Essential Math Weblog Thoughts on math for games

It occurs to me that while I’ve been plugging this on Twitter, I haven’t mentioned it here: Essential Mathematics for Games and Interactive Applications has just come out with a third edition, kindly published by our friends at AK Peters and CRC Press. The book has been brought up-to-date and certain chapters have been revised to flow better. The most significant change is probably the lighting chapter, which still uses a very simple lighting model but builds it out of a physically-based lighting approach. There are also updates in the discussions of floating point formats, shaders, color formats and random number generators, plus much more! Please take a look, I think you’ll find it worthwhile.

Another piece of big news is that the code with the book has been updated as well. The previous edition used OpenGL 2.0 and D3D 9 — now it uses OpenGL 3.2 Core Profile, and D3D 11. Anything that depended on the old fixed-function pipeline (such as the old OpenGL varyings and uniforms) has been updated. And the book no longer comes with a CD. All the code is freely (both in terms of beer and of speech) available at GitHub. This should be good news for those of you who purchased the electronic edition; other than the platform updates it should be compatible with the second edition.

Finally, I’d like to include a few notes on the demo code. Some of the code was written after the text for the book was largely complete, so some of the minor challenges and decisions in writing a cross-platform renderer aren’t really covered, or aren’t covered in much detail.
(more…)

After months of hard work, we’re finally done with the Second Edition.  It went to the presses last week, and it will be available May 16th.  Pre-order it now.

The following drove me crazy for the past few weeks, so I figured I’d better post about it just to get the word out.

For those who don’t know, VS 2005 added the notion of a “manifest” to manage DLLs. Every application must have a valid manifest, or you can’t run. In general, you can use the default settings, but if you’re running on a FAT32 partition (which I am, as I share it through BootCamp), for some reason it just doesn’t always create the manifest correctly. Beats me why since I’d think that sort of thing should be independent of what file system you have, but there you go. The solution is to check the “Use FAT32 work-around” option in the Manifest Tool section of the main project’s properties.

Now I can finally go through and update all of the examples to use our new rendering platform — it took a bit to put together, but we finally have a cross-platform renderer that supports both OpenGL and D3D9.

Sorry about the long delay between updates: things have been very busy here in Chez Jim.

Lars and I have been hard at work on the second edition, and are wrapping up the text this week to be shipped to the publisher. The major changes are:

• Brand new chapter on random numbers
• The three core rendering chapters have been completely rewritten for vertex and fragment shaders
• Direct3D 9 and OpenGL 2 support added

In addition, all the remaining chapters have been revised for clarity, corrections and updated content. Skinning and morphing unfortunately didn’t make it into the main text because of space, but may end up on the CD or may be posted on this site at some point. Availability of this edition will be sometime next year.

A few bits of other news:

• Lars and I are both at NVIDIA Corporation now. Lars is working on mobile technology, and I’m working on OpenGL drivers.
• I should be at GDC in 2008, although that may be up in the air.

That’s about it for now. I’ll update as the process continues to let you know how it’s going.

I’ve had a couple reports of issues with the OS X libraries as shipped with the book.  The problem appears to be that the libraries are compiled for Mac OS 10.2, but don’t work so well with 10.3 and particularly 10.4 and up.  And the fact that they are compiled for a PowerPC architecture doesn’t help the new Intel machines.

The solution is simple: recompile the libraries.  To do so, you’ll need to make sure that all the files are writeable.  Open a terminal window and change to the “common” directory and then type:

make clean PLATFORM=OSX
make PLATFORM=OSX

If you still have issues after doing this, let me know and we’ll try to track it down.

Note that this is the same procedure you’ll have to follow for the Linux builds, except that the platform doesn’t need to be specified.  While the libraries are compiled under an older version of Mandrake, there is no guarantee that they will work for other Linux builds or versions.

For those who are interested in the process of construction of a math library, or perhaps are interested in other people’s opinions on how such a library would be constructed, or perhaps would like to share your own opinions on such a library… er, I’ll start again.

In the sweng-gamedev mailing list, Noel Llopis started up a thread regarding the creation of a industry-wide standard math library. This has led to a very long discussion of such a library, and the creation of a wiki page. As of yet I don’t have much of an opinion on this other than the discussion is extremely verbose and so I can’t keep up with it all. However, someone out there might, and so I share its existence with you all.

Some of this may meander into the next edition of the book, particularly the management of SIMD operations which is something I’m dealing with in my company’s library. However, I can say for certain that there will not be a separate Point class in the book’s library, because a) it’s simpler to manage and b) I trust people not to do dumb things with Vectors when they’re actually Points. This may be a foolish assumption on my part.

Addendum (05/19/06): there’s also a SourceForge page to deposit potential code for said library.

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.

I had originally intended on writing up a post about some of the science and math I’ve been seeing on TV lately. However, as I got into it, I realized it was going to end up too long, too verbose and (more importantly) without a point. A boring rant for ranting’s sake, if you will. So… y’all (or youse guys, if you prefer) get this post instead: a series of fun math- and science-related links which provide a nice diversion on slow days.
(more…)

A bit of a digression here: the notes for the Future of Curved Surfaces roundtable are up in the publications area. Overall, a pretty good discussion. I don’t think anything was really resolved, but I certainly learned quite a bit. Hopefully others did too.

We now return you to your irregularly scheduled reparameterization discussion.

I had a few more topics left over from GDC, but I left my notes at work. And I’ll be on lead engineer duty this week and a bit of next so I’m not optimistic I’ll have time to post anything from there.

So instead I’ll write a bit about some lighting research I’ve been doing. Lately I’ve been interested in doing some improvements to lightmap generation — both making it efficient (in both speed and memory) and improving the quality of the lighting solution.
(more…)

I’ve uploaded the latest tutorial slides to the site. I made a few changes, mostly removing demo links (which require specific paths and wouldn’t necessarily work) and replacing some of them with direct web links. I also fixed the positive and negative elements in the collision response slides. In case I missed one or two, basically if the relative velocity along the normal or the relative force along the normal is positive, then the objects will be pushed together. So the correction (either impulse or constraint force) is in the opposite direction of the normal, and needs to be negative.

I’ll be doing a few more updates throughout the week. Tomorrow I’ll upload the latest demo code, at least for Windows. There was also a lot of good conversation during the breaks and after the talk, so I’ll post some comments, corrections and clarifications based on that. So stay tuned.

Been a little busy lately trying to get a game out, but I did manage to squeeze in some time to create this new site using WordPress. It has some advantages in that I can display math and code a little easier, as you can see. I’m using MimeTeX for the math display — it’s got some issues with bold fonts, but otherwise I can enter the formulas I need in a LaTeX-like way without anyone needing to install MathML fonts. For the code, I’m using iG: Syntax Hiliter, with some tweaks to the colors.

Hopefully I’ll have some time in the next few weeks to type up some more errata, and what I and my co-lecturers are up to as we prep for GDC 2005.