand everything. It was definately worth it.

The book assumes no prior knowledge of linear algebra, and teaches you from the ground up the critical concepts behind 3d engines. At the end of the book, I was able to write my own software engine implementing many of the concepts talked about in the text, having absolutely no prior knowledge of any of the concepts before.

Knowledge of the concepts presented in this book are absolutely critical to you being able to understand and use graphics apis such as direct x. This book will demystify what goes on inside a 3d engine, and will clearly detail to you the steps required to render a scene. Of course, it can’t teach you everything, but by the time you have read it you will have a good working knowledge of what it takes to write a decent 3d engine. Definately worth it - you’ve got to know this material eventually, and this book is a good choice.

Great Introduction to the Math and Algorithms Behind Rendering

The first time I tried to read this book, I took frequent breaks and only made it to about chapter 10, not really understanding a few of the proofs and algorithms. However, after going through the entire book all at once in about a week, I was able to understand everything. It was definately worth it.

The book assumes no prior knowledge of linear algebra, and teaches you from the ground up the critical concepts behind 3d engines. At the end of the book, I was able to write my own software engine implementing many of the concepts talked about in the text, having absolutely no prior knowledge of any of the concepts before.

Knowledge of the concepts presented in this book are absolutely critical to you being able to understand and use graphics apis such as direct x. This book will demystify what goes on inside a 3d engine, and will clearly detail to you the steps required to render a scene. Of course, it can’t teach you everything, but by the time you have read it you will have a good working knowledge of what it takes to write a decent 3d engine. Definately worth it - you’ve got to know this material eventually, and this book is a good choice.

Not for Novices or Intermediate

Not an easy read. I thought of myself as being an intermediate level mathematician - leaning slightly towards the novice, but this was beyond my expectations. After the first few chapters on Vectors, getting into Matrices he lost me. Even some of the vector math lost me. Sure, if I want to find the cross product of two 3d vectors I can do it, I’d just go look up his source code, but *why* it works exactly? Don’t know.

I don’t think the examples were quite clear enough. I would have preferred a much more thorough explanation of what the author was doing throughout most of his work (proofs, examples, just about everything).

If you have a pretty good background / understanding of linear algebra, go ahead and get this book, you’ll probably learn a lot - the author definitely knows what he’s talking about - he’s just not the greatest at explaining it.

Not for Novices or Intermediate

Not an easy read. I thought of myself as being an intermediate level mathematician - leaning slightly towards the novice, but this was beyond my expectations. After the first few chapters on Vectors, getting into Matrices he lost me. Even some of the vector math lost me. Sure, if I want to find the cross product of two 3d vectors I can do it, I’d just go look up his source code, but *why* it works exactly? Don’t know.

I don’t think the examples were quite clear enough. I would have preferred a much more thorough explanation of what the author was doing throughout most of his work (proofs, examples, just about everything).

If you have a pretty good background / understanding of linear algebra, go ahead and get this book, you’ll probably learn a lot - the author definitely knows what he’s talking about - he’s just not the greatest at explaining it.

Very good condition and no hassle

The item was shipped promptly and was in very good condition. I’m very pleased.

Very good condition and no hassle

The item was shipped promptly and was in very good condition. I’m very pleased.

Good for understanding math for DirectX

I bought this book with another to try and learn linear algebra (and linear transformations) from scratch. This book is not good for that, since it omits key concepts here and there that would facilitate the learning process. For example, they present a formula that is to be used to derive a matrix for a rotation around an arbitrary axis. It made no sense to me, since they omitted the fact that they were using the vectors in that equation as basis vectors.

So, I am learning the math now from the other book (that teaches it from the OPENGL coordinate system) and will go back to this book to help me see those concepts for the DirectX view.

The people that rated this book highly, must have already learned linear algebra elsewhere and just need a refresher, or have genius level IQs (I do not). I need things clearly explained, not assumed.

Since the purported purpose of the book is to teach the math, and there are others that teach DirectX and assume you know the math, I am only giving this 3 stars. See my other reviews for the best math books.

Good for understanding math for DirectX

I bought this book with another to try and learn linear algebra (and linear transformations) from scratch. This book is not good for that, since it omits key concepts here and there that would facilitate the learning process. For example, they present a formula that is to be used to derive a matrix for a rotation around an arbitrary axis. It made no sense to me, since they omitted the fact that they were using the vectors in that equation as basis vectors.

So, I am learning the math now from the other book (that teaches it from the OPENGL coordinate system) and will go back to this book to help me see those concepts for the DirectX view.

The people that rated this book highly, must have already learned linear algebra elsewhere and just need a refresher, or have genius level IQs (I do not). I need things clearly explained, not assumed.

Since the purported purpose of the book is to teach the math, and there are others that teach DirectX and assume you know the math, I am only giving this 3 stars. See my other reviews for the best math books.

Great Coverage in Some Areas Fail Miserably in Others

The book is meant for Introductory to Intermediate audiences, but some of the chapters makes too many assumptions that you have background in the topic. Take the chapter on Vector, for example, it dives right into vectors without telling you how vectors are derived. Moreover, I believe the author takes a very lazy approach to his examples. He offers very little illustrations and explanations to demonstrate the problem. When he does offer it, he tends to skip a number steps before arriving at the answer. I do not recommend this book for Beginners; perhaps Intermediate users may find it more informative. Too bad Amazon does not reimburse for shipping returns; otherwise, it will be awaiting at their front door.

Great Coverage in Some Areas Fail Miserably in Others

The book is meant for Introductory to Intermediate audiences, but some of the chapters makes too many assumptions that you have background in the topic. Take the chapter on Vector, for example, it dives right into vectors without telling you how vectors are derived. Moreover, I believe the author takes a very lazy approach to his examples. He offers very little illustrations and explanations to demonstrate the problem. When he does offer it, he tends to skip a number steps before arriving at the answer. I do not recommend this book for Beginners; perhaps Intermediate users may find it more informative. Too bad Amazon does not reimburse for shipping returns; otherwise, it will be awaiting at their front door.

Highly recommended

I love this book, and it has payed off very well for me.
The author has a remarkable skill to explain even the most difficult subjects in a way that everyone understands. For example, The Cartesian coordinate system is abstracted to a system of roads.
However, this simplification is not an issue for intermediate/advanced programmers or math students. All topics are provided with formulas and concise material; making this book good for everyone.
Topics covered (but not limited to) vectors, coordination systems, dot-product, cross-product, quaternions, matrices, Auler-angles, bsp-trees, screen projection, culling, bounding-boxes (and a load of other intersection tests).

Still I missed something. The author(s) also covers gourad shading, texture mapping and several other techniques, but they don’t go into depth. Different lighting models were given a formula at best, which fortunately is good enough for me. Just don’t expect the book to be API-specific or contain information about rendering methods.
The source code which came with the book compiled, but looks awful and very messy. The source code works very well as a reference, but it you are buying the book mainly for the code; don’t. I hope they’ll update their source code from the webpage soon.

Conclusion: This is a very good book to start with. It contains all the linear algebra math you’ll need to start with 3D-programming, and is explained remarkably well. Yet the simplification is nevertheless no con for non-beginners, which will probably use this book as a reference laying on their desktop at all times :-)

Highly recommended

I love this book, and it has payed off very well for me.
The author has a remarkable skill to explain even the most difficult subjects in a way that everyone understands. For example, The Cartesian coordinate system is abstracted to a system of roads.
However, this simplification is not an issue for intermediate/advanced programmers or math students. All topics are provided with formulas and concise material; making this book good for everyone.
Topics covered (but not limited to) vectors, coordination systems, dot-product, cross-product, quaternions, matrices, Auler-angles, bsp-trees, screen projection, culling, bounding-boxes (and a load of other intersection tests).

Still I missed something. The author(s) also covers gourad shading, texture mapping and several other techniques, but they don’t go into depth. Different lighting models were given a formula at best, which fortunately is good enough for me. Just don’t expect the book to be API-specific or contain information about rendering methods.
The source code which came with the book compiled, but looks awful and very messy. The source code works very well as a reference, but it you are buying the book mainly for the code; don’t. I hope they’ll update their source code from the webpage soon.

Conclusion: This is a very good book to start with. It contains all the linear algebra math you’ll need to start with 3D-programming, and is explained remarkably well. Yet the simplification is nevertheless no con for non-beginners, which will probably use this book as a reference laying on their desktop at all times :-)

Good math book, even for beginners

The book explains vectors and matrix math very well.
It helps you create a good matrix classes and vector classes.

But other than that it does not show how to apply the knowledge to create a 3D engine. It mostly just covers the math, which it does very well. If the scope was only math and not code then I would have given it 5 stars but it says on the front page of the book:

"Put mathematical theory into practice with working C++ classes....".

And it does give you an idea of how to do things. It just does not help you tie it all together. But few books cover everything, so its still a very good buy.

Clear and explanatory text about core 3d math.

This book is a rare find. Many advanced math texts suffer from unclear prose or use cryptic symbols, but not this one. What you’ll find are clear and well written explanations of each 3d math topic, followed by illustrative pictures and easy to read formulas. Highly recommended, especially as a starting point for learning 3d math.

Excellent for Linear Algebra Students In Computer Science

If you are taking Linear Algebra in college, you know that most of the available textbooks are a little short on practical details and examples of how vectors and matrices will matter to you later on in your programming career. This book provides excellent pictures, diagrams and explanations on the basics of how you can put your Linear Algebra knowlege to work. You don’t need to be interested in game development to benefit from the clear and very readable presentation that this book provides. Thank you Fletcher Dunn and Ian Parberry - for the outstanding work.

Exceptionally good book

The authors of this book is a game programmer and a professor of Computer Science. This team is excellent!

The game programmer has alot of focus on making the material understandable, and the professor has focus on the mathematically correct semantics. Unlike other books, that teaches game programming (of which many have an author with his strength on either field), this book has the right blend of understandable text parred with the right mathematical semantics.

Furthermore the text is supported by code, so if you are shaky on some of the math, you can see the implementation in C++ code.

As a total math newbie, this book helped me alot, and today I understand totally and in detail what is going on in my 3D programming.

An ABSOLUTE MUST, if you want to learn 3D on top level.

Amazing for begineers and advanced programmers

Beginners:

I would like to start off by saying that if you are a complete beginner, then you have come to the right place. This book is amazing in its introduction of maths concepts to beginner 3D programmers. The way that the author has written this book means that you won’t be left with gappy knowledge on this already complex subject. Beginners will come away from this book knowing a good deal of the 3D math necessary for a game today.

Advanced:

Advanced users will not find the book as rewarding as beginners but will definitly learn a few new tricks. I personally found that the little concepts I new in vectors was deeply clarified by the author

Negatives:

Lack of CD and unavailable code via the URL when I looked..Buy this NOW!

Amazing for begineers and advanced programmers

Beginners:

I would like to start off by saying that if you are a complete beginner, then you have come to the right place. This book is amazing in its introduction of maths concepts to beginner 3D programmers. The way that the author has written this book means that you won’t be left with gappy knowledge on this already complex subject. Beginners will come away from this book knowing a good deal of the 3D math necessary for a game today.

Advanced:

Advanced users will not find the book as rewarding as beginners but will definitly learn a few new tricks. I personally found that the little concepts I new in vectors was deeply clarified by the author

Negatives:

Lack of CD and unavailable code via the URL when I looked..Buy this NOW!