Essential Math Weblog Thoughts on math for games


Second Edition

Filed under: General — Jim @ 8:04 pm

Just a quick note to say that a second edition for Essential Mathematics for Games… is in the works.  If you have items that you would like to see updated, expanded, or just plain included in a new edition, please let me know.  Also, if you’re an educator and you’re using this book as part of a course, please drop me a line as well.  We may be interested in having you do a detailed review of the first edition.
You can send me email at ‘jim’ at this domain, or use the form on the front page of the site.

Thanks in advance.


  1. I hope you will give forward and inverse kinematics more attention in the next ed.

    Comment by guest — 7/4/2006 @ 7:07 pm

  2. Dear authors,

    thanks a lot for a splendid book. My students and I are very happy to use it. I have a few comments that I did not find on the list of errata or at the blog. I might of course be wrong on some of them. Please, excuse me if I am.

    By the way, it would be very nice if some material on the A* algorithm could be included in a future version. The literature on A* can be a little confusing.

    Best, Olav Geil

    $33_9$: “$\mid \mid \vec{w}_0 \mid \mid$” should be
    “$\mid \mid \vec{w}_0 \mid \mid^2$”.

    $33_4$: “$\mid \mid \vec{w}_0 \mid \mid$” should be
    “$\mid \mid \vec{w}_0 \mid \mid^2$” and “$\mid \mid \vec{w}_1 \mid \mid$” should be
    “$\mid \mid \vec{w}_1 \mid \mid^2$”.

    $33_1$: “$\mid \mid \vec{w}_j \mid \mid$” should be
    “$\mid \mid \vec{w}_j \mid \mid^2$”.

    p. $51$, Figure 1.31: “$r$” should be “$\rho$”.

    p. $52$, Figure 1.32: “$r$” should be “$\rho$”.

    p. $58$, Figure 1.37: “$\vec{n}=(a,b)$” should be

    $68^8$: It might be a good idea to add “We define $dim({\cal{T}})=dim(V)$.”

    $105_6$: Last line in matrix should read
    $$C_{n-1,0} C_{n-1,1} \cdots C_{n-1,n-1}$$

    p. $119$: I think the last three formulas on the page could be derived in a very direct way without introducing the angle $\varphi$.

    p. $227$, figur 5.16a: I believe corrections should be made as follows:
    $(top,right,-near)$ should be $(right,top,-near)$ (or just
    $(r,t,-n)$). $(bottom,right,-near)$ should be $(right,bottom,-near)$ (or just
    $(r,b,-n)$). $(top,left,-near)$ should be $(left,top,-near)$ (or just
    $(l,t,-n)$). $(bottom,left,-near)$ should be $(left,bottom,-near)$ (or just

    $429^6$ In the formula for $\vec{a}$ “$\vec{P}_1$” should possible be changed to “$\vec{P}_1^{\prime}$”

    Comment by Olav Geil — 9/8/2006 @ 3:26 am

  3. Hello~! I’m an 18 year old student software developer from the UK, who is passionate about computing and gaming, and is also looking to go to university (Liverpool University – Computer Science and Electronic Engineering) and then into the games coding industry.

    I ordered your excellent book for Christmas a few weeks ago and was surprised and excited to find that the companion CD’s source files would compile on the Macintosh…

    However, it will not compile on my machine. The Macintosh readme file states that the sources are compatible up to 10.3, but I am running 10.4 Intel :” header files for libaries, however these seem to have died down and replaced with more obvious errors relating to mismatched CPU architectures:

    /usr/bin/ld: warning ../../../../common/Libs/OSXRelease/libIvEngine.a archive’s cputype (18, architecture ppc) does not match cputype (7) for specified -arch flag: i386 (can’t load from it)

    Seeing as a revision is in the works, I don’t suppose there is a fix for this? If there isn’t I shall be working from your book in Xcode, and can supply a fixed version back to you chapter by chapter (including the Xcode project files if you want them). Although, as you most likely know, student life can be hectic and this may take a long time.

    Thank you so much for reading this, and for sharing your knowledge with me, from reading the first chapter I can tell you are going to make a great influence on my life :3.

    Thanks again ^_^~!

    Comment by Dowell Conning — 1/4/2007 @ 4:59 pm

  4. My response to comment 3 can be found in this post here: Mac OS Issues.

    And much delayed thanks for Professor Geil’s notes. They’re very helpful.

    Comment by Jim — 1/16/2007 @ 9:09 pm

  5. Can you provide examples with worked out solutions and end of chapter exercise and projects in the next edition? Also when is the next ed scheduled to be released?

    Comment by Anonymous — 2/4/2007 @ 11:53 am

  6. End of chapter exercises and solutions are the primary impetus for the revision and so are definitely planned. As far as release date, I should have a better idea of that in a month or so, after I meet with the publisher at the Game Developer’s Conference.

    Comment by Jim — 2/4/2007 @ 1:53 pm

  7. Thanks for the quick response. I’ll be checking for your news update over the next couple of months.

    Comment by Anonymous — 2/4/2007 @ 9:32 pm

  8. Please maintain support for windows xp as many students, hobbyists and others may not have the funds to upgrade to Vista, not to mention that Vista seems kinda shaky when it comes to opengl.

    Comment by Anonymous — 2/9/2007 @ 3:26 pm

  9. Please include material on character animation. Topics like skeletal animation and morph target animation/per-vertex animation are very important but very hard to find presented in a manner accessible to beginning, student and hobbyist game programmers.

    Comment by Anonymous — 3/16/2007 @ 8:43 am

  10. Would like to see more material on splines, TCB and/or Catmull, possibly with a discussion around their usage with respect to script-driven cameras, etc.

    Possibly some material on Convex Hull generation, using gift or ribbon wrapping.

    Comment by Mr. B. — 4/12/2008 @ 10:38 pm

  11. At this point, the book is at the printers. However, I’ve added TCB splines, and revised the section on camera manipulation. What precisely are you looking for?

    There’s also a convex hull question in the exercises, though clearly I don’t go into the details there. I’d recommend O’Rourke’s _Computational Geometry in C_ (

    Comment by Jim — 4/13/2008 @ 11:41 am

  12. First of all thank you for this book.
    I have downloaded pdf version of this book for free.
    Its hard to understand concepts without exercises and examples!
    Please provide us some exercises and examples for free! 🙂

    Comment by Ankit singh kushwah — 4/7/2015 @ 1:12 pm

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