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3D Math Primer for Graphics and Game Development, 2nd Edition [Hardcover]

Fletcher Dunn , Ian Parberry
5.0 out of 5 stars  See all reviews (2 customer reviews)
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Book Description

19 Oct 2011

This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.


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3D Math Primer for Graphics and Game Development, 2nd Edition + Game Coding Complete + Mathematics for 3D Game Programming and Computer Graphics
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Product details

  • Hardcover: 846 pages
  • Publisher: A K Peters/CRC Press; 2 edition (19 Oct 2011)
  • Language: English
  • ISBN-10: 1568817231
  • ISBN-13: 978-1568817231
  • Product Dimensions: 23.9 x 19.8 x 3.8 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 33,226 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

"With solid theory and references, along with practical advice borne from decades of experience, all presented in an informal and demystifying style, Dunn & Parberry provide an accessible and useful approach to the key mathematical operations needed in 3D computer graphics."
—Eric Haines, author of Real-Time Rendering

"The book describes the mathematics involved in game development in a very clear and easy to understand way, layered on the practical background of years of game engine programming experience."
—Wolfgang Engel, editor of GPU Pro

About the Author

Fletcher Dunn has been programming video games professionally since 1996. He served as principle programmer at Terminal Reality in Dallas, where he was one of the architects of the Infernal engine and lead programmer on BloodRayne. He was a technical director for the Walt Disney Company at Wideload Games in Chicago, where he was the lead programmer for Disney Guilty Party, which won IGN's Family Game of the Year at E3 2010. He is currently a developer at Valve Software in Bellevue, Washington.

Ian Parberry is a professor in the Department of Computer Science and Engineering at the University of North Texas. Dr. Parberry has more than a quarter century of experience in research and teaching and is nationally known as one of the pioneers of game programming in higher education.


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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most Helpful Customer Reviews
12 of 12 people found the following review helpful
Format:Hardcover
Since I first started working as a programmer in the game industry in the mid 1990s I have been looking for a book that explains the maths that underpin 3D games from first principles, doesn't assume any more than absolutely neccessary about the mathematical experience of the reader, and doesn't just throw pages of mathematical notation at you.

I never found maths difficult at school, but I did find pure maths boring and so I ditched it as soon as I was able. Ironically it was the topic of vector and matrix maths that was the final straw that made me decide to drop maths as a subject. D'oh. I still studied physics, chemistry, and biology so I was able to get onto a Jt hons BSc in Computer Science / AI and Psychology which was pretty light on maths, and do the course without any trouble and as little maths as possible.

Anyway, my first task in my first job was to see if I could re-write and optimise the collision system in a fully 3D car dynamics prototype (which would eventually go on to form the basis of the ToCA Touring Cars and Colin McRae Rally physics engines).
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5.0 out of 5 stars Math & Code 28 Dec 2013
Format:Hardcover|Verified Purchase
It covers the principles of computer graphics with good C++ examples. A true must-have for any one that wants to enter in the gaming world.
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Amazon.com: 4.6 out of 5 stars  19 reviews
16 of 16 people found the following review helpful
5.0 out of 5 stars Excellent introduction to math required for game development 2 Feb 2012
By Pavel Krajcevski - Published on Amazon.com
Format:Hardcover
This book is a shining example of how mathematics for games should be taught to people who may not have had the best time learning calculus or analytic geometry but still want to take the plunge into game development. Every concept that is described in this book is introduced first intuitively and then is expanded upon mathematically. Moreover, unlike other math books, this book can actually be read like a book. There is no obtuse notation or symbol vomit that seems to be prevalent in other books that try to teach similar subjects. Much of the book is presented with a casual tone as well, which makes it seem like you're actually taking a class rather than poring over formulas. I would highly recommend this book to anyone armed with critical reasoning skills but without the experience to jump head-first into programming for game development.

That being said, be wary of the title of the book. It is a PRIMER for graphics and game development. Those that are looking for formalized theorems and proofs will not be satisfied. Moreover, while the book does provide an introduction to more advanced topics, this is not a book about advanced techniques such as global illumination or physically based simulation (although there is a chapter on linear rigid-body dynamics). The references provided will point the interested reader in the right direction, and the book does a very good job of introducing you to the preliminary concepts.
10 of 10 people found the following review helpful
5.0 out of 5 stars Spectacularly Helpful Math Book 12 Sep 2012
By philipb - Published on Amazon.com
Format:Hardcover
This book is the single best introduction to 3D math I've ever read. Written by a developer from Valve (notice how the graphical style of the cover is similar to Team Fortress 2?), there are two big reasons I think this is the best book for people who are just starting to learn about 3D math as it's used in video games, as well as old hands who are looking for a fresh perspective on the material.

1) It's a very easy read. They clearly spent painstaking hours making sure the book was as easily accessible as possible. They start with a one-dimensional number line and grow from there, to 3D, to points, to matrices, and to polygons and beyond. The buildup is as gradual as can be, and their informal writing style helps them as they present topics in multiple ways, making it even easier to understand what they're talking about.

2) Perhaps even more importantly, everything they teach is grounded in practical use. My problem with, say, Eric Lengyel's book as a starting point is that Lengyel's book gives the formulas, but does not really explain why these topics are useful in graphics. That makes his book great for a reference for a professional, but impractical for a beginner. This book, on the other hand, uses words and illustrations to show exactly why you are learning what you are learning. The writers understand that once you grasp the underlying concepts of 3D math, the formulas will be intuitive to the point that you could even deduce them on your own if you didn't know them. That's the level of understanding a game programmer needs (just ask the guy from Valve!) and that's what this book is aiming for.

If you are looking for an intro to the topic of 3D math, I just don't know how any book could top this one. Written by a game programmer and aimed at people who want to be graphics programmers and game developers themselves, you are going to be hard pressed to find a book that will make for an easier intro to the topic. For a reference book, something like Eric Lengyel's may help you better a few years down the road, but if you want a book that takes you from being able to count to being able to understand 3D representations of sprites, this is the one for you.

Bravo Mr. Dunn and Mr. Parberry for such a great book!
8 of 9 people found the following review helpful
4.0 out of 5 stars Excellent But Gets Complicated 23 Jan 2013
By Gary Smith - Published on Amazon.com
Format:Kindle Edition|Verified Purchase
I adopted this book as the textbook for my computer gaming math course. The first 7 chapters are easy to read and follow for Freshman-level students. After that the math gets really complicated; however, it is still the best that I found on the topic and I highly recommend the book. Don't forget to check out the PowerPoint presentations and Interview Questions on the publisher's web site. My only complaint is the textbook provides ALL answers to exercises at the end of chapters, forcing me to make up new questions for homework. It would be nice to see an instructor version with additional exercises and answers not available to the student. (I bought both the hardcopy and Kindle Editions and the Kindle Edition is an excellent reflection of the hardcopy.)
4 of 4 people found the following review helpful
4.0 out of 5 stars You don't make Games or Computer Graphics; Heavy on Math 25 Aug 2013
By Anonymous787 - Published on Amazon.com
Format:Hardcover
This is my 1st book on the subject which I have some prior knowledge.

CONS
1. You don't make computer graphics or games ; thus can't practice this
way with this book alone.
2. It covers an extensive amount of math, uses lots of math formulas , &
some calculus. Certain sections especially later get complex &
difficult to grasp. If studied alone & you're a new learner, the book
will probably be a bit too hard & at time overwhelming for you.

PROS
1. A valuable stand-alone reference book ; useful as a complementary book.
2. Excellent coverage on this subject which definitely contains the
essentials; notably strong in presenting the fundamentals. For instance,
Coordinate Systems, Vectors & Matrices are important concepts in 3D for
Computers. This information among others is written very well, thorough
& has lots of examples . I understand determinants now & calculus
better.
3. It explains how graphics work & has useful gaming info. like physics,
collision, intersections.

Some Favorites: fundamentals, calculus, bezier curves, some chapter exercises, code snippets,
collision detection

Prepare to get your feet wet should you read this book all the way through. This Primer book intended not to include making Computer Graphics or Games. Its main objective is to teach you in detail how to describe an object's position, orientation, & trajectory on a 2d, 3d coordinate space.
The easiest & best way for beginners to start this new learning of math is to first read a book such as Frank Luna's "Introduction to 3D Game Programming with DirectX 11" which integrates 3D Math , Graphics & Game Programming all in one. In comparison to the Primer in terms of the math, Frank's book makes it easier to learn the 3D math because it's lighter, less technical on it & lets you visually practice it with computer graphics. You'll find math learning thus more understandable, interesting & pleasant to work with.
I went the harder way yet I enjoyed reading this book very much. The authors did an exceptional job writing it. They certainly have expertise in 3d Math & painstakingly lay the ground work for you in the 2nd Edition of this Primer. Their writing style is clear , easy going in many parts & along the way has some humor. Throughout, you reinforce your learning by things like helpful tips, repeated content, code snippets (in C) as well as chapter exercises with their answers to help you practice them. Watch out, some exercises are challenging. For more information about the book go to [...] .

Improvements: 1. difficult parts, formulas need better explaining & with more examples please
2. To appreciate the math more, make this book work hand in hand with a Graphics Book like Frank Luna's.

Here's a Snapshot Overview of Many Things To Learn

Cartesian Coordinate System- origin, axis -uses left-handedness
Vectors - arithmetic, dot & cross product
Linear Algebra - mathametic definition & geometric
interpretation of things
Multiple Coordinate Spaces- basis vectors , transformations , nested
Upright Space - authors' defined Transitioning Space to help
you in the study of 3D Math
Matrices - linear transformations, determinant , inverse,
projection (homogenous & perspective)
Polar Coordinate Systems
Rotations in 3 Dimensions- matrix, Euler , axis angle & exponential map,
quaternions : (comparison, conversion among
the methods)
Geometric Primitive- representation techniques, lines, rays,
spheres, circles, bounding boxes, planes,
triangles, polygons
3D Graphics - how graphics work, viewing 3d, coordinate
spaces, polygon meshes, texture mapping,
standard local lighting model, light sources,
skeletal animation, bump mapping,
Real Time Graphics Pipeline, HLSL (code)

Linear Kinematics- basic quantities, units, velocity (average,
instantaneous), derivative, acceleration,
motion under constant acceleration,
uniform circular motion
Calculus- integral, differential
Linear & Rotational Dynamics- Newton's 3 laws, some simple force laws,
momentum, impulsive forces & collisions,
real-time rigid body simulators
Curves in 3D- parametric polynomial curves, polynomial
interpretation, hermite, bezier, splines,
continuity, automatic tangent control

Intersection formulas: Closest Points:
1. on a 2D implicit line
2. on a parametric ray
3. plane
4. on a circle & a sphere
5. closest point in an AABB
(axis-aligned bounding box)
Intersection:
1. Tests you can use
2. 2 implicit 2D lines
3. 2 rays in 3D
4. ray & a plane
5. AABB & a plane
6. 3 planes
7. ray & a circle or sphere
8. 2 circles or spheres
9. sphere & AABB
10. sphere & a plane
11. ray & a triangle
12. 2 AABBs
13. ray & a AABB

Errata- As of this data not found on the errata web page.
Corrected form is listed here: P =paragraph, [] = where mistake found.

244 1st P [it is] possible........
246 last P euphemistic
358 1st sentence [Dirac] delta
456 in 4 Alpha test: ......may not cause any change [to] the frame buffer..
489 2nd P ... even if it was [in] motion...
548 3rd P .....we wish [to] measure...
600 2nd P ....we've also included a perfectly [elastic] collision.....
660 2nd column of polynomials [ l 2 ] (t1) = 0
4 of 4 people found the following review helpful
5.0 out of 5 stars Extremely Helpful 19 May 2012
By parka - Published on Amazon.com
Format:Hardcover|Verified Purchase
This book is especially useful for people who have no background in Computer Graphics and would like to understand how to apply all that wonderful senseless math you were made to learn and actually make it useful. This book made my Computer Graphics course especially easy it's a keeper.
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